Edwin Catmull, Co-Founder and President of Pixar Animation Studios, the creators of the computer-animated giants Toy Story and A Bug's Life and of the new release Monsters, Inc., and winner of an Academy Award of Merit, grew up planning to be an animator. Or a physicist. Or a computer scientist. Ed graciously took time to talk with Math Horizons about his work in the early days of and on the frontier of computer graphics, and the mathematics behind his movies.
How Many Women Mathematicians Can You Name?
Until my last semester as an undergraduate student in 1964, my answer to the question of the title would have been "One: Emmy Noether, the German algebraist." That semester a woman mathematician, Yvonne Choquet-Bruhat, was a visiting professor at my undergraduate institution, Cornell, so my list increased to two! If you restrict your answer to those women who were active by the middle of the twentieth century, you are unlikely to be able to name more than seven: Hypatia, Gabrielle-Emilie Le Tonnelier de Breteuil, Marquise du Chatelet, Maria Gaetana Agnesi, Sophie Germain, Mary Somerville, Sofia Kovalevskaia, and Emmy Noether.
If Pascal Had a Computer
The year is 1654. The young French scientist and mathematician Blaise Pascal has just been presented with a deceptively simple mathematical question, a question whose solution would in short time mark the birth of the theory of probability.
Sums of Squares of Distances
Given n fixed points in a plane, a point moving in the plane of these points in such a way that the sum of the squares of the distances from the points is constant traces out a circle whose center is at the centroid of the fixed points.
Things Aren't Always What They Seem
Careful statistical analysis reveals that some well-known truths are in fact in doubt or even false.
Another Verse, Changed from the First
"The stairway tempts with unseen limits, the ice forbids and beckons you, and sideways your foot glides into strange and sunless spaces."
A Mathematical Life
Entering college I was fascinated by virtually every subject. I ended up a mathematics major because of a fifteen minute conversation.
Packing Rectangles with the L and P Pentominoes
We wish to determine which pentominoes can pack a rectangle, and the set of packable rectangles for each of them.
Problem Section
S-59.
Proposed by Robin Hur, Albuquerque, NM. Let S be the set of all circles in a rectangular coordinate system whose centers are on the line y=0 and which pass through the fixed point A(0,a). Tangents are drawn from the fixed point B(0,b) with b>a>0 to the circles S. Determine the locus of the points of tangency.
S-60.
Proposed by Arpad Benyi, University of Kansas and Ioan Casu, West University of Timisoara, Romania. Solve the equation ay^3 + 3y^2 - 4 = 0 where a is a given constant in [0,1].
S-61.
Proposed by E. M. Kaye, Vancouver, BC. Eliminate x, y, z, w from the set of equations x^a=yzw, y^b=zwx, z^c=wxy, w^d=xyz.
The Final Exam: Listen up!
What do David Letterman, God, and Math Horizons all have in common? We're all purveyors (or, in our case, would-be purveyors) of top-ten lists! We would love to break onto the scene with our own top-ten list of top-ten lists, were we to have one. Unfortunately, we have some good top-seven lists, and a few top-four lists, but we always seem to come up short: top ten groups of order four, top ten mathematicians turned movie stars, top ten digits in base seven.
