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655:. The torus is made out of cast bronze, and is mounted on a stainless steel column. The total weight of the sculpture is 65 tonnes, and has a height of 28 feet (8.5 m). The torus has a diameter of 24 feet (7.3 m), the same diameter as the granite base. Various mathematical formulas defining the torus are inscribed on the base. Installation was completed in September, 2012.
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based on the shape in 1989, this had a triangular cross-section rather than a deltoid of a true
Umbilic bracelet. This appeared on the cover of Geometric Differentiation by
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is a single-edged 3-dimensional shape. The lone edge goes three times around the ring before returning to the starting point. The shape also has a single external face. A
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but with the ends rotated 120 degrees before connecting them. This gave an endless corridor in which after three passes one came back to the point where one started.
168:. The equivalence classes of such cubics form a three-dimensional real projective space and the subset of parabolic forms define a surface – the umbilic torus.
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had commissioned an
Umbilic Torus sculpture to be constructed outside the Math and Physics buildings at
420:{\displaystyle y=\cos u\left(7+\cos \left({u \over 3}-2v\right)+2\cos \left({u \over 3}+v\right)\right)}
296:{\displaystyle x=\sin u\left(7+\cos \left({u \over 3}-2v\right)+2\cos \left({u \over 3}+v\right)\right)}
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519:{\displaystyle z=\sin \left({u \over 3}-2v\right)+2\sin \left({u \over 3}+v\right)}
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588:{\displaystyle {\text{for }}-\pi \leq u\leq \pi ,\quad -\pi \leq v\leq \pi }
743:. Ed. Charles Hartford. 6th ed. Boston: Houghton Mifflin Company, 1998.
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Helaman
Ferguson, "Two Theorems, Two Sculptures, Two Posters",
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Analog
Science-Fiction, November 1949 at The Internet Archive
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720:(2nd ed.), Cambridge University Press, p. 350,
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has created a 27-inch (69 centimeters) bronze sculpture,
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The umbilic torus occurs in the mathematical subject of
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161:{\displaystyle ax^{3}+3bx^{2}y+3cxy^{2}+dy^{3}}
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172:named this set the umbilic bracelet in 1976.
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739:Larson, Roland E., et al.
785:Discussion of Robinson's
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803:Mathematics and culture
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641:Umbilic Torus
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690:Möbius strip
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701:References
645:Jim Simons
583:π
580:≤
574:≤
571:π
568:−
561:π
558:≤
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549:π
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542:for
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797:Category
787:Eternity
741:Calculus
679:See also
612:Eternity
32:Eternity
62:deltoid
724:
685:Torus
722:ISBN
48:The
667:by
629:at
485:sin
444:sin
381:cos
340:cos
320:cos
257:cos
216:cos
196:sin
52:or
34:by
799::
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20:)
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