Tuesday, January 24, 2006
Shadowing
A shadow is a projection from higher to lower dimensions. Here an octahedron is projected to its shadow.
Drawing by Justing Baker
Mathing
Mathematics is the language of structure and of course 3 and 4D objects have lots of structure.
Symmetry...
Drawing by Michael Matthews
Drawing
Drawing helps you see. It does not matter if you draw well, the visual benefit is the same. Go to this web page ; read page 1, draw the figures on page 1. Second try to draw the 4 figures on page 3. Y
Picture by Caleb Gatlin showing octagonal view of hypercube and the 24 cell constructed a connections between centers of faces.
GSPing
Geometer’s Sketchpad is a 2D program. As such one would think that it does not do 3D well. But we have worked out ways to make this a great 3D program.
The Paideia 3D and 4D technique. This was mostly
Parametric surfaces
Graphing
Understand graphing by seeing 2D graphs in 3D ones and then 3D graphs in 4D ones.
1D line in 2D space
1D line in 3D space
2D surface in 3D space
1D line in 3D space
2D surface in 3D space
Graphs in 4D.
The parts of the Zome system. The bottom pictures are a cloeup five of a 720 cell on the left;
Modeling
Zome tools is one of the most effective ways to create models. The models we create are 3D shadows of 4D objects as well as models of 3D shapes.
Picture by Michael Matthews showing the folding of 4 cubes into a portion of a hypercube.
Folding
Paper represents a flat 2D surface. A fold takes it into the third dimension. Analogously we can imagine a fold from 3 to 4 dimensions as illustrated in the picture.
Here is a picture of topological
Welcome to the 4D web page
We wish to do the impossible, to visualize four dimensional object. Each page below gives a technique to help you visualize 4D objets. Visualization is more effective when you change dimensions.
