Simple yet 5000 years missed ?

Good news! You really can still discover new beautiful maths without being a PhD mathematician.
Stumbled across this one while working on the magic squares video. Another curious discovery by recreational mathematician Lee Sallows. A simple and beautiful and curious fact about triangles that, it appears, was first discovered only 10 years ago. Really quite amazing that this one got overlooked, considering the millennia old history of triangles.
Wiki page dedicated to Lee Sallows
en.wikipedia.org/wiki/Lee_Sal...
His personal homepage
www.leesallows.com
The relevant subpage
tinyurl.com/y6tzsbjt
t-shirt: www.teepublic.com/t-shirt/300...
music: Campagna - Adventure of a Lifetime
Enjoy!
Burkard

[@Just.Kidding]

The absurd grammar in that title leads me to believe you are indeed a mathematician.

[@asheep7797]

Sometimes you wonder how mathematicians come up with things...

[@marksteers3424]

I love the second "simpler" proof. It is intuitive and I can even explain it to members of the family who are not true maths lovers.

[@zzzaphod8507]

This is a great length of a Mathologer video, nothing wrong with this! Thanks

[@JeanYvesBouguet]

The duality relationship between the triangle and its folded form is simply beautiful. As a triangle lover, I absolutely love this video. I cannot believe this was not known.

[@nosy-cat]

I think I'd honestly prefer the first proof, but I was too busy shouting at the screen about the second proof to enjoy it.

[@jonadabtheunsightly]

You had me going at the beginning. Because of the particular choice of original triangle, you briefly had me wondering whether the "folded" triangle might be (geometrically similar to) the mirror image of the original. But no, not in the general case.

[@bentationfunkiloglio]

The dot proof is more emotionally satisfying. :)

[@m4mathematix381]

Another gem from Mathologer. It's because of Mathematicians like you out there, Maths is still beautiful and elegant.

[@tolkienfan1972]

I like both proofs. They scratch different intuitional itches. 😁

[@Kram1032]

so this is a kind of duality between two different triangles, neat

[@rv706]

Very nice theorem!

[@davewilson13]

One of the best math channels out there. Your glee is contagious!

[@jacoblojewski8729]

My first thought with seeing this was a way of defining a Dual of a triangle (up to scaling), following up with some theorems saying "A triangle has property X iff its dual has property Y". Time to explore.

[@3moirai]

Thanks! Lovely reminder why I love elegant mathematics like this.

[@kamaljain5228]

beautiful! thanks!!

[@anon_y_mousse]

I wouldn't say it was missed, but rather everyone who noticed it never bothered to write a paper on it. It's all part of the beautiful symmetry of mathematics in nature.

[@maxsievers8251]

And I thought train spotters were strange. Now I'm aware there are triangle spotters, too.

[@N7492]

Beautiful theorems. Elegant presentation. Bravo!

[@user-gd9vc3wq2h]

I did a bit of trigonometry to express the six angles with the coloured dots in terms of the angles of the given triangle. Here's what I figured out. (I'm sure this is known to the triangle experts.)