Klein’s Quartic Curve

Klein's Quartic Curve

This is Klein’s Quartic Curve, by Greg Egan.

The quartic curve is formed by Klein’s quartic equation - u3v+v3w+w3u=0. Greg has had a very nice (though complicated) explanation of how he constructed the quartic curve. You can read it here.

I am most unfortunately, unable to tell you further, as the explanation can be quite confusing too (even when I use UVW in my work). However, I do like this image, despite my stunted algebra understanding. It’s a concept of movement - a 4-dimensional image and contstant returns to normalcy that I like. No matter how you turn, it always returns to normal.

Now, off I am to find (or write) a software that generates these wonderful algebraic images.

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Published:
November 26, 2007 / 8:14 pm
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Art in Math
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