5.3 KiB
| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Square Numbers | Obsidian::STEM | algebra::sequence |
|
Overview
The n$th term of the **square numbers** (s_n)_{n \geq 0} is $n^2. The first few terms are $0, 1, 4, 9, 16, 25, 36, 49, 64, \ldots$
%%ANKI Basic What shape do gnomons associated with square numbers take on? Back: L-shapes. Reference: “Square Number,” in Wikipedia, May 10, 2023, https://en.wikipedia.org/w/index.php?title=Square_number&oldid=1154182731.
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Basic
How are gnomons of the square numbers visualized?
Back:
!
Reference: “Square Number,” in Wikipedia, May 10, 2023, https://en.wikipedia.org/w/index.php?title=Square_number&oldid=1154182731.
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Basic
What general term refers to the different colored segments in the following?
!
Back: Gnomons.
Reference: “Square Number,” in Wikipedia, May 10, 2023, https://en.wikipedia.org/w/index.php?title=Square_number&oldid=1154182731.
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Basic
What are the first five square numbers (s_n)_{n \geq 0}?
Back: 0, 1, 4, 9, 16
Reference: “Square Number,” in Wikipedia, May 10, 2023, https://en.wikipedia.org/w/index.php?title=Square_number&oldid=1154182731.
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Basic
How is square number 16 graphically depicted?
Back:
* * * *
* * * *
* * * *
* * * *
Reference: “Square Number,” in Wikipedia, May 10, 2023, https://en.wikipedia.org/w/index.php?title=Square_number&oldid=1154182731.
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Basic
What closed formula is used to find the $n$th square number?
Back: n^2
Reference: “Square Number,” in Wikipedia, May 10, 2023, https://en.wikipedia.org/w/index.php?title=Square_number&oldid=1154182731.
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Basic
What is the recurrence relation in the recursive definition of square numbers (s_n)_{n \geq 0}?
Back: s_n = s_{n-1} + (2n - 1)
Reference: “Square Number,” in Wikipedia, May 10, 2023, https://en.wikipedia.org/w/index.php?title=Square_number&oldid=1154182731.
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What is the initial condition(s) in the recursive definition of square numbers (s_n)_{n \geq 0}?
Back: s_0 = 0
Reference: “Square Number,” in Wikipedia, May 10, 2023, https://en.wikipedia.org/w/index.php?title=Square_number&oldid=1154182731.
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Basic
How is the n$th square number $s_n represented with sigma notation?
Back: s_n = \sum_{k=1}^n (2k - 1)
Reference: “Square Number,” in Wikipedia, May 10, 2023, https://en.wikipedia.org/w/index.php?title=Square_number&oldid=1154182731.
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%%ANKI Basic Which polygonal numbers are the "next" generalization of triangular numbers? Back: The square numbers. Reference: “Triangular Number,” in Wikipedia, January 13, 2024, https://en.wikipedia.org/w/index.php?title=Triangular_number&oldid=1195279122.
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%%ANKI Cloze The sum of {1:natural numbers} is to {2:triangular numbers} whereas the sum of {2:odd natural numbers} is to {1:square numbers}. Reference: “Square Number,” in Wikipedia, May 10, 2023, https://en.wikipedia.org/w/index.php?title=Square_number&oldid=1154182731.
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Basic
What polygonal number is k equal to after the following for loops?
int k = 0;
for (int i = 1; i <= n; ++i) {
k += 2 * i - 1;
}
Back: The $n$th square number. Reference: “Square Number,” in Wikipedia, May 10, 2023, https://en.wikipedia.org/w/index.php?title=Square_number&oldid=1154182731.
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%%ANKI Basic Why are square numbers a sum of odd numbers? Back: The gnomon of a square number is twice the width of the previous square, plus the corner. Reference: “Square Number,” in Wikipedia, May 10, 2023, https://en.wikipedia.org/w/index.php?title=Square_number&oldid=1154182731.
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Bibliography
- Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
- “Square Number,” in Wikipedia, May 10, 2023, https://en.wikipedia.org/w/index.php?title=Square_number&oldid=1154182731.