Update History

Ching-Kuang Shene (冼鏡光), Professor Emeritus
Department of Computer Science
Michigan Technological University
Houghton, MI 49931
USA
Created October 18, 2025

Sepetmber 17, 2025 had the earliest page online at this site. Then, this site was updated very frequently from late September to mid October. Lately, this site has become steadier annd seems worth to start a update history. This update history is a stack showing the most recent one at the top.

Updates

April 4, 2026 The original page on Euclid Could Be the First One Who Proved the Pythagorean Theorem Using Trigonometry is replaced by five new pages on Proposition I.47, II.12 and II.13 in Elements and their connection to the Law of Cosines with some discussion. These new pages are:

Elements: Book I Proposition 47 (I.47), the Pythagorean Theorem

Elements: Book II Propositions 12 and 13 (II.12 and II.13), the Original Proofs

Elements: Book II Propositions 12 and 13 (II.12 and II.13), Euclid's Scissors

Elements: Book II Propositions 12 and 13 (II.12 and II.13), The Law of Cosines
Elements: Book II Propositions 12 and 13 (II.12 and II.13), Euclid's Scissors: Discussion

Some pages also received minor changes.

March 17, 2026 Pages Mollweide's Formulas, Proving the Pythagorean Theorem via Mollweide's Formulas, The Law of Sines and The Law of Tangents were added.

November 9, 2025 Page Michael Hardy's Proof was added.

October 24, 2025 Page A Simplified Version of Mike Staring's Proof was added.

October 21, 2025 Page A Mike Staring's Calculus Based Proof was added.

October 18, 2025 Page A Proof Using Binomial Expansion was added.

October 15, 2025 Pages Is Proving the Pythagorean Identity a Conspiracy Theory? and The Use of a Dense Set were added.

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