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5998 Alcala Park
San Diego, CA, 92110
United States


Satyan Devadoss, Professor of Mathematics, Professor of Computer Science, University of San Diego



ONe-Cut Helper

D. Johnston (Harvey Mudd), J. Lee (Boston), J. Warley (UMass, Amherst)

The Fold-and-Cut Theorem allows any polygon to be cut from a single sheet of paper by folding it flat and making a single straight complete cut. This interactive visualization displays how the polygon is folded along its straight skeleton and some perpendiculars, endowed with mountain and valley information, enabling the boundary of the polygon to fall on a line.


D. Dimas (Amazon), Y X. Hong (Pomona)

This visualization shows the star unfolding for a box, given a source point on the purple face. Cutting along the black lines and folding into a box will identify all eight black copies of the source point, whose Voronoi diagram is given in red.  Use the sliders below to change the relative dimensions of the box, and click and drag the white dot to change the source point location on the opposite purple face.

GKZ Associahedron Realizer

D. Johnston (Harvey Mudd), J. Lee (Boston), J. Warley (UMass, Amherst)

Given a convex hexagon and a triangulation of it, each vertex can be assigned an area vector. By the Gelfand-Kapranov-Zelevinsky theory on secondary polytopes, taking the convex hull of these coordinates results in a geometric realization of the associahedron. As one deforms the underlying hexagon, this visualization shows the associahedron also continuously deform.

Scissors congruence

Dima Smirnov (MIT), Zivvy Epstein (MIT Media Labs)

This is an interactive demonstration of the Wallace-Bolyai-Gerwien theorem, algorithmically showing that any simple polygon can be cut into finite pieces and rearranged to form any other simple polygon of equal area.

2018 Popular Science + NSF Visualization of the Year Award !


Hayley Brooks (Williams), Kaison Tanabe (Williams)

This graphic showcases the trajectories of 15,600 Williams alum.  The left side of the circle is broken into different categories of majors, and the right side into categories of careers, where each alum has an arc going from left to the right, from their choice of major to their resulting career.  

There are two stories in this graphic.  First, there is a strong correlation between biology and chemistry majors with the health and medical field. And second, each career receives a fair percentage of students from every major grouping.  In other words, your major does not determine your career.