Posts Tagged ‘Euler’

Königsberg (Or how I much I love Google Maps)

April 23, 2008

Some of my students gave a presentation today on graph theory, and talked about the Bridges of Königsberg. Königsberg was founded in 1254 and is part of the Russian enclave Kaliningrad. And it shows up in math talks because of its bridges. As a brief background, the Pregal River runs through the city and splits in two; there’s also an island, so there are four different land masses. You can kind of see this in the following map from 1652 (which appears in almost any math talk on the subject): Click for the picture, and also for a cool satellite photo of Königsberg today (which I hid behind the jump because it takes a few seconds to load).

Beauty in Mathematics

December 10, 2007

Mathematicians often speak of a particular theorem or proof as being “beautiful”. Those of us who have seen beautiful mathematics know exactly what it means, but what if you’ve never seen beauty in mathematics before? Is it one of those “I know it when I see it” kinds of things? Paul Erdös thought so:

Why are numbers beautiful? It’s like asking why is Beethoven’s Ninth Symphony beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.

Ask your favorite mathematician (we all have one, don’t we?) what they find beautiful, and I’m sure you’ll get an immediate response. Read more (Warning: Long post.)