## A perfect sphere?

July 18, 2011 Leave a comment

Beauty … perfection … words many non-math people don’t expect to hear when it comes to mathematics. But talk to any math person and, sooner or later, one of these words will be used to describe the subject. As the legendary number theorist G.H. Hardy once described it, “Beauty is the first test: there is no permanent place in the world for ugly mathematics.”

For most people, their first opportunity to see such beauty and perfection comes with a course in high school geometry. Studying the properties of polygons or learning that the ratio of a circle’s circumference to its diameter is exactly pi are opportunities to witness first hand the elegance of the subject.

Unfortunately, as math people know too well, the perfection of geometry exists only in our minds. Thanks to the laws of physics, in the “real world”, the perfect forms of geometry just do not exist. A rhombus is never quite a rhombus. The ratio of a circle’s circumference to its diameter is close to pi but never exactly pi.

However, before we all run into the woods to hide from the hideous and ugly real world of imperfection, TAKE A DEEP BREATH! It turns out that there is new hope for us!

According to recent research from Imperial College in London, we need not look farther than the electron to see geometric perfection – well, almost perfection. Previously thought to be a distorted sphere (aspheric), scientists were surprised when they discovered just how spherical an election is. According to their research, the electron differs from a perfect sphere by only 1×10^-27 cm or, if you are a more visual person, .000000000000000000000000001 cm. To understand this in more practical terms, if the electron were blown up to the size of our solar system, it would differ from a perfect sphere by the width of a human hair! (Thanks to sciencedaily.com for the example.)

So, lovers of beauty and perfection, fear not – maybe mathematics in the real world isn’t that ugly after all.

If you are interested in reading more about this on sciencedaily.com, click here: http://www.sciencedaily.com/releases/2011/05/110525131707.htm

If you would like to read the official abstract for the paper, click here: http://www.nature.com/nature/journal/v473/n7348/full/nature10104.html