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Practice English Speaking&Listening with: ViHart on Tetrahedral Dice - Numberphile

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VI HART: Yo, Brady.

It's Vi Hart, and as promised, I'm going throw you a Yahtzee.

But to make it easier, I'm going to use tetrahedral dice,

but to make it harder again-- ooh, that

was four out of five.

To make it harder again, I'm going to use six of them.

So you figure that out.

Tetrahedral dice have many survival advantages over the

cubular dice, among which is that they are very difficult

to pick up because they're pointy.

So I'm going to have to sweep them off the table.

They also don't roll as far as your cube dice because they

have sharper angles.


We are at roll number 100, as you can see by the counter

that I'm pressing with my foot, which means it's time--

time for your next tetrahedral superiority fact.

Tetrahedra are also superior to the cube in that they

always end point-up.

They don't have the faces opposite each other, unlike a

cube and, in fact, all other platonic solids.

When they land on the face, the other face is facing up.

But these have the point facing up, which means that

they are dangerous as a natural defense, which is I

guess why caltrops are designed as a tetrahedron.

They have tetrahedral points, so that when

you throw them at--

they're always going to land point-up.

And if you stepped on one of these, it would hurt.

Unlike the cube, which is weak and soft.


We've gotten past 200.

Time for your next tetrahedral survival advantage fact.

Tetrahedra don't roll as easily as cube dice, because

they have this kind of sharper angle.

They are less likely to accidentally

get lost and lonely.

Moving onward.


All right.

So our 300th roll tetrahedron fact time.

As a platonic solid, Plato thought that the tetrahedron

represented the element of fire, because one, they're

pointy and they hurt you like fire hurts you, and related to

the fact that they don't roll easily, unlike the

icosahedron, which rolls so easily, with that very wide

angle, that it rolls kind of like water does.

So that's what the icosahedron was water, tetrahedron was

fire, and the cube, being stable and boring, is earth.



I guess I got it.

Man, and here I was busily trying to think of more

tetrahedron facts.

I did not expect to get it this soon at all.

I'm on 382.

Here I was just thinking that I should have gotten an intern

to do this for me and that I was going to have nightmares

of tetrahedral dice attacking me.

But this actually wasn't that bad.

And yet I don't think the chances of six four-sided dice

is actually that much lower than of five cubes.

(SINGING) Brady, I got a Yahtzee, I got a Yahtzee.



Hey, Brady, it's the number two.

Just for you.

Isn't that appropriate?

BRADY HARAN: Oh, oh, ooh.

Ah, ow!

VI HART: Sorry, 2.

But you know, you look good this way.

All right.

I guess I might as well go through some other tetrahedral

dice facts, although I don't ever want to move my Yahtzee

from being a Yahtzee ever again.

Keeping those 2s up.

Tetrahedra are also superior to the cube in that, well, as

a survival advantage, cubes pack space.

So like if you have a lot of cubes, they might pack

together nice and tightly like this.

Which you might think is a plus, because they use space

very efficiently.

But on the other hand, if you get your cube all surrounded

tightly by other cubes, the cubes might suffocate and die.

Whereas the tetrahedra, though they look almost like they

might kind of pack space, like you can fit five of them

around like this and it looks like they almost fit

perfectly, but they don't.

There's just like a tiny little gap.

And this gap enables even a super-close-huddling group of

tetrahedra to breathe and not suffocate.

I thought I was going to be in for a whole afternoon of

tetrahedron mania.

The Description of ViHart on Tetrahedral Dice - Numberphile