Euclid's Big Problem - Numberphile

Trisecting angles and calculating cube roots was a big problem for Euclid and his cohorts. Discussed by Zsuzsanna Dancso at MSRI.
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NUMBERPHILE

Videos by Brady Haran

[Lutranereis]

I had a professor who insisted on taking a few weeks to teach us all of this, and I really didn't get why it was such a big deal until we continued on throughout the semester. Turns out, using a straight edge and compass is a great way to not only understand geometry, but to also to become aware of just how many assumptions we never knew we were making about mathematics when we are taught it.

[joseapar]

exactly 7 years later and this video still bangs. What a fantastic bit of teaching

[TreuloseTomate]

Revolutionize math.
Turn 19.
Die in a duel.

What a life story.

[numberphile]

Message from Zsuzsanna (in the video)

Hello Everyone,

Everett Sass and Fenrakk101 (possibly others as well) posted correct
solutions on constructing a segment of length square root 3.
[Spoiler Alert! If you read them, you can discover that the idea behind
both is the same: to construct a right triangle with hypotenuse 2 and one
leg of length 1, so the other leg will be length sqrt(3).]
This solves the puzzle of "tripling a square", that is, you can now
construct a square of area 3. As some of you point out, this is not the
same as doubling the cube, which comes down to constructing a segment of
length cube root of 2, which is impossible by Euclidean means.

Some of you mention the idea of trisecting an angle by constructing an
isosceles triangle and trisecting the base. This does not work: if you
look closely, the middle part will be a bigger angle than the two side
parts. In other words, the three thin triangles are not congruent. As one
person points out, what you'd need to do is trisect a circle arc, not the
base of the triangle, and that is impossible by straight edge and compass.

Of course you can trisect _some_ angles, like a right angle or a 45 degree
angle, but there is no general procedure using straight edge and compass
that will trisect any arbitrary angle.

Sorry about staining that nice straight edge with the marker! I felt bad.

[GreenMachine]

12:58 Brady not only cracks this classic dad joke but then actively chooses to include it in the edit. Decisions like these are key to the channel’s success

[kiprs]

Ths one is really great. She explained points very well, she created tension in the storytelling ("before I tell you the answer" and goes onto another segment) and generally was clear and fun.

[xmachina]

"...and then people thought about it for 2000 years..." : my favorite line of the video.

[TheIslandwaters]

I really enjoined this video; with my limited knowledge of math, this is one of the few videos I can fully understand without a single question. She had shown many examples and clear, understood proof. I really enjoined her!

[secularmonk]

Euclidean geometry uses a straight edge and compass in two dimensions.

Origami does not allow drawing of circles within the paper (within those two dimensions) ... but ...

Folding is equivalent to the use of a compass, in a third dimension!

And utilizing three dimensions allows third roots. Marvelous!

[DJay]

it sounds like galois was a legend. revolutionising a fundamental part of mathematics before he turned 19 and then fighting a duel. i feel so useless right now

[amielmatt]

There is something so beautiful about these simple geometric ideas. Love this content!

[joeldick]

When lines and circles come together and intersects, points are born.

[gnosomai]

Good video. I was spellbound by the simple complexity and complex simplicity underlying the Brady's questions are always to the point and he says insightful and poetic things like "so the cube root is the point you can't reach".

[bluefandango]

what an interesting subject and such a soft spoken guest.
thank you for this vid.

[fearofdark]

I always had his question.
Lets say you are the first to prove something in math. What do you do after? Do you contact someone? :/

[guilemaigre]

This video is odly calming and relaxing, probably from the way and rate she speaks with. And most of all, it was intresting. 

[faramund]

It is UNBELIEVABLE we don't learn this in school where I live. THIS is the foundation.

[daledude]

Trisection of angles? It is certainly possible. I have discovered a truly marvelous proof of this, which this comment box allows too few characters to contain.

[Muppajevel]

I'm a completely halfwit when it comes to maths, yet i still do find these Numberphile videos so entertaining. I'm puzzled. But great to watch while recovering from knee surgery and way to much time indoor for the next couple of months.

[electricdreamer]

Everything Euclid couldn't. People thought about it for 2000 years.