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  • When you hear the word symmetry,

  • maybe you picture a simple geometric shape

  • like a square or a triangle,

  • or the complex pattern on a butterfly's wings.

  • If you are artistically inclined,

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

  • or the effortless poise of a prima ballerina.

  • When used in every day life,

  • the word symmetry represents vague notions of

  • beauty, harmony and balance.

  • In math and science, symmetry has a different,

  • and very specific, meaning.

  • In this technical sense,

  • a symmetry is the property of an object.

  • Pretty much any type of object can have symmetry,

  • from tangible things like butterflies,

  • to abstract entities like geometric shapes.

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

  • Here's the definition:

  • 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,

  • like this equilateral triangle.

  • If we rotate our triangle through 120 degrees,

  • around an access through its center,

  • 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

  • is rotation through 120 degrees.

  • 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

  • we haven't mentioned yet:

  • 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.

  • Biologists call this bilateral symmetry.

  • As with all symmetries found in living things,

  • it's only approximate,

  • but still a striking feature of the human body.

  • We humans aren't the only bilaterally symmetric organisms.

  • Many other animals, foxes, sharks, beetles,

  • that butterfly we mentioned earlier,

  • have this kind of symmetry,

  • as do some plants like orchid flowers.

  • Other organisms have different symmetries,

  • ones that only become apparent

  • when you rotate the organism around its center point.

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

  • But when it occurs in animals,

  • this kind of symmetry is known as radial symmetry.

  • For instance, some sea urchins and starfish

  • have pentaradial or five-fold symmetry,

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

  • This symmetry also appears in plants,

  • 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.

  • They are completely asymmetric.

  • But why do organisms exhibit these different symmetries?

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

  • Let's look at one particular group:

  • bilaterally symmetric animals.

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

  • and, of course, humans.

  • 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,

  • it helps to have a front end

  • where you can group your sensory organs--

  • your eyes, ears and nose.

  • It helps to have your mouth there too

  • since you're more likely to run into food

  • or enemies from this end.

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

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

  • It's called a head.

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

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

  • aerodynamic wings if you're a bird,

  • 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.

  • But really what we should have said was

  • adult starfish and sea urchins.

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

  • For biologists, this is strong evidence

  • that we're more closely related to starfish

  • than we are, to say, corals,

  • or other animals that don't exhibit bilateral symmetry

  • at any stage in their development.

  • One of the most fascinating and important problems in biology

  • is reconstructing the tree of life,

  • discovering when and how the different branches diverged.

  • Thinking about something as simple as body symmetry

  • can help us dig far into our evolutionary past

  • and understand where we, as a species, have come from.

When you hear the word symmetry,

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【TED-Ed】對稱的科學--科姆-凱萊赫。 (【TED-Ed】The science of symmetry - Colm Kelleher)

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    許芷熒 發佈於 2021 年 01 月 14 日
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