In honor of the new year, the OU Math Club blog has gotten a new look. Most of it is self explanatory, but you might be wondering about the image at the top. Maybe it will help to see the whole picture:
The header is an excerpt from this work of art by Don Relyea.
What is it? It is an artistic interpretation of Hilbert’s curve. First considered by Hilbert in 1891, it’s an early example of a fractal type construction in mathematics. It is defined as the limit of curves . The first few are given below:
The strange consequence is that there is the same number of points in a square as on just one edge of that same square! Strange but true. As you might remember from your discrete math class, even though the integers are a subset of the rational numbers, there are the same number elements in each set (ie. they have the same cardinality). This is another example of the same strange phenomenon.
Here is another example of Hilbert curve art by Don Relyea.