"Mitered Fractal Tree I," by Koos Verhoeff and Anton Bakker

(This sculpture was awarded Best of Show at the Bridges conference.) " Mitered Fractal Tree (designed late 1980s, first executed in wood), constructed from a beam with a rectangular cross section in the ratio 1:√2....[More]

"Mitered Fractal Tree I," by Koos Verhoeff and Anton Bakker

(This sculpture was awarded Best of Show at the Bridges conference.) "Mitered Fractal Tree (designed late 1980s, first executed in wood), constructed from a beam with a rectangular cross section in the ratio 1:√2. When this beam is cut at 45 degrees, the result is a square cut face. When this beam is cut twice at 45 degrees, where the cuts are perpendicular, the result is a "roof" consisting of two smaller square panels. On this roof, two smaller copies of the entire tree are grown. No two branches point in the same direction. The result is an awe inspiring organic structure that is both highly structured and chaotic."—Koos Verhoeff  [Less] [Link to this slide]

"Loopy Love," by Barry Cipra

"The story, a dialogue presenting both sides (or is there only one side?) of a twisting love–hate relationship between two characters named Daniel and Danielle, was letterpress printed by Red Dragonfly Press in Red Wing, Minn., on Fabriano paper using the font FF Quadraat....[More]

"Loopy Love," by Barry Cipra

"The story, a dialogue presenting both sides (or is there only one side?) of a twisting love–hate relationship between two characters named Daniel and Danielle, was letterpress printed by Red Dragonfly Press in Red Wing, Minn., on Fabriano paper using the font FF Quadraat. Assembled by hand with tape, the resulting scrollable sculpture retains its shape yet remains flexible, so that the reader can easily read the story without ever having to turn the page. Viewers are invited to pick it up, play with the paper, and read the story from start to finish—except there is no start nor any finish!"—Barry Cipra  [Less] [Link to this slide]

"Simple as the Number Nine," by Kerry Mitchell

"This image presents a linear combination of four chaotic orbits of boundary points of the Mandelbrot set [one of the most famous fractals]....[More]

"Simple as the Number Nine," by Kerry Mitchell

"This image presents a linear combination of four chaotic orbits of boundary points of the Mandelbrot set [one of the most famous fractals]. The individual orbits were weighted so as to approximate the first derivative of the orbit. Logarithmic scaling was used to convert the frequency of pixel visitation to a color. The title of the image was taken from a line in the song, "Burning Bush," by Earth, Wind and Fire."— Kerry Mitchell  [Less] [Link to this slide]

"Pythagorean Proof," by Donna Loraine Contractor

This tapestry shows a proof of a special case of the  Pythagorean theorem . The blue and gray squares touching the short sides of the multicolored center triangle can be rearranged to create the square touching the triangle's long side....[More]

"Pythagorean Proof," by Donna Loraine Contractor

This tapestry shows a proof of a special case of the Pythagorean theorem. The blue and gray squares touching the short sides of the multicolored center triangle can be rearranged to create the square touching the triangle's long side.  [Less] [Link to this slide]

"Dual Half 120- and 600-Cells," by Henry Segerman

Segerman used 3-D printing to create these representations of regular four-dimensional polytopes, the four-dimensional analogues of three-dimensional polyhedrons—geometric solids with polygons as faces....[More]

"Dual Half 120- and 600-Cells," by Henry Segerman

Segerman used 3-D printing to create these representations of regular four-dimensional polytopes, the four-dimensional analogues of three-dimensional polyhedrons—geometric solids with polygons as faces. The left and right objects are "dual" to each other, meaning the vertices of one correspond to the faces of the other. The center object is the combination of the two dual objects. This display won the "Best Use of Mathematics" award at the Bridges conference.  [Less] [Link to this slide]

"Untiled Faces," by Nathan Selikoff

(This interactive exhibit won the "Most Innovative" award at the Bridges conference.)

"Untiled Faces is an interactive sculpture that mixes a chaotic dynamical system with its "meta" representation, allowing the viewer to explore the four-dimensional parameter space by moving a series of levers....[More]

"Untiled Faces," by Nathan Selikoff

(This interactive exhibit won the "Most Innovative" award at the Bridges conference.)

"Untiled Faces is an interactive sculpture that mixes a chaotic dynamical system with its "meta" representation, allowing the viewer to explore the four-dimensional parameter space by moving a series of levers. The left pane of Untiled Faces shows a 32 by 32 grid of images. As the left lever is moved, a red square over one of the small images moves, updating two variables that affect the center and right panes. The right pane shows the selected image from the left pane at a larger size. The right lever moves a small red target within this image, updating another two variables that affect the center pane. The center pane shows a chaotic attractor, whose four coefficients are taken from the positions of the left and right levers. The center lever adjusts the virtual camera viewing this strange attractor. Thus, all three images are linked, and in a somewhat mysterious way show the relationship between a strange attractor and its Lyapunov exponent."—Nathan Selikoff   [Less] [Link to this slide]

"NYC MetroCard PHIZZ unit Buckyball," by Joy Hsiao

"Brooklyn Technical High School has over 5,000 students. This spring my Origami Club collected and recycled student MetroCards with the help of the Green Leaf Recycling Club at our school....[More]

"NYC MetroCard PHIZZ unit Buckyball," by Joy Hsiao

"Brooklyn Technical High School has over 5,000 students. This spring my Origami Club collected and recycled student MetroCards with the help of the Green Leaf Recycling Club at our school. This buckyball is a product of this collaboration. It unites my love for mathematics and origami. The large student body certainly helped make it possible to acquire all of the necessary construction materials. We actually could obtain 90 green-colored MetroCards in one day! The technical aspect of our school is also reflected in the design of the truncated icosahedron."—Joy Hsiao  [Less] [Link to this slide]

"Meander #6," by David Chappell

Inspired by a mathematical formula geologists use to describe river bends, called a sine-generated curve, Chappell plays with the parameters to create the curves in his Meander series....[More]

"Meander #6," by David Chappell

Inspired by a mathematical formula geologists use to describe river bends, called a sine-generated curve, Chappell plays with the parameters to create the curves in his Meander series. Although they do not look like actual rivers, Chappell feels that the images still retain a sense of organic flow. To learn more about these patterns and explore them using an applet Chappell created, click here.  [Less] [Link to this slide]

"Umbilic Torus," by Daniel Whalen

Whalen's work is inspired by pixels. The LEGOS here are a kind of three-dimensional version of them. The form created is an  umbilic torus , first created by Helaman Ferguson....[More]

"Umbilic Torus," by Daniel Whalen

Whalen's work is inspired by pixels. The LEGOS here are a kind of three-dimensional version of them. The form created is an umbilic torus, first created by Helaman Ferguson. It has only one edge that wraps around the torus three times.  [Less] [Link to this slide]

"Spectra," by Maya Freelon Asante

"I use 'bleeding' tissue paper, water and archival pulp substrate to capture the chaotic movement of water and color blending on a spinning surface....[More]

"Spectra," by Maya Freelon Asante

"I use 'bleeding' tissue paper, water and archival pulp substrate to capture the chaotic movement of water and color blending on a spinning surface. By mounting my project on a potter's wheel, I'm able to stand above my work, and while in motion use the wet tissue like a brush. As the wheel turns at different velocities and intervals, the ink spreads and mixes with other colors while simultaneously the intricate stains are absorbed into the pulp substrate permanently. The distribution of ink undergoing circular motion evolves in such a way that the gradient of the paint density changes with time and regions such as attractors, islands or basins appear. The colors then escape to infinity forming chaos artwork."—Maya Freelon Asante  [Less] [Link to this slide]

"Klein Sangaku," by Jean Constant

Sangaku, Japanese geometry problems, used to be presented as offerings at shrines. This is a depiction of the following problem: "In a square PQRS, there are two circles touching SP and the incircle of the square, where one of which touches PQ and the other touches RS....[More]

"Klein Sangaku," by Jean Constant

Sangaku, Japanese geometry problems, used to be presented as offerings at shrines. This is a depiction of the following problem: "In a square PQRS, there are two circles touching SP and the incircle of the square, where one of which touches PQ and the other touches RS. Let A be the point of tangency of QR and the incircle and let the tangents of the two small circles through A intersect the segment SP at B and C. Given the inradius of the square, find the inradius of the circle in the triangle ABC. The answer is that the medium circle is also half the size of the largest circle."—Jean Constant  [Less] [Link to this slide]

"Gentle Earthquake," by Erik Demaine and Martin Demaine

"The sculpture is a modular combination of nine interacting pieces. Each piece is folded by hand from a circle of paper, using a compass to score the creases and cut out a central hole....[More]

"Gentle Earthquake," by Erik Demaine and Martin Demaine

"The sculpture is a modular combination of nine interacting pieces. Each piece is folded by hand from a circle of paper, using a compass to score the creases and cut out a central hole. This transformation of flat paper into swirling surfaces creates sculpture that feels alive. Paper folds itself into a natural equilibrium form depending on its creases. These equilibria are poorly understood, especially for curved creases. We are exploring what shapes are possible in this genre of self-folding origami, with applications to deployable structures, manufacturing and self-assembly."—Erik Demaine and Martin Demaine  [Less] [Link to this slide]

"The Platonic Solids," by Bob Rollings

Bob Rollings was a cabinetmaker who turned to geometry in retirement. This is a set of the Platonic solids, the five three-dimensional forms whose faces are congruent regular polygons....[More]

"The Platonic Solids," by Bob Rollings

Bob Rollings was a cabinetmaker who turned to geometry in retirement. This is a set of the Platonic solids, the five three-dimensional forms whose faces are congruent regular polygons. The Platonic solids won the "Best Craftsmanship" award at the Bridges conference.  [Less] [Link to this slide]