Umbilic torus

Umbilic Torus

The umbilic torus is a single-edged 3-dimensional figure created by Helaman Ferguson as a mathematical artwork. Ferguson created a 27-inch (69 centimeters) bronze sculpture, Umbilic Torus, and it is his most widely known piece of art. The lone edge goes three times around the ring before returning to the starting point. A cross section of the surface taken from an umbilic torus corresponds with a hypocycloid. The torus is defined by the following set of parametric equations.

$x = \sin u \left(7+\cos\left({u \over 3} - 2v\right) + 2\cos\left({u \over3} + v\right)\right)$

$y = \cos u \left(7 + \cos\left({u \over 3} - 2v\right) + 2\cos\left({u \over 3} + v\right)\right)$

$z = \sin\left({u \over 3} - 2v\right) + 2\sin \left({u \over 3} + v\right)$

$\mbox{for }-\pi \le u \le \pi,\quad -\pi \le v \le \pi \,$

In 2010, it was announced that Jim Simons had commissioned an Umbilic Torus sculpture to be constructed outside the Math and Physics buildings at Stony Brook University, in proximity to the Simons Center for Geometry and Physics. The torus will be made out of cast bronze, and will be mounted on a stainless steel column. The total weight of the sculpture will be 65 tonnes, and will have a height of 28 feet (8.5 m). The torus will have a diameter of 24 feet (7.3 m), the same diameter as the granite base. Various mathematical equations will be inscribed on the base. Installation should be complete by Summer of 2011.

See also

• Torus
• Möbius strip
• Mathematics and art

References

• Larson, Roland E., et al. Calculus. Ed. Charles Hartford. 6th ed. Boston: Houghton Mifflin Company, 1998.

External links

• Umbilic Torus