The Fantastic New Trigonometric Proof of the Pythagorean Theorem

In the spring of 2023, two high-school seniors, Calcea Johnson and Ne'Kiya Jackson, let it be known that they had come up with a new proof of the Pythagorean Theorem. Not only was it new and innovative, but it used only the trigonometric definition of the sine function, and the law of sines, which means it was a trigonometric proof. It was once thought that such a proof would have to use circular logic to reach its conclusion, but it was shown to be possible by Jason Zimba in a 2009 paper: https://forumgeom.fau.edu/FG2009volum...

At the time I made this video, the new proof was not published. But it had been presented at the American Mathematical Society's Annual Southeastern Conference, and pictures from this presentation were posted and interviews were published which allowed astute YouTubers to deduce the details of the proof and create videos explaining their best guess at how the proof goes. The ones I used as source material are linked below. In my interpretation, I strive to be as clear and concise as possible, and assume no prior knowledge of things like the law of sines or geometric series.

ThatMathThing:    • What did we all miss in this 2000 year old...  
MathTrain:    • How High Schoolers Proved Pythagoras Using...  
polymathematic:    • Pythagoras Would Be Proud: High School Stu...  

Articles about the authors:

The Guardian: https://www.theguardian.com/us-news/2...
Yahoo!: https://ca.style.yahoo.com/teens-foun...

Animations were created using Apple Keynote and Desmos Graphing Calculator (https://www.desmos.com/calculator) with the help of Desmos Player (https://github.com/MathyJaphy/DesmosP...)

Edited with Apple iMovie.
Music: "Greasy Wheels", iMovie Song (   • Greasy Wheels Long | iMovie Song-Music  ), “Fifth Avenue Stroll”, iMovie Song (   • Fifth Avenue Stroll | iMovie Song-Music  )