MAM2000 (Dimension/Cone)

Our central image depicts an ever-growing cone, or cornucopia, which expands not only in size, but in dimension.

• The 0-dimensional portion of the image consists of points displayed along a curve spiraling out from a center.

• As we reach the 1-d position, the curve itself comes into view as a 1-dimensional curve.

• Beginning at the 2-d position, the curve becomes the image of a 2-dimensional strip, which becomes wider and wider.

• When it reaches the 3-d postion, the strip is replaced by a conical shell, with circular cross-sections centered on the curve. But mathematics does not stop there.

• At the 4-d position, the figure should become a 4-dimensional object, with spherical cross-sections centered on the continuation of the curve. Such an image is difficult to portray on a flat poster, but it can be represented, at least partially, by computer simulation.

If you have a Java-capable browser, you can investigate one of the interactive versions of the central cone; or you can view some animations of the central cone that display predefined rotations and slicings of the cornucopia.

You can find technical information about the equations for the curve and the function describing the radius of the strip or the circles or the spheres.

If you want your own copy of the MAM2000 poster, you can order a copy of the poster from the MAA.

 Math Awareness Month 2000 Last modified: Mar 30, 2000 1:40:35 PM Comments to: thomas_banchoff@brown.edu Hosted by: The Math Forum