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 www.scientificamerican.com
2 High School Students Prove Pythagorean Theorem. Here's What That Means | Scientific American
| | www.mathplanet.com
The Pythagorean Theorem (Pre-Algebra, Right triangles and algebra) - Mathplanet
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| | www.johndcook.com
Trigonometry theorems for hyperbolic geometry
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| | How the Pythagorean theorem, law of sines, and law of cosines translate to hyperbolic geometry.
| | sriku.org
On the Pythagorean "theorem" | Codaholic
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| | [AI summary] The author argues that the Pythagorean theorem is not a true theorem derived from axioms but rather a fundamental definition required to establish the concepts of length, right angles, and Euclidean geometry.
| | adam.chlipala.net
InductiveTypes
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| [AI summary] This text provides an in-depth exploration of advanced Coq proof techniques, focusing on manual proofs, recursion, and induction principles for complex data structures. It covers topics like nested inductive types, custom induction principles, and the design philosophy behind Coq's approach to proof automation. The text includes detailed examples of proof scripts, such as manual proofs for discrimination and injectivity of constructors, and discusses the use of tactics like discriminate and injection. It also touches on the implementation of functions like pred and the role of hints in improving proof readability and automation.