Hi, I have a friend who has transitioned through
many stages of life, from being married to raising
children and eventually becoming a grandparent.
She once described those transitions as moving
from being the picture to becoming the frame.
I think that perspective is beautiful. Ironically,
I see something similar illustrated in math.
Think of a simple circle. with radius one. Now
we could spend all day exploring the wonderful
properties of the circle itself, its circumference,
its area, and eventually the beautiful relationship
involving pi. But instead, let's allow the circle
to become the frame. Let it become the boundary
of a little mathematical world where new ideas
can grow. Imagine placing the circle on an x
-y coordinate plane with its center at the origin.
Now, draw a right triangle inside the circle
so that the hypotenuse stretches from the center
to a point on the circle. Now, because the radius
of the circle is 1, the hypotenuse of the triangle
is also 1. And if the point on the circle is
x -y, Then the Pythagorean theorem tells us that
x squared plus y squared equals 1. Already, we
see geometry, algebra, and circles all connecting
together. But now let's add another dimension.
Suppose we know the angle between the hypotenuse
and the x -axis. Suddenly, we need trigonometry.
the height of the triangle becomes the sine of
the angle. But now, let's really open things
up. Rather than studying one triangle at a time,
imagine every possible triangle that is formed
as the angle changes continuously around the
circle. And if we graph the height of each triangle,
we create a sine wave. Now a static triangle
suddenly becomes a flowing curve. Studying a
single triangle is only the starting point, but
what transforms our thinking is placing the triangle
inside the circle and letting the two shapes
dance together. And out of that dance, emerges
one of the foundational patterns in all of math.
And of course this sine wave is not just an abstract
mathematical curiosity. It is a theory born for
reality. It helps describe sound waves and light
waves, vibrations, electricity, and much more.
It is literally... woven into the invisible structure
behind many of our senses. When Eddie Wu says
mathematics develops a new sense within us, I
think this is part of what he means. We begin
seeing how simple shapes connect and grow into
entirely new dimensions of understanding. A circle
is no longer just a circle. It becomes a framework
for discovering triangles, waves, motions, and
patterns hidden underneath reality itself. Now,
in my creative world, I think we are all wired
a bit like that circle. It is good to understand
who we are and how we are uniquely and wonderfully
made. But life grows into new dimensions. when
what we have been given becomes a blessing to
others. Over time, we begin realizing that our
role is not only to be the picture. Sometimes,
we are also becoming the frame, creating space
for others to grow, to flourish, and to discover
beauty themselves. Yesterday, we talked about
how transformation often begins with small beginnings.
So, maybe one small step in this transformation
is simply realizing that we can become a frame
for others. Not to control them, of course, but
to support them, to encourage them, and help
their unique shape come alive.