About the Central Image
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.