WEBVTT

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Hi, have you ever noticed how much beauty comes

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from motion? Ocean waves rolling towards the

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shore. Leaves moving in the wind. A dancer spinning

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across the stage. The rhythm of music. The steady

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beating of a heart. Even my tee shot in golf

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that flies into the air and suddenly slices into

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the tree has its own mysterious kind of beauty.

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Movement has a kind of beauty that static things

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often do not. And mathematics is filled with

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motion. Earlier this week, I mentioned those

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fishing photos where someone stretches the fish

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towards the camera so the fish looks enormous.

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Now, the fish itself has not changed, but perspective

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changes what we see. And artists have discovered

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this a long time ago. When painters learn how

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to create perspective, suddenly flat paintings

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begin to feel alive and three -dimensional. Depth

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appeared. Distance appears. Movement appears.

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And underneath that artistic breakthrough was

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mathematics. The mathematics of angles, distance,

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projection, and transformation. I love that connection

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because it reminds me that mathematics is not

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merely about symbols on paper. Mathematics helps

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us understand how reality moves and changes.

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One of the most beautiful examples begins with

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something simple. Take two points on a plant.

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We know the shortest distance between them is

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a straight line. Now, draw horizontal and vertical

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lines through those points. that line becomes

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the hypotenuse of a right triangle. a squared

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plus b squared equals c squared. Now, imagine

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placing that triangle inside a circle so that

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the hypotenuse becomes the radius. And as the

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point moves around the circle, the triangle changes

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shape continuously. Tall triangles, wide triangles,

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steep triangles, shallow triangles. An entire

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family of triangles flowing through motion. And

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from that motion emerges another beautiful shape.

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A wave. A sine wave. And that wave appears everywhere.

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In sound, in light, music, electricity, ocean

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tides. Even the vibrations that allow us to hear

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someone's voice. Just think about that for a

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moment. The song that moves you. The colors in

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a sunset, the light reaching your eyes from distant

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stars, the voice of someone you love. These experiences

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feel completely different. Yet underneath them

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lies the same mathematical pattern. And what

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amazes me is that all these beautiful flowing

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forms emerge from something as simple as circular

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motion. A circle becomes a triangle. A triangle

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becomes a wave. A wave becomes music, light,

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and sound. I just find that breathtaking. Because

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it reminds me that mathematics is not cold or

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lifeless. It pulses. It oscillates. It dances.

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And this week, we are exploring beautiful mathematics.

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Now, our thought today is not only to think of

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beauty in stillness, but also we find beauty

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in the patterns that are created by movement

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itself.