A Beautiful Proof of Ptolemy's Theorem.

Ptolemy's Theorem seems more esoteric than the Pythagorean Theorem, but it's just as cool.  In fact, the Pythagorean Theorem follows directly from it.  Ptolemy used this theorem in his astronomical work.  Google for the historical details.

Thanks to this video for the idea of this visual proof:  VISUAL PROOF - PTOLEMY THEOREM.  There are others that use the same three-triangle method too, but none that I've seen present a complete proof, which I believe I've done here.  I have been told that this proof may have first been published by William Derrick and James Hirstein, "Proof Without Words: Ptolemy’s Theorem", in The College Mathematics Journal, Vol. 43, No. 5 (November 2012), p. 386.

Animations were created using Desmos Graphing Calculator (https://www.desmos.com/calculator) with the help of DesmosPlayer, a browser plug-in that I wrote to control the graph (https://github.com/MathyJaphy/DesmosP...)  Screen capture turned that into a video; edited with iMovie.

Music:  “Off Broadway”, iMovie Song (Off Broadway | iMovie Song-Music), “Acoustic Sunrise “, iMovie Song (Acoustic Sunrise | iMovie Song-Music)

• #education
• #desmos
• #pythagoras
• #geometry
• #quadrilateral