## Monday, February 28, 2011

## Wednesday, February 23, 2011

"This image depicts the interaction of nine plane waves—expanding sets of ripples, like the waves you would see if you simultaneously dropped nine stones into a still pond. The pattern is called a quasicrystal because it has an ordered structure, but the structure never repeats exactly. The waves produced by dropping four or more stones into a pond always form a quasicrystal."

## Thursday, February 17, 2011

Hyperbolic geometry differs greatly from what we are used to in that the longest path between two points is a straight line. You can think of hyperbolic space like Euclidean space, but with a different way of defining the distance between two points (we call this a metric). Above is the hyperbolic equivalent of an icosidodecahedron. Check out more hyperbolic tilings here.

## Sunday, February 13, 2011

## Monday, February 7, 2011

Above are hypocycloids, curves produced by fixing a point on the circumference of a small circle of radius b, rolling around the inside of a large circle of radius a > b. If a/b is rational, i.e. it can be expressed as a fraction, the path will return to it's starting point. If the ratio is irrational, the path will never touch the same spot on the circumference of the larger circle more than once, and images such as the ones above result.

## Tuesday, February 1, 2011

Relativity predicts that gravity warps the shape of space and time so that light will no longer move along a straight path. One of the earliest confirmations of the theory was during a total eclipse which allowed us to see a star that wasn't quite in the right place. The sun's gravitational force bent the light rays so that the star appeared about an inch away from where it actually was.

In the image above, the galaxy in the center bends the light waves coming off of the object behind it so that we see 4 different images of the same object. This is called gravitational lensing.

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