31 lines
1.1 KiB
Markdown
31 lines
1.1 KiB
Markdown
---
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title: Geometry
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TARGET DECK: Obsidian::STEM
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FILE TAGS: geometry
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tags:
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- geometry
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---
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## Overview
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Two sets are **congruent** if their points can be put in one-to-one correspondence in such a way that distances are preserved.
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%%ANKI
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Basic
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Suppose sets $P$ and $Q$ are congruent. What does this imply the existence of?
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Back: A bijection between $P$ and $Q$ that preserves distances between points.
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Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
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<!--ID: 1732381333449-->
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END%%
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%%ANKI
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Basic
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Suppose sets $P$ and $Q$ are congruent and $f$ is the corresponding bijection. What FOL proposition follows?
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Back: $\forall p_1, p_2 \in P, \lvert p_1 - p_2 \rvert = \lvert f(p_1) - f(p_2) \rvert$
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Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).
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<!--ID: 1732381333454-->
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END%%
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## Bibliography
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* Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). |