A Miraculous Proof (Ptolemy's Theorem) - Numberphile
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it as a vivid example of inversion proving Ptolemy's theorem, both as background reading and when asking how its key equation or similar triangles arise.
Recommended by 1 people across 1 different months, 2020 to 2021.
What it is
A Numberphile video in which Berkeley mathematician Zvezdelina Stankova walks through a proof of Ptolemy's theorem about cyclic quadrilaterals using circle inversion. It is the first part of a two-part series, with the second covering pentagons and the golden ratio.
Cited in 1 Wikipedia article, including Ptolemy's theorem.
What people said
Recommends Wakabaloola · 2020-02 · Mathematics Stack Exchange · on “Special conformal transformation maps line and circle to line and circle”
there is a related and fun youtube video, [this video] (with a punchline at 19:33, but it is definitely worth watching the whole thing)
Cites lockedscope · 2020-10 · Mathematics Stack Exchange · on “Similar triangles in Ptolemy and inversion”
In this video at 30:56 seconds an equation is given. [this video] How could that equation achieved? So, are those triangles similar? [LINK]
Cites Clemens Bartholdy · 2021-01 · Mathematics Stack Exchange · on “Similar to inversion, what other geometric transformations have been used to prove theorems easily?”
I just learned of the proof of Ptlomey's theorem and was just amazed by it (see here) [this video] and it made me wonder, are there other such transformations which gives out difficult geometrical results easily?