Triangle to square transformation

A few days ago, I stumbled upon a fascinating mathematical problem posed by the self-taught English mathematician and puzzle columnist, Henry Dudeney. He challenged his readers to dissect an equilateral triangle into the minimum number of pieces that could be rearranged to form a square. Remarkably, Charles William McElroy, a clerk who frequently corresponded with Dudeney with puzzle solutions, presented a four-piece solution. Two weeks later, Dudeney reported that no other readers of the newspaper could improve upon this, and the four-piece dissection has remained the record ever since.

Intrigued, I watched a quick animation of what appeared to be a symmetrical dissection of the square. I couldn't have been more wrong! My own attempt, which I showcase in this video, results in a dissection of an isosceles triangle, making it technically 'incorrect' when considering Dudeney's original equilateral triangle problem.

Despite this deviation from the initial challenge, it's still quite interesting that it took 122 years for a proof of this particular dissection to emerge. Join me as I explore this geometric puzzle and share my findings.

If you're interested in geometry, tessellations, aperiodic tilings (like those of Roger Penrose), and the beauty of mathematics, then this video is for you!

Видео Triangle to square transformation канала jax79