Trigonometry and relocation entries.

notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json

@@ -235,7 +235,29 @@
     "dfs-edge-classification.png",
     "complex-plane-point.png",
     "nfa-example.png",
-    "topological-sort.png"
+    "topological-sort.png",
+    "unit-circle.png",
+    "circle-right.png",
+    "circle-left-down.png",
+    "abs-right.png",
+    "abs-left.png",
+    "abs-up.png",
+    "abs-down.png",
+    "abs-right-down.png",
+    "abs-left-down.png",
+    "circle-left-up.png",
+    "unit-circle-1-0.png",
+    "unit-circle-0-1.png",
+    "unit-circle-n1-0.png",
+    "unit-circle-0-n1.png",
+    "iterative-command.png",
+    "function-bijective.png",
+    "function-injective.png",
+    "function-surjective.png",
+    "function-general.png",
+    "function-kernel.png",
+    "triangular-gnomon.png",
+    "pascals-triangle.png"
   ],
   "File Hashes": {
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@@ -342,7 +364,7 @@
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     "_journal/2024-02/2024-02-20.md": "af2ef10727726200c4defe2eafc7d841",
-    "algebra/radices.md": "474178afb07f3d5037c1547cc1a132f2",
+    "algebra/radices.md": "01fbaba8f81929581707d8df5ad0d912",
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@@ -375,7 +397,7 @@
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     "_journal/2024-03/2024-03-01.md": "70da812300f284df72718dd32fc39322",
-    "algebra/sequences/triangular-numbers.md": "aafaf54e5aff9ca3c7354591fce9f833",
+    "algebra/sequences/triangular-numbers.md": "12c81fa4d79d67c4853efcbc7b26f4c8",
     "algebra/sequences/square-numbers.md": "171f7c5a8dac088afba40923ab86c68e",
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@@ -538,7 +560,7 @@
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     "git/remotes.md": "6fbbc95efa421c720e40500e5d133639",
-    "programming/pred-trans.md": "5b271eebe32e33108d7a36ad98600148",
+    "programming/pred-trans.md": "007ac23931f767c84c5979ec83e28989",
     "set/axioms.md": "063955bf19c703e9ad23be2aee4f1ab7",
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@@ -607,7 +629,7 @@
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     "lambda-calculus/alpha-conversion.md": "a68f3cc1565fb26335218986808a1190",
-    "lambda-calculus/index.md": "14bf297d4314414723c11a11211b35b5",
+    "lambda-calculus/index.md": "d68f65313a62110c5afa668b282149f3",
     "x86-64/instructions/condition-codes.md": "9c05ed99f5c96162e25f0ec4db55c656",
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@@ -627,7 +649,7 @@
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-    "set/functions.md": "bd4fbd92ac87631ba26637ac812b218b",
+    "set/functions.md": "a8f7fd819c27cdde6202da30787ea44c",
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     "lambda-calculus/beta-reduction.md": "0935987f2bac0e6298735f2b26fd5885",
@@ -912,7 +934,7 @@
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     "_journal/2024-10-22.md": "4af65962007cfecdb2c679b44b56d25f",
-    "algorithms/dfs.md": "12a95fbc2fafaf87ee648c480ee041c3",
+    "algorithms/dfs.md": "aa499369c42a85c21861954b389a5819",
     "_journal/2024-10/2024-10-21.md": "de1a0861e87df29aeff11a291f8fbd45",
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@@ -944,7 +966,7 @@
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     "_journal/2024-11/2024-11-07.md": "434ec3f15d7065ea740127aa8477dd17",
     "x86-64/directives.md": "019c1c1d04efb26c3e8758aac4543cc7",
-    "geometry/cartesian.md": "102453159fdb8525118d3995a132c997",
+    "geometry/cartesian.md": "68281a73f3949db43ad6a54e3e8c5cc2",
     "geometry/index.md": "cac68c1b624dbb0552e56cce47bcc21d",
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@@ -1003,7 +1025,7 @@
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     "_journal/2024-12/2024-12-07.md": "bfb6c4db0acbacba19f03a04ec29fa5c",
     "linkers/static.md": "cc56ddfc33f605d26b954ec242abc4cf",
-    "linkers/index.md": "c6c2af6aab2773054b394c624bd2ddb6",
+    "linkers/index.md": "80e418eac44ad6e7d8bee799c7b11b18",
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     "_journal/2024-12-10.md": "c12d380d24d7d1dc2e74a57a1b79399e",
@@ -1049,7 +1071,7 @@
     "_journal/2024-12/2024-12-21.md": "1c1a5791f7519c92e882957cf417b51f",
     "formal-system/language.md": "7797d33a0b0eb187d43dda46a138fb25",
     "computability/automaton.md": "1dd5048ea2a66d8090a85945593fcf68",
-    "computability/index.md": "d7938428ed0b0224c1fe1e59d1fab118",
+    "computability/index.md": "16ae7a270363055f7096b7dd8c09a977",
     "_journal/2024-12-23.md": "72b0964a8a5ed8ba0acf7fe10b5de279",
     "_journal/2024-12/2024-12-22.md": "75375a867efc5b3aff406c73394d4814",
     "computability/language.md": "9ee8bd16c231e71855ab1d8dae3188cb",
@@ -1059,13 +1081,13 @@
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     "_journal/2024-12/2024-12-24.md": "dcd3bd8b82ca4d47a9642a46d8bece0d",
-    "linkers/relocatable.md": "b6f0c13e07ed57ea73dea6b4a72560d1",
+    "linkers/relocatable.md": "ac24efbabe07222a89acb2fd5135cdb3",
     "data-models/federation.md": "1d92747304186bd2833a00a488fcac48",
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-    "combinators/index.md": "8e324bbcf49cca9c0c0f9bbf843cbebb",
+    "combinators/index.md": "8b55b44c955da88368b0b5635909b064",
     "_journal/2024-12-28.md": "1ad3caec4ea6f597cc5156f19b274c50",
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     "_journal/2024-12-29.md": "e7808872f56a12b51165fc86a1c48e60",
@@ -1425,7 +1447,7 @@
     "_journal/2025-01/2025-01-06.md": "20030a4b6a1f8f4b2cb882c6d4c59f29",
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     "_journal/2025-01/2025-01-07.md": "bd5aa36eff9211a9a89cc47f1c2dbdcd",
-    "data-models/rdf/rdfs.md": "f891b5385d3f41acc0c6a8ce88186419",
+    "data-models/rdf/rdfs.md": "705777f026ea8bf4d8311f1c47621cd4",
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@@ -1440,8 +1462,14 @@
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-    "_journal/2025-01-17.md": "ba60278a6cca1832ad28c273b01b0745",
+    "_journal/2025-01-17.md": "08a5f05bb572db9495bfc2b4feb8e0a9",
-    "_journal/2025-01/2025-01-16.md": "e3a21059205784a4e88bfe3b4deac7f7"
+    "_journal/2025-01/2025-01-16.md": "e3a21059205784a4e88bfe3b4deac7f7",
+    "trigonometry/index.md": "6d07d5ba5e352f182a19b8a3d804321b",
+    "geometry/circle.md": "751a5aada6521281f1d8edb463572943",
+    "_journal/2025-01-18.md": "8655fbf94aeec13efe9b6d2087c1f37e",
+    "_journal/2025-01/2025-01-17.md": "08a5f05bb572db9495bfc2b4feb8e0a9",
+    "_journal/2025-01-19.md": "a37c6f534cf5e272619c5f813974afcf",
+    "_journal/2025-01/2025-01-18.md": "7a1655887093f37ffe86309d90459b3b"
   },
   "fields_dict": {
     "Basic": [

notes/_journal/2025-01-17.md

@@ -1,9 +0,0 @@
----
-title: "2025-01-17"
----
-
-- [ ] Anki Flashcards
-- [x] KoL
-- [x] OGS
-- [ ] Sheet Music (10 min.)
-- [ ] Korean (Read 1 Story)

notes/_journal/2025-01-19.md

@@ -0,0 +1,11 @@
+---
+title: "2025-01-19"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [x] OGS
+- [ ] Sheet Music (10 min.)
+- [ ] Korean (Read 1 Story)
+
+* More notes on relocation entries.

notes/_journal/2025-01/2025-01-17.md

@@ -0,0 +1,13 @@
+---
+title: "2025-01-17"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [x] OGS
+- [ ] Sheet Music (10 min.)
+- [ ] Korean (Read 1 Story)
+
+* Distinguish asserted and inferred RDF triples.
+* Notes on the [[circle]] and [[trigonometry/index#Unit Circle|unit circle]].
+* Formal definition of the [[pred-trans#Iterative|iterative]] command.

notes/_journal/2025-01/2025-01-18.md

@@ -0,0 +1,11 @@
+---
+title: "2025-01-18"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [x] OGS
+- [ ] Sheet Music (10 min.)
+- [ ] Korean (Read 1 Story)
+
+* Notes on [[relocatable#Relocation Entries|relocation entries]].

notes/algebra/radices.md

@@ -202,6 +202,33 @@ Tags: binary::hex
 <!--ID: 1707432641583-->
 END%%
 
+%%ANKI
+Basic
+What hexadecimal value does $2^{0 + 4(0)}$ evaluate to?
+Back: `0x1`
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
+<!--ID: 1737232783457-->
+END%%
+
+%%ANKI
+Basic
+What hexadecimal value does $2^{0 + 4(2)}$ evaluate to?
+Back: `0x100`
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
+<!--ID: 1737232783462-->
+END%%
+
+%%ANKI
+Basic
+Write `0x10000` in form $2^{i + 4j}$. What values of $i$ and $j$ satisfy this?
+Back: $i = 0$ and $j = 4$.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
+<!--ID: 1737232783466-->
+END%%
+
 %%ANKI
 Basic
 How is the $1$ in $2^{1 + 4j}$ translated to hex?
@@ -211,6 +238,33 @@ Tags: binary::hex
 <!--ID: 1707432641585-->
 END%%
 
+%%ANKI
+Basic
+What hexadecimal value does $2^{1 + 4(2)}$ evaluate to?
+Back: `0x200`
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
+<!--ID: 1737232783469-->
+END%%
+
+%%ANKI
+Basic
+What hexadecimal value does $2^{1 + 4(3)}$ evaluate to?
+Back: `0x2000`
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
+<!--ID: 1737232783480-->
+END%%
+
+%%ANKI
+Basic
+Write `0x200` in form $2^{i + 4j}$. What values of $i$ and $j$ satisfy this?
+Back: $i = 1$ and $j = 2$.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
+<!--ID: 1737232783488-->
+END%%
+
 %%ANKI
 Basic
 How is the $2$ (power) in $2^{2 + 4j}$ translated to hex?
@@ -220,6 +274,24 @@ Tags: binary::hex
 <!--ID: 1707432641586-->
 END%%
 
+%%ANKI
+Basic
+What hexadecimal value does $2^{2 + 4(1)}$ evaluate to?
+Back: `0x40`
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
+<!--ID: 1737232783492-->
+END%%
+
+%%ANKI
+Basic
+Write `0x4000` in form $2^{i + 4j}$. What values of $i$ and $j$ satisfy this?
+Back: $i = 2$ and $j = 3$.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
+<!--ID: 1737232783497-->
+END%%
+
 %%ANKI
 Basic
 How is the $3$ in $2^{3 + 4j}$ translated to hex?
@@ -229,6 +301,24 @@ Tags: binary::hex
 <!--ID: 1707432641587-->
 END%%
 
+%%ANKI
+Basic
+What hexadecimal value does $2^{3 + 4(0)}$ evaluate to?
+Back: `0x8`
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
+<!--ID: 1737232783501-->
+END%%
+
+%%ANKI
+Basic
+Write `0x80` in form $2^{i + 4j}$. What values of $i$ and $j$ satisfy this?
+Back: $i = 3$ and $j = 1$.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: binary::hex
+<!--ID: 1737232783505-->
+END%%
+
 %%ANKI
 Basic
 How is $n$ in $2^n$ factored to quickly write the decimal value's hex representation?

notes/algebra/sequences/triangular-numbers.md

@@ -15,7 +15,7 @@ The $n$th term of the **triangular numbers** $(T_n)_{n \geq 0}$ is the sum of wh
 Basic
 What is a polygonal number?
 Back: A number of pebbles that can be arranged into the shape of a regular filled polygon.
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325851-->
 END%%
 
@@ -23,7 +23,7 @@ END%%
 Basic
 What is a figurate number?
 Back: Polygonal numbers and their generalizations to other dimensions.
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325856-->
 END%%
 
@@ -31,7 +31,7 @@ END%%
 Basic
 What are considered the simplest polygonal numbers?
 Back: The triangular numbers.
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325859-->
 END%%
 
@@ -39,7 +39,7 @@ END%%
 Basic
 How do polygonal numbers relate to figurate numbers?
 Back: Polygonal numbers are a subset of the figurate numbers.
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325862-->
 END%%
 
@@ -47,7 +47,7 @@ END%%
 Basic
 What is a gnomon?
 Back: The "piece" added to a figurate number to transform it to the next larger one.
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325865-->
 END%%
 
@@ -55,7 +55,7 @@ END%%
 Basic
 What shape do gnomons associated with triangular numbers take on?
 Back: Lines.
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325874-->
 END%%
 
@@ -64,7 +64,7 @@ Basic
 How are gnomons of the triangular numbers visualized?
 Back:
 ![[triangular-gnomon.png]]
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325878-->
 END%%
 
@@ -73,7 +73,7 @@ Basic
 What general term refers to the highlighted portion of pebbles in the following?
 ![[triangular-gnomon.png]]
 Back: Gnomons.
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325883-->
 END%%
 
@@ -81,15 +81,24 @@ END%%
 Basic
 The triangular numbers correspond to what kind of triangles?
 Back: Equilateral triangles.
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325887-->
 END%%
 
+%%ANKI
+Basic
+How do the triangular numbers correspond to *equilateral* triangles?
+Back:
+![[triangular-gnomon.png]]
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+<!--ID: 1737233067030-->
+END%%
+
 %%ANKI
 Basic
 What is the first triangular *and* square number?
 Back: $36$
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325891-->
 END%%
 
@@ -97,7 +106,7 @@ END%%
 Basic
 What are the first five triangular numbers $(T_n)_{n \geq 0}$?
 Back: $0, 1, 3, 6, 10$
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325904-->
 END%%
 
@@ -111,7 +120,7 @@ Back:
  * * *
 * * * *
 ```
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325909-->
 END%%
 
@@ -119,7 +128,7 @@ END%%
 Basic
 How is the $n$th triangular number written as a summation?
 Back: $\sum_{k=1}^n k$
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325914-->
 END%%
 
@@ -127,7 +136,7 @@ END%%
 Basic
 What polygonal sequence is the summation analog of factorial?
 Back: The triangular numbers.
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325918-->
 END%%
 
@@ -135,7 +144,7 @@ END%%
 Basic
 What notation does Knuth introduce to denote the $n$th triangular number?
 Back: $n?$
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325922-->
 END%%
 
@@ -143,14 +152,14 @@ END%%
 Basic
 What name does Knuth give the LHS of $n? = \sum_{k=1}^n k$?
 Back: The termial.
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325927-->
 END%%
 
 %%ANKI
 Cloze
 The {1:term}ial is to {2:$n?$} as the {2:factor}ial is to {1:$n!$}.
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325931-->
 END%%
 
@@ -158,7 +167,7 @@ END%%
 Basic
 What closed formula is traditionally used to compute the $n$th triangular number?
 Back: $\large{\frac{n(n + 1)}{2}}$
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325936-->
 END%%
 
@@ -166,7 +175,7 @@ END%%
 Basic
 What is the recurrence relation in the recursive definition of triangular numbers $(T_n)_{n \geq 0}$?
 Back: $T_n = T_{n-1} + n$
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709422558652-->
 END%%
 
@@ -174,7 +183,7 @@ END%%
 Basic
 What is the initial condition(s) in the recursive definition of triangular numbers $(T_n)_{n \geq 0}$?
 Back: $T_0 = 0$
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709422558656-->
 END%%
 
@@ -196,7 +205,7 @@ END%%
 Basic
 What combinatorial closed formula is used to compute the $n$th triangular number?
 Back: $\binom{n + 1}{2}$
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325949-->
 END%%
 
@@ -204,7 +213,7 @@ END%%
 Basic
 What is the combinatorial explanation as to why the $n$th triangular number is $\binom{n + 1}{2}$?
 Back: $\sum_{k=1}^n k$ is the number of ways distinct pairs can be made from $n + 1$ objects.
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325956-->
 END%%
 
@@ -213,7 +222,7 @@ Basic
 Where in Pascal's triangle are the natural numbers embedded?
 Back: Along the second leftward diagonal:
 ![[pascals-triangle.png]]
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325963-->
 END%%
 
@@ -222,7 +231,7 @@ Basic
 Where in Pascal's triangle are the triangular numbers embedded?
 Back: Along the third leftward diagonal:
 ![[pascals-triangle.png]]
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325970-->
 END%%
 
@@ -236,7 +245,7 @@ for (int i = 1; i <= n; ++i) {
 }
 ```
 Back: The $n$th triangular number.
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325976-->
 END%%
 
@@ -250,7 +259,7 @@ Back: $2 \cdot T_n$ is the number of units in an $n \times (n + 1)$ rectangle, e
 * * - - -
 * - - - -
 ```
-Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+Reference: “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
 <!--ID: 1709419325981-->
 END%%
 
@@ -265,4 +274,4 @@ END%%
 ## Bibliography
 
 * Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
-* “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).
+* “Triangular Number,” in _Wikipedia_, January 13, 2024, [https://en.wikipedia.org/w/index.php?title=Triangular_number](https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122).

notes/algorithms/dfs.md

@@ -534,6 +534,7 @@ END%%
 
 %%ANKI
 Basic
+Why is edge $\langle b, s \rangle$ classified as a back edge?
 ![[dfs-edge-classification.png]]
 Back: Because $s$ is an ancestor of $b$.
 Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

notes/combinators/index.md

@@ -335,6 +335,77 @@ Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combi
 <!--ID: 1735413657674-->
 END%%
 
+%%ANKI
+Basic
+Assume basis $\mathbf{S}$, $\mathbf{K}$, and $\mathbf{I}$. *Why* isn't $((\mathbf{S}(\mathbf{K}\mathbf{S}))\mathbf{K})$ a combinator?
+Back: N/A. It is.
+Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
+<!--ID: 1737212699921-->
+END%%
+
+%%ANKI
+Basic
+Assume basis $\mathbf{S}$, $\mathbf{K}$, and $\mathbf{I}$. *Why* isn't $((\mathbf{S}(\mathbf{K}x))((\mathbf{S}\mathbf{K})\mathbf{K}))$ a combinator?
+Back: It contains atom $x$ which isn't a basic combinator.
+Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
+<!--ID: 1737212699927-->
+END%%
+
+%%ANKI
+Basic
+Assume basis $\mathbf{S}$, $\mathbf{K}$, and $\mathbf{I}$. *Why* isn't $((\mathbf{S}(\mathbf{K}0))((\mathbf{S}\mathbf{K})\mathbf{K}))$ a combinator?
+Back: It contains atom $0$ which isn't a basic combinator.
+Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
+<!--ID: 1737212699932-->
+END%%
+
+%%ANKI
+Basic
+Assume basis $\mathbf{S}$, $\mathbf{K}$, and $\mathbf{I}$. *Why* isn't $((\mathbf{S}(\mathbf{K}\mathbf{S}))\mathbf{K})$ a closed term?
+Back: N/A. It is.
+Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
+<!--ID: 1737212699937-->
+END%%
+
+%%ANKI
+Basic
+Assume basis $\mathbf{S}$, $\mathbf{K}$, and $\mathbf{I}$. *Why* isn't $((\mathbf{S}(\mathbf{K}x))((\mathbf{S}\mathbf{K})\mathbf{K}))$ a closed term?
+Back: It contains variable $x$.
+Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
+<!--ID: 1737212699942-->
+END%%
+
+%%ANKI
+Basic
+Assume basis $\mathbf{S}$, $\mathbf{K}$, and $\mathbf{I}$. *Why* isn't $((\mathbf{S}(\mathbf{K}0))((\mathbf{S}\mathbf{K})\mathbf{K}))$ a closed term?
+Back: N/A. It is.
+Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
+<!--ID: 1737212699947-->
+END%%
+
+%%ANKI
+Cloze
+By convention, parentheses in combinatory logic are {left}-associative.
+Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
+<!--ID: 1737245400699-->
+END%%
+
+%%ANKI
+Basic
+How is $CL$-term $UVWX$ written with parentheses reintroduced?
+Back: $(((UV)W)X)$
+Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
+<!--ID: 1737245400709-->
+END%%
+
+%%ANKI
+Basic
+In combinatory logic, is $UVW \equiv ((UV)W)$?
+Back: Yes.
+Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
+<!--ID: 1737245400737-->
+END%%
+
 ## Basic Combinators
 
 The combinatory logic is a notation that eliminate the need for quantified variables. We start with basis $\mathbf{S}$, $\mathbf{K}$, and $\mathbf{I}$. These **basic combinators** are defined as:

notes/computability/index.md

@@ -247,11 +247,10 @@ Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third ed
 END%%
 
 %%ANKI
-Basic
+Cloze
-A language is a set satisfying what?
+A {language} is a set containing {strings} over some {alphabet}.
-Back: It contains strings over some alphabet.
 Reference: Michael Sipser, _Introduction to the Theory of Computation_, Third edition, international edition (Australia Brazil Japan Korea Mexiko Singapore Spain United Kingdom United States: Cengage Learning, 2013).
-<!--ID: 1734903366709-->
+<!--ID: 1737232847428-->
 END%%
 
 %%ANKI

notes/data-models/rdf/rdfs.md

@@ -8,7 +8,7 @@ tags:
 
 ## Overview
 
-The simplest extension to RDF that allows a modeler to manage inference is **RDF Schema** (RDFS).
+The simplest extension to RDF that allows a modeler to manage inference is **RDF Schema** (RDFS). Triples that are inserted directly into an underlying RDF store are called **asserted triples**. Triples that are derived from inference rules are called **inferred triples**.
 
 %%ANKI
 Basic
@@ -26,6 +26,44 @@ Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web
 <!--ID: 1736629473653-->
 END%%
 
+%%ANKI
+Cloze
+An {asserted} triple is contrary to an {inferred} triple.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1737167693491-->
+END%%
+
+%%ANKI
+Basic
+What does it mean for a triple to be asserted?
+Back: The triple exists directly in the underlying RDF store.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1737167693496-->
+END%%
+
+%%ANKI
+Basic
+What does it mean for a triple to be inferred?
+Back: The triple is derived from some set of inference rules.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1737167693501-->
+END%%
+
+%%ANKI
+Cloze
+{Asserted} triples are used to derive {inferred} triples.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1737167693506-->
+END%%
+
+%%ANKI
+Basic
+When might a triple be both asserted and inferred?
+Back: When the inference engine infers an already existing triple.
+Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
+<!--ID: 1737167693510-->
+END%%
+
 ## Classes
 
 All things described by RDF are called **resources**. Resources may be divided into groups called **classes**. Classes are themselves resources. The `rdf:type` property may be used to state that a resource is an instance of a class. Associated with a class is a set, called the **class extension** of the class, which is the set of the instances of the class. A class may be a member of its own class extension.

notes/geometry/cartesian.md

@@ -213,22 +213,6 @@ Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” acces
 <!--ID: 1734620943926-->
 END%%
 
-%%ANKI
-Basic
-Which of horizontal and/or vertical transformations "act inversely"?
-Back: Horizontal transformations.
-Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
-<!--ID: 1734620943931-->
-END%%
-
-%%ANKI
-Basic
-Which of horizontal and/or vertical transformations "act normally"?
-Back: Vertical transformations.
-Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
-<!--ID: 1734620943937-->
-END%%
-
 %%ANKI
 Basic
 How is the graph of $y = f(x)$ transformed in the graph of $y = \frac{1}{2}f(\frac{x}{3})$?

notes/geometry/circle.md

@@ -0,0 +1,200 @@
+---
+title: Circle
+TARGET DECK: Obsidian::STEM
+FILE TAGS: geometry::circle
+tags:
+  - circle
+  - geometry
+---
+
+## Overview
+
+A **circle** is a shape consisting of all points in a plane at a given distance from a given point, i.e. the **center**. In this way, a circle is characterized by its center and **radius**, the distance from the center to any point of the circle. The perimeter of a circle is known as its **circumference**.
+
+On the [[cartesian|Cartesian coordinate system]], the equation of a circle with radius $r$ and center $\langle h, k \rangle$ is $$(x - h)^2 + (y - k)^2 = r^2.$$
+
+Such a circle has circumference $2\pi r$ and [[area]] $\pi r^2$.
+
+%%ANKI
+Basic
+A circle is characterized by what two properties?
+Back: Its center and its radius.
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693438-->
+END%%
+
+%%ANKI
+Basic
+In plain English, describe what a circle is.
+Back: A set of points at a given distance from some given point.
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693441-->
+END%%
+
+%%ANKI
+Basic
+The perimeter of a circle is known as what?
+Back: Its circumference.
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693445-->
+END%%
+
+%%ANKI
+Basic
+What is the Cartesian equation of a circle with radius $r$ and center $\langle h, k \rangle$?
+Back: $(x - h)^2 + (y - k)^2 = r^2$
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693448-->
+END%%
+
+%%ANKI
+Basic
+Given indeterminates $x$ and $y$, the following equation describes what shape? $$(x - h)^2 + (y - k)^2 = r^2$$
+Back: A circle with radius $r$ and center $\langle h, k \rangle$.
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693451-->
+END%%
+
+%%ANKI
+Basic
+Consider a circle with radius $r$. What does its circumference evaluate to?
+Back: $2 \pi r$
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693455-->
+END%%
+
+%%ANKI
+Basic
+Consider a circle with radius $r$. What is its area?
+Back: $\pi r^2$
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693458-->
+END%%
+
+%%ANKI
+Basic
+Consider a circle with diameter $d$. What does its circumference evaluate to?
+Back: $\pi d$
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693462-->
+END%%
+
+%%ANKI
+Basic
+Consider a circle with diameter $d$. What its area?
+Back: $\pi \left(\frac{d}{2}\right)^2$
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693465-->
+END%%
+
+%%ANKI
+Basic
+Consider a circle with radius $r$. What does the following evaluate to? $$2 \pi r$$
+Back: Its circumference.
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693468-->
+END%%
+
+%%ANKI
+Basic
+Consider a circle with radius $r$. What does the following evaluate to? $$\pi r^2$$
+Back: Its area.
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693472-->
+END%%
+
+%%ANKI
+Basic
+What is the Cartesian equation of the following shape?
+![[unit-circle.png]]
+Back: $x^2 + y^2 = 1$
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693476-->
+END%%
+
+%%ANKI
+Basic
+What is the Cartesian equation of the following shape?
+![[circle-right.png]]
+Back: $(x - 2)^2 + y^2 = 4$
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693481-->
+END%%
+
+%%ANKI
+Basic
+What is the Cartesian equation of the following shape?
+![[circle-left-down.png]]
+Back: $(x + 1)^2 + (y + 1)^2 = 4$
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167693485-->
+END%%
+
+%%ANKI
+Basic
+What is the Cartesian equation of the following shape?
+![[circle-left-up.png]]
+Back: $(x + 1)^2 + (y - 1)^2 = 4$
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737167904156-->
+END%%
+
+%%ANKI
+Basic
+Rewrite equation $x^2 + y^2 = 1$ shifted left by $a > 0$.
+Back: $(x + a)^2 + y^2 = 1$
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737168379559-->
+END%%
+
+%%ANKI
+Basic
+Rewrite equation $x^2 + y^2 = 1$ shifted up by $b > 0$.
+Back: $x^2 + (y - b)^2 = 1$
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737168379562-->
+END%%
+
+%%ANKI
+Basic
+Rewrite equation $x^2 + y^2 = 1$ shifted right by $a > 0$.
+Back: $(x - a)^2 + y^2 = 1$
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737168379565-->
+END%%
+
+%%ANKI
+Basic
+Rewrite equation $x^2 + y^2 = 1$ shifted down by $b > 0$.
+Back: $x^2 + (y + b)^2 = 1$
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737168379568-->
+END%%
+
+%%ANKI
+Basic
+In what direction(s) is the unit circle shifted in the following? $$(x - 3)^2 + (y - 3)^2 = 1$$
+Back: Right by $3$ and up by $3$.
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737168379571-->
+END%%
+
+%%ANKI
+Basic
+In what direction(s) is the unit circle shifted in the following? $$(x + 3)^2 + (y - 3)^2 = 1$$
+Back: Left by $3$ and up by $3$.
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737168379574-->
+END%%
+
+%%ANKI
+Basic
+In what direction(s) is the unit circle shifted in the following? $$(x - 3)^2 + (y + 3)^2 = 1$$
+Back: Right by $3$ and down by $3$.
+Reference: “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).
+<!--ID: 1737168379578-->
+END%%
+
+## Bibliography
+
+* “Circle,” in _Wikipedia_, January 8, 2025, [https://en.wikipedia.org/w/index.php?title=Circle](https://en.wikipedia.org/w/index.php?title=Circle&oldid=1268270102).

notes/lambda-calculus/index.md

@@ -214,7 +214,7 @@ END%%
 
 %%ANKI
 Basic
-How is expression $\lambda x. \lambda y. MN$ written with parentheses reintroduced?
+How is $\lambda$-term $\lambda x. \lambda y. MN$ written with parentheses reintroduced?
 Back: $(\lambda x. (\lambda y. (MN)))$
 Reference: Hindley, J Roger, and Jonathan P Seldin. “Lambda-Calculus and Combinators, an Introduction,” n.d. [https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf](https://www.cin.ufpe.br/~djo/files/Lambda-Calculus%20and%20Combinators.pdf).
 <!--ID: 1716498992530-->

notes/linkers/index.md

@@ -10,10 +10,8 @@ tags:
 
 To build an executable, a linker must perform two main tasks:
 
-1. **Symbol resolution**. The linker must associate each symbol reference with exactly one symbol definition.
+1. **Symbol resolution**. The linker phase in which each symbol reference is associated with exactly one symbol definition.
-2. **Relocation**. The linker must relocate code and data sections by associating a memory location with each symbol definition, and then modifying all of the references to those symbols so that they point to this memory location.
+2. **Relocation**. The linker phase in which code and data sections across input modules are combined. Each section, along with the symbols defined in them, are assigned unique run-time memory addresses. Additionally, references to symbols are updated so they point to the correct run-time addresses.
-
-The linker blindly performs relocations using detailed instructions generated by the assembler called **relocation entries**.
 
 %%ANKI
 Basic
@@ -31,6 +29,14 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
 <!--ID: 1733671136078-->
 END%%
 
+%%ANKI
+Basic
+After which linker phase is the size of the code and data sections of each input object module known?
+Back: Symbol resolution.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1737257167718-->
+END%%
+
 %%ANKI
 Basic
 What is the goal of symbol resolution?
@@ -39,6 +45,13 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
 <!--ID: 1733671136081-->
 END%%
 
+%%ANKI
+Cloze
+The {symbol resolution} phase associates each {symbol reference} with exactly one {symbol definition}.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1733671136092-->
+END%%
+
 %%ANKI
 Basic
 What is the goal of relocation?
@@ -55,13 +68,6 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
 <!--ID: 1733671136088-->
 END%%
 
-%%ANKI
-Cloze
-The {symbol resolution} phase associates each {symbol reference} with exactly one {symbol definition}.
-Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
-<!--ID: 1733671136092-->
-END%%
-
 %%ANKI
 Cloze
 The {relocation} phase assigns a {memory location} to each symbol and {updates references} accordingly.
@@ -79,24 +85,25 @@ END%%
 
 %%ANKI
 Basic
-What is emitted by the assembler to help the linker relocate sections?
+Which linker phase combines code and data sections of the same type into a new aggregate section?
-Back: Relocation entries.
+Back: Relocation.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
-<!--ID: 1733671136107-->
+<!--ID: 1737257167723-->
+END%%
+
+%%ANKI
+Basic
+Which linker phase is responsible for building up the `.symtab` section?
+Back: Symbol resolution.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1737257167727-->
 END%%
 
 %%ANKI
 Cloze
-The assembler outputs {relocation entries} to guide the linker during {relocation}.
+{Relocatable} object files are merged together to make an {executable} object file.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
-<!--ID: 1733671136112-->
+<!--ID: 1737257167732-->
-END%%
-
-%%ANKI
-Cloze
-The {1:assembler} outputs relocation entries to guide the {1:linker} during relocation.
-Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
-<!--ID: 1733671136117-->
 END%%
 
 ## Object Files

notes/linkers/relocatable.md

@@ -637,6 +637,335 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
 <!--ID: 1736632025924-->
 END%%
 
+## Relocation Entries
+
+Whenever the assembler encounters a reference to an object whose ultimate location is unknown, it generates a **relocation entry** that tells the linker how to modify the reference when it merges the object file into an executable. Each entry looks something like:
+
+```c
+struct Elf64_Rela {
+  long offset;       // Offset of the reference to relocate
+  long type : 32,    // Relocation type
+       symbol : 32;  // Symbol table index
+  long addend;       // Additional constant used to bias the value
+};
+```
+
+%%ANKI
+Basic
+What is emitted by the assembler to help the linker relocate sections?
+Back: Relocation entries.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1733671136107-->
+END%%
+
+%%ANKI
+Cloze
+The assembler outputs {relocation entries} to guide the linker during {relocation}.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1733671136112-->
+END%%
+
+%%ANKI
+Cloze
+The {1:assembler} outputs relocation entries to guide the {1:linker} during relocation.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1733671136117-->
+END%%
+
+%%ANKI
+Basic
+Which component of a compiler driver produces relocation entries?
+Back: The assembler.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1737257167650-->
+END%%
+
+%%ANKI
+Basic
+How many relocation entries are produced for any given object module?
+Back: One for every reference whose ultimate address is unknown.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1737257167677-->
+END%%
+
+%%ANKI
+Basic
+*Why* aren't relocation entries relevant for executable object files?
+Back: All memory addresses should be resolved once the executable is produced.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1737257167683-->
+END%%
+
+%%ANKI
+Cloze
+Relocation entries for {data} are placed in {`.rel.data`}.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1737257167690-->
+END%%
+
+%%ANKI
+Cloze
+Relocation entries for {code} are placed in {`.rel.text`}.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1737257167696-->
+END%%
+
+%%ANKI
+Basic
+At what point during linking are relocation entries no longer necessary?
+Back: When the fully merged executable object file is produced.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1737257167702-->
+END%%
+
+%%ANKI
+Basic
+Relocation entries are included in what kind of object module?
+Back: Relocatable object modules.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1737257167707-->
+END%%
+
+%%ANKI
+Basic
+A relocation entry corresponds to what kind of C construct?
+Back: A `struct`.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17
+<!--ID: 1737257167712-->
+END%%
+
+%%ANKI
+Basic
+Consider the following ELF relocation entry. What is the purpose of `offset`?
+```c
+struct Elf64_Rela {
+  long offset;
+  long type : 32;
+  long symbol : 32;
+  long addend;
+};
+```
+Back: It is the offset of the reference to relocate.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385837-->
+END%%
+
+%%ANKI
+Basic
+Consider the following ELF relocation entry. What is the `offset` measured relative to?
+```c
+struct Elf64_Rela {
+  long offset;
+  long type : 32;
+  long symbol : 32;
+  long addend;
+};
+```
+Back: The start of the section the reference is located in.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385840-->
+END%%
+
+%%ANKI
+Basic
+Consider the following ELF relocation entry. What is the purpose of `symbol`?
+```c
+struct Elf64_Rela {
+  long offset;
+  long type : 32;
+  long symbol : 32;
+  long addend;
+};
+```
+Back: It identifies the symbol the modified reference should point to.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385843-->
+END%%
+
+%%ANKI
+Basic
+Consider the following ELF relocation entry. `symbol` is an index into what table?
+```c
+struct Elf64_Rela {
+  long offset;
+  long type : 32;
+  long symbol : 32;
+  long addend;
+};
+```
+Back: `.symtab`
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385846-->
+END%%
+
+%%ANKI
+Basic
+Consider the following ELF relocation entry. What is the purpose of `addend`?
+```c
+struct Elf64_Rela {
+  long offset;
+  long type : 32;
+  long symbol : 32;
+  long addend;
+};
+```
+Back: To bias the value of the modified reference.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385849-->
+END%%
+
+%%ANKI
+Basic
+Consider the following ELF relocation entry. What is the purpose of `type`?
+```c
+struct Elf64_Rela {
+  long offset;
+  long type : 32;
+  long symbol : 32;
+  long addend;
+};
+```
+Back: To indicate to the linker what algorithm should be used to compute the relocated address.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385853-->
+END%%
+
+%%ANKI
+Basic
+Consider the following ELF relocation entry. What are the two most basic values of `type`?
+```c
+struct Elf64_Rela {
+  long offset;
+  long type : 32;
+  long symbol : 32;
+  long addend;
+};
+```
+Back: `R_X86_64_32` and `R_X86_64_PC32`.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385856-->
+END%%
+
+%%ANKI
+Cloze
+{1:`R_X86_64_32`} is to {2:absolute} whereas {2:`R_X86_64_PC32`} is to {1:relative}.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: linker::elf x86-64
+<!--ID: 1737320385860-->
+END%%
+
+%%ANKI
+Basic
+What is the significance of `R` in type `R_X86_64_32`?
+Back: It is the prefix used for relocation entry `type` values.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385864-->
+END%%
+
+%%ANKI
+Basic
+What is the significance of `32` in type `R_X86_64_32`?
+Back: The reference is relocated using a 32-bit absolute address.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385867-->
+END%%
+
+%%ANKI
+Basic
+What is the significance of `PC` in type `R_X86_64_PC32`?
+Back: It is short for **p**rogram **c**ounter.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385871-->
+END%%
+
+%%ANKI
+Basic
+What is the significance of `PC32` in type `R_X86_64_PC32`?
+Back: The reference is relocated using a 32-bit PC-relative address.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385875-->
+END%%
+
+%%ANKI
+Basic
+`R_X86_64_32` is a possible value for what field in the following ELF relocation entry?
+```c
+struct Elf64_Rela {
+  long offset;
+  long type : 32;
+  long symbol : 32;
+  long addend;
+};
+```
+Back: `type`
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385879-->
+END%%
+
+%%ANKI
+Basic
+`R_X86_64_PC32` is a possible value for what field in the following ELF relocation entry?
+```c
+struct Elf64_Rela {
+  long offset;
+  long type : 32;
+  long symbol : 32;
+  long addend;
+};
+```
+Back: `type`
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385883-->
+END%%
+
+%%ANKI
+Basic
+Consider the following ELF relocation entry. What should `type` be if relocating PC-relatively?
+```c
+struct Elf64_Rela {
+  long offset;
+  long type : 32;
+  long symbol : 32;
+  long addend;
+};
+```
+Back: `R_X86_64_PC32`.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385887-->
+END%%
+
+%%ANKI
+Basic
+Consider the following ELF relocation entry. What should `type` be if relocating absolutely?
+```c
+struct Elf64_Rela {
+  long offset;
+  long type : 32;
+  long symbol : 32;
+  long addend;
+};
+```
+Back: `R_X86_64_32`.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17 linker::elf x86-64
+<!--ID: 1737320385894-->
+END%%
+
 ## Bibliography
 
 * Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.

notes/programming/pred-trans.md

@@ -1035,6 +1035,9 @@ END%%
 
 The general form of the **iterative command** is: $$\begin{align*} \textbf{do } & B_1 \rightarrow S_1 \\ \textbf{ | } & B_2 \rightarrow S_2 \\ & \quad\cdots \\ \textbf{ | } & B_n \rightarrow S_n \\ \textbf{od } & \end{align*}$$
 
+We denote the iterative command as $\text{DO}$ and define $\text{DO}$ in terms of $wp$ as: $$wp(\text{DO}, R) = \exists k \geq 0, H_k(R)$$
+where $H_k$ is given [[algebra/sequences/index|recursive definition]]: $$\begin{align*} H_0(R) & = \neg (B_1 \lor \cdots \lor B_n) \land R \\ H_{k+1}(R) & = H_0(R) \lor wp(\text{IF}, H_k(R)) \end{align*}$$
+
 %%ANKI
 Basic
 The conventional `while` statement corresponds to what command?
@@ -1123,6 +1126,130 @@ Reference: Gries, David. *The Science of Programming*. Texts and Monographs in
 <!--ID: 1735873599850-->
 END%%
 
+%%ANKI
+Cloze
+{1:$\text{IF}$} is to {2:$abort$} whereas {2:$\text{DO}$} is to {1:$skip$}.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737187609860-->
+END%%
+
+%%ANKI
+Basic
+Given associated recursive definition $H_k$, what is the formal definition of $\text{DO}$?
+Back: For some predicate $R$, $wp(\text{DO}, R) = \exists k \geq 0, H_k(R)$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737187609865-->
+END%%
+
+%%ANKI
+Basic
+In the following definition, what does $H_k(R)$ represent? $$wp(\text{DO}, R) = \exists k \geq 0, H_k(R)$$
+Back: The set of states in which execution of $\text{DO}$ terminates in $k$ or fewer iterations.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737187609868-->
+END%%
+
+%%ANKI
+Basic
+In the following definition, how is $H_0$ defined? $$wp(\text{DO}, R) = \exists k \geq 0, H_k(R)$$
+Back: Given guards $B_1, \ldots, B_n$, as $H_0 = \neg (B_1 \lor \cdots \lor B_n) \land R$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737187609870-->
+END%%
+
+%%ANKI
+Basic
+In the following definition, what set of states does $H_0(R)$ correspond to? $$wp(\text{DO}, R) = \exists k \geq 0, H_k(R)$$
+Back: Those in which $\text{DO}$ finishes execution in $0$ iterations with $R$ true.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737188069810-->
+END%%
+
+%%ANKI
+Basic
+In the following definition, how is $H_{k+1}$ defined? $$wp(\text{DO}, R) = \exists k \geq 0, H_k(R)$$
+Back: As $H_{k+1}(R) = H_0(R) \lor wp(\text{IF}, H_k(R))$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737187609873-->
+END%%
+
+%%ANKI
+Basic
+In the following definition, what set of states does $H_k(R)$ correspond to? $$wp(\text{DO}, R) = \exists k \geq 0, H_k(R)$$
+Back: Those in which $\text{DO}$ finishes execution in $k$ or fewer iterations with $R$ true.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737188069815-->
+END%%
+
+%%ANKI
+Basic
+Let $H_k$ denote the associated recursive definition of $wp(\text{DO}, R)$. *Why* does $H_k \Rightarrow H_{k+1}$?
+Back: $H_{k+1}$ is the set of states in which $\text{DO}$ finishes execution in $k$ *or fewer* iterations.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737188069819-->
+END%%
+
+%%ANKI
+Basic
+Let $H_k$ denote the associated recursive definition of $wp(\text{DO}, R)$. *Why* does $H_{k + 1} \Rightarrow H_k$?
+Back: N/A. It doesn't.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737188069822-->
+END%%
+
+%%ANKI
+Basic
+How is the associated recursive definition of $wp(\text{DO}, R)$ described in plain English?
+Back: As the set of states in which execution of $\text{DO}$ terminates in a finite number of iterations with $R$ true.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737187609876-->
+END%%
+
+%%ANKI
+Cloze
+Iterative command {$\textbf{do od}$} is equivalent to command {$skip$}.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737187609879-->
+END%%
+
+%%ANKI
+Basic
+*Why* does command $\textbf{do od}$ skip?
+Back: The $\text{DO}$ command iterates until no guard is satisfied.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737187609882-->
+END%%
+
+%%ANKI
+Basic
+What does $wp(\textbf{do } T \rightarrow skip \textbf{ od}, R)$ evaluate to?
+Back: $F$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737187609885-->
+END%%
+
+%%ANKI
+Basic
+*Why* does $wp(\textbf{do } T \rightarrow skip \textbf{ od}, R)$ evaluate to $F$?
+Back: $\textbf{do } T \rightarrow skip \text{ od}$ never terminates.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737187609888-->
+END%%
+
+%%ANKI
+Cloze
+The {$\text{DO}$} command corresponds to zero or more {$\text{IF}$} commands.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737187609892-->
+END%%
+
+%%ANKI
+Cloze
+Let $R$ be a predicate. Then $wp(\text{DO}, R) = \exists k,$ {$k \geq 0$} $\land$ $H_k(R)$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1737187609895-->
+END%%
+
 ## Bibliography
 
 * Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.

notes/set/functions.md

@@ -199,7 +199,7 @@ END%%
 %%ANKI
 Basic
 Let $A$ and $B$ be disjoint sets. $f \colon A \rightarrow B$ is an operation on what set?
-Back: N/A.
+Back: N/A. $f$ is not an operation.
 Reference: “Operation (Mathematics).” In _Wikipedia_, October 10, 2024. [https://en.wikipedia.org/w/index.php?title=Operation_(mathematics)](https://en.wikipedia.org/w/index.php?title=Operation_(mathematics)&oldid=1250395938).
 <!--ID: 1729804914207-->
 END%%

notes/trigonometry/index.md

@@ -0,0 +1,215 @@
+---
+title: Trigonometry
+TARGET DECK: Obsidian::STEM
+FILE TAGS: trigonometry
+tags:
+  - trigonometry
+---
+
+## Overview
+
+Trigonometry was originally derived from a Greek word meaning "triangle measuring". It has generalized to studying periodicity.
+
+%%ANKI
+Basic
+Trigonometry was originally the study of what geometric shape?
+Back: Triangles.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737167693405-->
+END%%
+
+## Unit Circle
+
+On the [[cartesian|Cartesian coordinate system]], the **unit circle** is the [[circle]] with center at the origin and radius $1$.
+
+%%ANKI
+Basic
+On the Cartesian coordinate system, what is the unit circle?
+Back: The circle with center at the origin and radius $1$.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737167693410-->
+END%%
+
+%%ANKI
+Basic
+On the Cartesian coordinate system, where is the center of the unit circle located?
+Back: At $\langle 0, 0 \rangle$, i.e. the origin.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737167693413-->
+END%%
+
+%%ANKI
+Basic
+What is the radius of the unit circle?
+Back: $1$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737167693416-->
+END%%
+
+%%ANKI
+Basic
+What is the diameter of the unit circle?
+Back: $2$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737167693419-->
+END%%
+
+%%ANKI
+Basic
+What is the circumference of the unit circle?
+Back: $2\pi$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737167693428-->
+END%%
+
+%%ANKI
+Basic
+What is the area of the unit circle?
+Back: $\pi$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737167693435-->
+END%%
+
+%%ANKI
+Basic
+Which real numbers does the point $\langle 0, 0 \rangle$ on the unit circle map to?
+Back: N/A. This point is not on the circle itself.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737168795237-->
+END%%
+
+%%ANKI
+Basic
+Which real numbers does the point $\langle 1, 0 \rangle$ on the unit circle map to?
+Back: $2\pi k$ for all $k \in \mathbb{Z}$.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737168795241-->
+END%%
+
+%%ANKI
+Basic
+Which point on the unit circle does number $2\pi$ map to?
+Back: $\langle 1, 0 \rangle$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737168795265-->
+END%%
+
+%%ANKI
+Basic
+Which point on the unit circle does number $\frac{3\pi}{2}$ map to?
+Back: $\langle 0, -1 \rangle$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737168795244-->
+END%%
+
+%%ANKI
+Basic
+Which real numbers does the point $\langle 0, -1 \rangle$ on the unit circle map to?
+Back:$\frac{3\pi}{2} + 2\pi k$ for all $k \in \mathbb{Z}$.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737168795269-->
+END%%
+
+%%ANKI
+Basic
+Which real numbers does the point $\langle 0, 1 \rangle$ on the unit circle map to?
+Back: $\frac{\pi}{2} + 2\pi k$ for all $k \in \mathbb{Z}$.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737168795248-->
+END%%
+
+%%ANKI
+Basic
+Which point on the unit circle does number $\frac{\pi}{2}$ map to?
+Back: $\langle 0, 1 \rangle$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737168795261-->
+END%%
+
+%%ANKI
+Basic
+Which point on the unit circle does number $\pi$ map to?
+Back: $\langle -1, 0 \rangle$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737168795252-->
+END%%
+
+%%ANKI
+Basic
+Which real numbers does the point $\langle -1, 0 \rangle$ on the unit circle map to?
+Back: $\pi + 2\pi k$ for all $k \in \mathbb{Z}$.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737168795256-->
+END%%
+
+%%ANKI
+Basic
+Which real numbers correspond to the highlighted point on the unit circle?
+![[unit-circle-1-0.png]]
+Back: $2 \pi k$ for all $k \in \mathbb{Z}$.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737169243685-->
+END%%
+
+%%ANKI
+Basic
+Which real numbers correspond to the highlighted point on the unit circle?
+![[unit-circle-0-1.png]]
+Back: $\frac{\pi}{2} + 2\pi k$ for all $k \in \mathbb{Z}$.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737169243690-->
+END%%
+
+%%ANKI
+Basic
+Which real numbers correspond to the highlighted point on the unit circle?
+![[unit-circle-n1-0.png]]
+Back: $\pi + 2\pi k$ for all $k \in \mathbb{Z}$.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737169243692-->
+END%%
+
+%%ANKI
+Basic
+Which real numbers correspond to the highlighted point on the unit circle?
+![[unit-circle-0-n1.png]]
+Back: $\frac{3\pi}{2} + 2\pi k$ for all $k \in \mathbb{Z}$.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737169243695-->
+END%%
+
+%%ANKI
+Basic
+*Why* does point $\langle 1, 0 \rangle$ on the unit circle coincide with real number $2\pi$?
+Back: Because the circumference of the unit circle is $2\pi$.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737169683142-->
+END%%
+
+%%ANKI
+Basic
+*Why* does point $\langle -1, 0 \rangle$ on the unit circle coincide with real number $\pi$?
+Back: Because half the circumference of the unit circle is $\pi$.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737169683151-->
+END%%
+
+%%ANKI
+Basic
+What is the "periodicity" of the unit circle?
+Back: $2 \pi$
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737230158153-->
+END%%
+
+%%ANKI
+Basic
+What property of the unit circle does its periodicity correspond to?
+Back: Its circumference.
+Reference: Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.
+<!--ID: 1737230158163-->
+END%%
+
+## Bibliography
+
+* Ted Sundstrom and Steven Schlicker, _Trigonometry_, 2024.