Robert Inventor

Prev Explore four and higher dimensional geometry Next

You can make anaglyphs, and stereoscopic pairs of higher dimensional shapes as well as three dimensional projections.

Hyper cube in hyper perspective

Click to show an anaglyph which you can turn and see from other angles - needs a VRML plug in installed such as the Cortona VRML client.

Optimised for a distance to the screen of twenty times the eye separation. For more anaglyphs to show how the hypercube is constructed, see my tesseracts page.

This looks like a normal anaglyph - but in Virtual flower, you can also turn it around in the fourth dimension, leave it spinning, and watch as the cube faces appear to deform and swap position as it turns. It's not really changing shape in 4D, only its 3D projection is changing.

For instance in the picture above, the cube that seems to be inside the other one is really exactly the same size, just further away in higher dimensional space. As you spin the shape, it will move towards you, so becoming larger in the 3D projection, and the outer cube will get smaller and change shape. The other cells that look like truncated pyramids are also cubes. As you spin it around each in turn will take its place as the outer cube in the picture.

Some people learn to visualise 4D space. Alicia Stott could do this - she invented the word polytope to describe higher dimensional figures, and discovered the six regular four dimensional geometrical shapes. She was an amateur mathematician in the sense that she had no higher mathematical training and discovered her results in a practical down to earth fashion by constructing models of the shapes.

She later collaborated with Harold Coxeter, a mathematician who helped revive modern geometry. See the introduction to his book Regular Polytopes,

Another person who could visualise 4D space was John Petrie, sone of Sir Flinders Petree, the Egyptologist. He could answer questions about four dimensional objects by visualising them He is the discoverer of the Petrie Polygon - see the introduction to Coxeter's book again

To read more about Virtual Flower, go on to:

Screen Saver

The program comes with a generous Free Test drive with all the features completely unlocked (start the test drive at any time):

Download Virtual Flower

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