# Marc Chamberland

Myra Steele Professor of Natural Sciences and Mathematics

Grinnell College

Grinnell, IA

I have long been enchanted by the aesthetic side of mathematics.

Most people view mathematics as a collection of tools and procedures

and get mired in the mechanics. Mathematical art communicates

the essential beauty found in mathematical truths.

As G. H. Hardy, wrote, "The mathematician's patterns, like the

painter's or the poet's must be beautiful; the ideas, like the colors

or the words must fit together in a harmonious way. Beauty is the

first test: there is no permanent place in this world for ugly mathematics."

Most people view mathematics as a collection of tools and procedures

and get mired in the mechanics. Mathematical art communicates

the essential beauty found in mathematical truths.

As G. H. Hardy, wrote, "The mathematician's patterns, like the

painter's or the poet's must be beautiful; the ideas, like the colors

or the words must fit together in a harmonious way. Beauty is the

first test: there is no permanent place in this world for ugly mathematics."

Inner Square

0.9 x 22.0 x 44.0 each in cm

High Performance Composite made with a 3D printer

2012

Inner Square illustrates a beautiful geometrical property.

Starting with a square whose side length is one, make four similar slices through each

corner to the opposite edge, one third of a unit from the adjacent corner.

What is the area of the (red) inner square?

While algebra could be used to calculate points and lines to solve

this problem, a simple geometric argument yields a solution

which a child can understand.

The answer can be seen by making two copies of the original

square, dissecting them into smaller colored pieces, then

recombined the pieces into five identically sized smaller squares (including the

red square). This tells us that the inner square has area 2/5.

The model invites visitors to move the pieces and experience the

transformation. The geometric thought and tactile motion combine to produce

a puzzle-like experience which embraces both mathematics and art.

Starting with a square whose side length is one, make four similar slices through each

corner to the opposite edge, one third of a unit from the adjacent corner.

What is the area of the (red) inner square?

While algebra could be used to calculate points and lines to solve

this problem, a simple geometric argument yields a solution

which a child can understand.

The answer can be seen by making two copies of the original

square, dissecting them into smaller colored pieces, then

recombined the pieces into five identically sized smaller squares (including the

red square). This tells us that the inner square has area 2/5.

The model invites visitors to move the pieces and experience the

transformation. The geometric thought and tactile motion combine to produce

a puzzle-like experience which embraces both mathematics and art.