Taken from "Experiencing Geometry on Plane and Sphere," a classic textbook
on Euclidean and non-Euclidean space. Used by permission of the author
Professor David W. Henderson, Department of Mathematics, Cornell University
by David Henderson
Logic can only go so far
after that I must see-perceive-imagine
This geometry can help
I may reason logically thru theorem
and propositions galore,
but only what I perceive is real.
If after studying I am not changed
if after studying I still see the same
then all has gone for naught.
Geometry is to open up my mind
so I may see what has always been behind
the illusions that time
and space construct.
Space isn’t made of point and line
the points and lines are in the mind.
The physicists see space as curved
with particles that are quite blurred.
And, when I draw, everything is fat
there are no point and that is that.
The artists and the dreamer knows
that space is where an image grows.
For me it’s a sea in which I swim
a formless sea of hope and whim.
Thru my fear on Infinity and One
I structure space to confine
my imagination away from the idea
That all in One.
But, I can from this trap escape
I can see the geometry in which I wander
as but a structure I made to ponder.
I can dare to let fo the structures
and my fears
and look beyond
to see what is always there to see.
But, to let go, I must first grab on.
Geometry is both the grabbing on
and the letting go.
It is a logical structure
and a perceived meaning
Q.E.D.’s and “Oh! I see”’s
It is formal abstractions
and beautiful contraptions.
It is talking precisely about that
Which we know only fuzzily.
But, in the end, and, most of all,
it is seeing-perceiving
The meaning that