Alexis Akira Toda

Alexis Akira Toda

Mathematical economist

A classical-type theorem about external squares on two sides of a triangle

less than 1 minute read

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I have been amazed by ChatGPT Pro recently, and here is another episode.

In 1994, when I was 14 years old and playing around with Pythagorean theorem-like figures, I discovered the following fact:

Let ABPQ and ACRS be squares erected externally on two sides of a triangle ABC. Then the lines CP and BR meet on the altitude from A to BC.

At the time, I was unable to prove the statement, but during high school I proved it analytically by setting coordinates (A(0,a)), (B(-b,0)), (C(c,0)).

Yesterday, it occurred to me to ask ChatGPT Pro to find an elementary proof and write a paper. With a single prompt, it did an amazing job. However, when I challenged it to do a literature review, it found that the result had already been published in an 1817 paper by Vecten. So of course, I’m not going to write a paper about this.

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