Hi, have you ever noticed how much beauty comes
from motion? Ocean waves rolling towards the
shore. Leaves moving in the wind. A dancer spinning
across the stage. The rhythm of music. The steady
beating of a heart. Even my tee shot in golf
that flies into the air and suddenly slices into
the tree has its own mysterious kind of beauty.
Movement has a kind of beauty that static things
often do not. And mathematics is filled with
motion. Earlier this week, I mentioned those
fishing photos where someone stretches the fish
towards the camera so the fish looks enormous.
Now, the fish itself has not changed, but perspective
changes what we see. And artists have discovered
this a long time ago. When painters learn how
to create perspective, suddenly flat paintings
begin to feel alive and three -dimensional. Depth
appeared. Distance appears. Movement appears.
And underneath that artistic breakthrough was
mathematics. The mathematics of angles, distance,
projection, and transformation. I love that connection
because it reminds me that mathematics is not
merely about symbols on paper. Mathematics helps
us understand how reality moves and changes.
One of the most beautiful examples begins with
something simple. Take two points on a plant.
We know the shortest distance between them is
a straight line. Now, draw horizontal and vertical
lines through those points. that line becomes
the hypotenuse of a right triangle. a squared
plus b squared equals c squared. Now, imagine
placing that triangle inside a circle so that
the hypotenuse becomes the radius. And as the
point moves around the circle, the triangle changes
shape continuously. Tall triangles, wide triangles,
steep triangles, shallow triangles. An entire
family of triangles flowing through motion. And
from that motion emerges another beautiful shape.
A wave. A sine wave. And that wave appears everywhere.
In sound, in light, music, electricity, ocean
tides. Even the vibrations that allow us to hear
someone's voice. Just think about that for a
moment. The song that moves you. The colors in
a sunset, the light reaching your eyes from distant
stars, the voice of someone you love. These experiences
feel completely different. Yet underneath them
lies the same mathematical pattern. And what
amazes me is that all these beautiful flowing
forms emerge from something as simple as circular
motion. A circle becomes a triangle. A triangle
becomes a wave. A wave becomes music, light,
and sound. I just find that breathtaking. Because
it reminds me that mathematics is not cold or
lifeless. It pulses. It oscillates. It dances.
And this week, we are exploring beautiful mathematics.
Now, our thought today is not only to think of
beauty in stillness, but also we find beauty
in the patterns that are created by movement
itself.