The figure shows the relation between a tetrahedron and a cube inscribed in a sphere. The diameter of the sphere has length AB, and you can drag the endpoints A and B to change the size of the sphere. The side of the cube has length BD, and the side of the tetrahedron has length AD. The cube is drawn with red edges while the tetrahedron is shaded light blue and drawn with blue edges. The center of the sphere is the red dot, and you can drag it to move the sphere around. The point E can be dragged anywhere on the surface of the sphere. The point F has to be at length BD from E on the surface of the sphere, and so it drags along a certain circle on the sphere. The rest of the cube and tetrahedron are then determined.

Note that you can't drag a point off the diagram, but frequently parts of the diagram will be moved off as you drag other points around. But if you type r or the space key while the cursor is over the diagram, then the diagram will be reset to its original configuration.

You can also lift the figure off the page into a separate window. When you type u or return the figure is moved to its own window. Typing d or return while the cursor is over the original window will return the diagram to the page. Note that you can resize the floating window to make the diagram larger.

*** If you can read this, you're only seeing an image, not the real java applet! ***

Above you see an icosahedron, that is, a regular 20-sided solid, constructed according to Euclid's construction in proposition XIII.16.

For more information on Euclid, see his page among the History of Mathematics pages.

References to Euclid's Elements on the web Including references to Perseus, the Visual Math Institute, and others.

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Copyright © 1996, 1997. (June, 1997.)
D.E.Joyce
Clark University

These pages are located at http://aleph0.clarku.edu/~djoyce/java/elements/elements.html.