Hi, what is it that draws you in? If you see
a beautiful flower, do you stop and take a second
look? Do you notice the colors that are stretching
across the sky at sunset? Does the face of a
newborn baby capture your attention? All three
of these draw me into a different world. For
a moment, I stop thinking about what I need to
do next. I find myself enjoying the beauty, reflecting,
and sometimes even wondering. Now, you may find
this odd, but shapes can do something similar
for me. Sometimes it is a simple design on a
t -shirt or a particular creative logo. Other
times it is a repeating pattern on a floor. or
a wall, or a building. I am drawn to shapes,
especially shapes that are filled with an interesting
pattern. Mathematician Paul Lockhart writes something
simple, yet profoundly simple. Paul says, every
equation has a shape. Think about that for a
moment. When we first encounter an equation,
we usually see a collection of letters, numbers,
and symbols. Consider the equation y equals x
squared. Now, on the page, it may not look particularly
inspiring. It is simply a rule. Choose a value
for x, square it, and that gives you the corresponding
value of y. place those points on a coordinate
plane, and something quite different happens.
The equation becomes a parabola. What looked
like a short line of mathematical notation opens
into a smooth symmetrical curve. The equation
has been given a visible shape. Okay, now change
the equation slightly to y equals minus. x squared.
Adding one small negative sign turns the entire
parabola upside down. Or consider this equation,
x squared plus y squared equals one. Now, it
may initially appear to be a strange collection
of squares and numbers, but when we graph it,
a circle emerges. Isn't it ironic that a circle
is somehow contained with the equation of squared
values? And of course, the graph did not create
it. The graph allowed us to see what had been
there all along. One of the things I love about
mathematics is that algebra and geometry seem
like two completely different worlds. Algebra
speaks through symbols and equations. Geometry
speaks through lines, curves, distances, and
shapes. But a graph allows those two worlds to
meet. The equation tells us how the numbers are
related. The shape lets us see that relationship
all at once. And perhaps that is why shapes draw
us in. We are not merely looking at individual
points or lines or even colors. Our minds gather
those separate details and recognize a larger
pattern. And through that pattern, we begin to
see meaning. Mathematics reminds us that reality
can contain more than what is immediately visible.
Sometimes a relationship is present long before
we have found the right way to see it. An equation
can remain nothing more than symbols on a page.
That happens many times for me. But math is at
its best is when it becomes a doorway into an
entirely different world. And perhaps the same
is true elsewhere in life. So, as we begin this
week, consider these questions. What might already
be present in your life, waiting for you to discover
a new way of seeing it? Perhaps it is a close
friend or family member whose presence has become
so familiar that you sometimes take it for granted.
And seeing that person every day can be a little
like looking at an equation. The meaning is there,
but we may no longer recognize the beautiful
shape it has created. Who has helped shape your
life for the better? And perhaps today is the
day to see that person differently and to let
them know how much their life has shaped yours.