Name: 数学者だけど「幾何学」について質問ある？| Tech Support | WIRED Japan
Uploaded: 2025-02-12T09:15:30.000Z
Duration: 17 min 54 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Let's answer some questions from the internet.

At S39GSY asked, who the F created geometry?

It's just part of the way we interact with the physical world.

The person who first codified it and formalized it was somebody named Euclid who lived in North Africa around 2000 years ago.

And we also know that a lot of what he wrote down was the work of a lot of other people that he was collecting and putting in written form.

But this idea of geometry as the set of formal rules we use to carefully put together demonstrations of facts about angles, triangles, circles, et cetera, that's when it sort of stops being purely intuitive and starts being something we can put in a book.

Alien Searcher asks, new shapes are just discovered?

New shapes are just discovered all the time.

One of the big misconceptions about math that people have is that math is finished.

People who are geometers are typically thinking about crazy stuff that's going on in high dimensions with all kinds of crazy curvature.

But four dimensional shapes are in some sense just as real as three dimensional shapes.

We just have to kind of train our minds to be able to perceive what shapes in those dimensions like a hypercube or a tesseract would look like.

Inkbot Kowalski asked, wait, wait, a tesseract is a real thing?

A tesseract is another name for what's usually called in math a hypercube.

MCU did not create the idea of the tesseract being in popular science fiction.

That really comes in in Madeline L'Engle's book,

All right, here you have a square, a two dimensional figure, and here you have its three dimensional counterpart, a cube.

A cube you can think of as two squares, the top square and the bottom square, and then you sort of connect them together.

If the cube is the three dimensional figure and the square is the two dimensional figure, what would be the four dimensional figure?

I guess the hypercube would have to be something that was two cubes joined together and it would have to have twice as many corners as the cube does or 16.

And now I've got to connect each corner of the little cube to the corresponding corner of the big cube.

And now you may say like, are there really four dimensions or is that just an invention?

When we do regular geometry, we're working in a perfectly flat plane.

The two dimensional plane or three dimensional space are just as much of an abstraction as four dimensional space.

Okay, Claudio Jacobo asks, if algebra is the study of structure, what is geometry?

Algebra is the logical and symbolic, right?

And like doing mathematics makes use of this tension between the algebraic side of our mind and the geometric side.

3Omega2 asks, how can I use the Pythagorean theorem to solve my problems in life?

I can't quite imagine what problem you might have in your life that would be solved by the Pythagorean theorem.

The problem that the Pythagorean theorem solves is the following one.

If for some reason I have some distance I wanna traverse and if I know how far West you have to go to get there and then how far North, and I happen to know these two distances then the Pythagorean theorem allows you to compute this diagonal distance, which we call C, but we can also write it as the square root of A squared plus B squared.

Is this the problem you're facing in your everyday life?

The Pythagorean theorem is here for you, but in most cases it is not.

TMScience asks, what is special about a Pringle's hyperbolic paraboloid geometry?

The Pringle is a wonderful geometric form.

What's special about it is this point right here at the center of the Pringle, if I move from left to right, I can't help but go up.

So it seems like I'm at the bottom of the Pringle, but if I move from front to back,

I can't help but go down from the center.

So it's somehow simultaneously at the top.

It's a peak and a valley at the same time.

And this special kind of point, which is called a saddle point in math, is what gives the Pringle it's particularly charming geometry.

Dr. Funky Spoon asks, sucker MCs maintain cool under pressure, but who f**ks with geometry like MC Escher?

MC Escher, beloved artist of all mathy people.

Escher was famous for studying and using in his art what are called tessellations, ways of taking a flat plane and covering it with copies.

It was something he learned actually in part from hanging out at the Alhambra, this incredible palace from Islamic Spain.

When you go to the Alhambra, you see these incredibly intricate, but also very repetitive figures, which by repetition across the entire wall, it becomes very complicated and rich.

And that's the feature of a tessellation.

The answer is the unnamed architects of the Alhambra in Granada, Spain.

Raspberry Pie asks, how many holes are there in a straw?

Fortunately, I always bring a straw with me wherever I go.

There are the one-holers who feel that, well, look, there's like one hole.

And there are the two-holers whose view is there's a hole at the top of the straw and there's a hole at the bottom of the straw.

For the people who think there's two holes,

I would say, imagine this straw, if you can, getting shorter and shorter.

Like imagine I sort of cut it and it was half as long and I cut it again until it's so short that it's actually like shorter than the distance around.

I think we all agree that would be like a very weird thing to say about a bagel.

So now I'm talking to you, triumphant one-holers.

If you think this straw is one hole, let's say I take it and I pinch the bottom like this.

There's just like the one hole at the top.

I mean, you could fill this with water, right?

How many holes are there in the water bottle?

Just the one at the top that you drink out of, right?

But if it has one hole now and I poked a hole in the bottom and I opened up the bottom, how many holes would it have?

I think the way to think about the straw is that, yeah, there's two holes, but one of them is the negative of the other.

Both the one-holers and two-holers are right in a way as long as they're willing to learn about the arithmetic of holes.

Liberated Soul asks, the golden ratio in art photography, is that something to do with perfect composition?

It's a number, a kind of unassuming number.

Subtitles ListPlay Video

数学者だけど「幾何学」について質問ある？| Tech Support | WIRED Japan

sort

incredible

context

figure