glome?

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glome?

Postby papernuke » Mon Jul 24, 2006 1:23 am

In the website where alkaline puts most of the information, it says that when a glome passess through the 3rd dimension, it just looks like a sphere that is shrinking and growing. But shouldn't it look like a lot of spheres attatched to eachothers somehow? Because a tesseract is cubes put together, wouldn't the glome look like that but with spheres in the 3d world?
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Postby Nick » Mon Jul 24, 2006 1:33 am

No; a tetracube is actually just a cube when inserted to a 3d world; its only becomes a bunch of cubes attached to each other when the tetracube is inserted at an angle. Since a glome is equivalent to a sphere, there is no angle that the sphere can be dipped into 3d.
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Postby pat » Wed Jul 26, 2006 8:07 pm

A solid tetracube would be a solid shape intersected with 3-d. The tessaract is a projection of a tetracube down to 3-d... it is not the intersection of a tetracube and 3-d.

Consider the 2-d analogy. If you took a 3-cube and intersected it with a plane, you would get, depending on how exactly you touched it to the plane, a point, a line, a triangle, a quadrilateral, a pentalateral, or a hexalateral. None of them would have lines crossing in the middle. They'd either be just the solid shape or just the outline of the shape (depending on whether your cube were solid).

On the other hand, there are many projections of 3-cubes down to 2-d that have intersecting lines and all manner of perspectives.
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Postby moonlord » Thu Jul 27, 2006 9:03 am

I always thought tesseract was just another name for the 4-cube...
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Postby Keiji » Thu Jul 27, 2006 2:22 pm

It is.
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Postby pat » Thu Jul 27, 2006 2:58 pm

I always thought the tesseract was another name for a projection of a 4-cube. But, I can't figure out where I got that impression. My apologies.

Still, the point holds... the intersection of a tetracube with 3-d is very different from the projection of a tetracube down to 3-d.
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