The Three Square Geometry Problem - Numberphile

Three Square Geometry Problem
More links & stuff in full description below ↓↓↓

Featuring Professor Zvezdelina Stankova.

NUMBERPHILE

Videos by Brady Haran

[strongeststrike]

‘This problem has not only 1, not only 2, but at least 54 solutions.’

That escalated quickly

[jk]

Wow, this whole thing felt like the climax of a Phoenix Wright case except instead of finding a murderer you're finding an angle.

[migfed]

I like her style, she explains the problem as telling you a detective story, it thrills you! Greetings from Colombia.

[nameguy]

"The size does not matter" - A renowned professional scientist

Take that, society

[numberphile]

There's a lot of links to go with this video (extra footage, associated video, brown paper, discuss on reddit, etc)... See the full video description for all these links.

[ivpantev]

This video is brilliant not because of the problem, but because it shows you the thinking behind reaching a solution. Everyone who said to use trigonometry is not wrong per se, but simply taking a more complicated route to reach the same conclusion. The beauty here is that you can get where you want to be just by drawing a few lines rather than using advanced functions, i.e. you can solve a much more complicated problem with simpler tools and some creativity :)

[yugyfoog]

This problem has a very simple solution using complex numbers.

(1+i)(2+i)(3+i) = 10i, which has an argument of 90 degrees.

Of course I didn't know about complex numbers in fifth grade.

[keithwilson]

The best part of this video was her accent.

[FlyingTurtleLP]

I really love vids like that. Will never regret that I subscribed this channel.

[Martial-Mat]

Jeez - if that's her idea of an easy solution that a 5th grader should be able to work out, she went to a different school to me! I don't think we touched algebra till 8th or 9th grade and cancelling of elements till a year or two after that.

It was elegant though, and she's very pleasant to listen to.

[ItsClint]

This is brilliant. Loved both this and 'Pebbling a chessboard'. I'd love to see more videos from her. Keep up the good work, Numberphile!

[gnomee]

She is so great at explaining! I think even people, who didn't work with angles for long, will understand it :)

[headrockbeats]

What scares me is that we only learned this sort of stuff in 7th grade, in geometry class for _advanced_ students...

[lucasschuetz]

It started so simple, then grew to something so exciting. Love these videos! Easily my favorite channel, keep it up!

[iammaxhailme]

arctan(1/1) + arctan (1/2) + arctan (1/3) = 90

A bit easier, but less interesting than the video's method, of course.

[triford]

Approx 3:10: "Or some ugly angle nearby?" Priceless...!

[PallasTurrets]

"Oh, it's a little bit obtuse" - my teachers about me in 5th grade

[slouch]

is this really something they taught in bulgarian elementary school? pretty sure i was still struggling to memorize multiplication tables back then

[eldiospadre]

Aw man, I haven't worked with geometry in years! This video took me back! Thanks for posting this it!

[aboubacaramine]

I wanted to try to resolve the problem myself just for fun, so I paused the video and I spent like 10 min on it. I really like the fact that even though the basis of the method is the same, I still resolved it in another way than Pr. Stankova did. And it was so fun to do. Basically I multiplied the squares to a small grid, then I recreated a similar construction but with the diagonals of the first squares as the sides of the new squares. I had then new 90° angles and with the use of all the parrallel lines I could put together alpha, beta and gamma in one of the 90° corner and they fit perfectly. Proving then that their sum is 90°.
I love how you can manipulate and distribuate angles using parallel lines. It's like the energy of the 2D geometric world x)