The Theorem We Overlooked for 2000 Years | Johnson's Circles
Автор: Tomáš Miškov
Загружено: 2023-10-24
Просмотров: 1590
A simple theorem of 3 circles meeting at a single point known as Johnson's Circles, Titeica's Theorem, or the 5 Lei Coin Problem. Let's visually prove why the fourth circle going through the intersection points is of the same size as the circles we started with!
Yet again, credits for bringing this theorem to my attention go to John D. Cook and his amazing blog: https://www.johndcook.com/blog/2023/1...
Original paper by Roger Arthur Johnson:
https://archive.org/details/jstor-297...
Alternative out-of-the-box proof of Gheorghe Țițeica's circles:
https://www.cut-the-knot.org/proofs/3...
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Tools used to make this video:
Cavalry, DaVinci Resolve, Affinity Designer
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Timestamps:
0:00 Intro
0:34 How so late?
1:59 Names
2:18 1st Proof
3:15 2nd Proof
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