Name: 【TED-Ed】對稱的科學--科姆-凱萊赫。 (【TED-Ed】The science of symmetry - Colm Kelleher)
Uploaded: 2021-01-14T05:05:25.000Z
Duration: 5 min 9 s
Description: 【看影片學英語】數萬部 YouTube 影片，搭配英漢字典即點即查，輕鬆掌握單字發音與用法，長久累積看電影不必再看字幕。

maybe you picture a simple geometric shape

or the complex pattern on a butterfly's wings.

you might think of the subtle modulations of a Mozart concerto,

or the effortless poise of a prima ballerina.

the word symmetry represents vague notions of

In math and science, symmetry has a different,

Pretty much any type of object can have symmetry,

to abstract entities like geometric shapes.

So, what does it mean for an object to be symmetric?

a symmetry is a transformation that leaves that object unchanged.

Okay, that sounds a bit abstract, so let's unpack it.

It will help to look at a particular example,

If we rotate our triangle through 120 degrees,

we end up with a triangle that's identical to the original.

In this case, the object is the triangle,

and the transformation that leaves the object unchanged

So we can say an equilateral triangle is symmetric

with respect to rotations of 120 degrees around its center.

If we rotated the triangle by, say, 90 degrees instead,

the rotated triangle would look different to the original.

In other words, an equilateral triangle is not symmetric

with respect to rotations of 90 degrees around its center.

But why do mathematicians and scientists care about symmetries?

Turns out, they're essential in many fields of math and science.

Let's take a close look at one example: symmetry in biology.

You might have noticed that there's a very familiar kind of symmetry

the symmetry of the right and left sides of the human body.

The transformation that gives this symmetry is reflection

by an imaginary mirror that slices vertically through the body.

As with all symmetries found in living things,

but still a striking feature of the human body.

We humans aren't the only bilaterally symmetric organisms.

Many other animals, foxes, sharks, beetles,

Other organisms have different symmetries,

when you rotate the organism around its center point.

It's a lot like the rotational symmetry of the triangle we watched earlier.

this kind of symmetry is known as radial symmetry.

For instance, some sea urchins and starfish

that is, symmetry with respect to rotations of 72 degrees around their center.

as you can see for yourself by slicing through an apple horizontally.

Some jellyfish are symmetric with respect to rotations of 90 degrees,

while sea anemones are symmetric when you rotate them at any angle.

Some corals, on the other hand, have no symmetry at all.

But why do organisms exhibit these different symmetries?

Does body symmetry tell us anything about an animal's lifestyle?

In this camp, we have foxes, beetles, sharks, butterflies,

The thing that unites bilaterally symmetric animals

is that their bodies are designed around movement.

If you want to pick one direction and move that way,

where you can group your sensory organs--

since you're more likely to run into food

You're probably familiar with a name for a group of organs,

plus a mouth, mounted on the front of an animal's body.

Having a head leads naturally to the development of bilateral symmetry.

And it also helps you build streamlined fins if you're a fish,

or well coordinated legs for running if you're a fox.

But, what does this all have to do with evolution?

Turns out, biologists can use these various body symmetries

to figure out which animals are related to which.

For instance, we saw that starfish and sea urchins have five-fold symmetry.

In their larval stage, they're bilateral, just like us humans.

that we're more closely related to starfish

or other animals that don't exhibit bilateral symmetry