Xah Lee, 2007-01-09
above: A screenshot of a location in Second Life.
This place is called The Future (111,70,239)↗. It is a place primarily built by Henry Segerman↗ (aka Seifert Surface).
The metal ball above the bridge is made of 4 nested spheres, rotating on different axes. Behind the sphere is a tower of octahedrons↗. (A octahedron is a regular solid, having 8 faces, each face is a equilateral triangle. (it's like two pyramids with their bases glued together)) On the right is a geodesic dome↗ made of glass. Inside is a garden with mathematical sculptures.
above: The middle sculpture is a double spiral. This sculpture is based on the Equiangular Spiral. Most spirals seen in nature's growths, for example, plants and seashells, are equiangular spirals. (See Seashells photo gallery.)
Equiangular spiral is equiangular because if you draw a line passing its center, the the angle of intersection of the line with the spiral curve will the same, regarless where or the direction of your line. (See: Equiangular Spiral (math detail))
above: This colorful spiral sculpture is a model of the Hopf bundle↗. You will need to have a phd in math to understand this one. For mere mortals, suffice it to say it is twisty.
Here's another photo giving a overview of the sculpture: hopf_bundle_2.jpg. Standing in front is a geisha↗ in traditional Japanese attire the kimono↗.
above: This surface is called hyperbolic-paraboloid, made my yours truely Xah Toll. It is a surface made entirely of (straight) lines. From this close up, one can see how this surface is curved, yet straight!
It is called hyperbolic-paraboloid because the horizontal cross sections are hyperbolas and diagonal vertical cross-sections are parabolas. This structure is commonly used as roofs for modern pavillions↗.
You can easily make a hyperbolic-paraboloid. Imagine a cube. Mark the top two opposite corners. These two corners will be the top two vertexes of the surface you see in the above image. Now, also mark the two opposite corners at the bottom of the cube. Draw diagonal lines from these corners. (look at the figure above. Your diagonal lines will be the edges of the surface) Mark regular intervals on these diagonal lines. Now, connect lines from one diagonal to the other side. You are all done!
For more info about this surface, see Paraboloid↗. For a Java applet that does live rotation of hyperbolic-paraboloid, see hyperbolic-paraboloid.
above: The girl Eureka of the Japanese animation Eureka Seven↗. (The creator of this avatar is Yamiki Ayakashi)
The background blueish strip is the Moebius strip↗. Moebius strip is a example of a surface that has only one side. (If you are a ant crawling on the strip, you'll end up on the other side without crossing any edge.) The rim of this strip, is a Trefoil knot↗. Tie a overhand knot↗, then connect the lose ends, and you have it!
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Page created: 2007-01. © 2007 by Xah Lee.