Selected works by Helaman Ferguson
Installation: Stony Brook University on the plaza of the Simons Center for Geometry and Physics
Size: Monumental--28 feet high on base; bronze torus is 24 feet in diameter.
Weight: 65 tons
Materials: Torus is Silicon Bronze with antique patina; base is Lake Superior Green Granite
Installation: University of California, Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley, California
Dimensions: 60" x 54" x 54"
Weight: 3,000 lbs
Materials: White Carrara Marble, Virginia Albemarle Serpentine
Availability: for a Silicon bronze casting of the original, three months
Installed at the Mathematical Sciences Research Institute at Berkeley, the Eight Fold Way overlooks the San Francisco Bay from the Berleley hills. A black serpentine colummn, rising from the center of a black circular tiling, grabs a white polished Carrara Marble tetrahedron- as though catching a falling star.
The tiling represents hyperbolic space projected into a circular disk. Water jets blasting at 55,000 pounds per square inch cut 232 stone blocks into 232 unique seven-sided tiles within an accuracy of one thousandth of an inch. The size of the heptagonal tiles diminishes as you near the edge of the disk, to an eventual accretion. A select number of these tiles, darker than the others, make up the fundamental domain- that set of tiles which cover the tetrahedron.
Ridges and grooves wind over the gleaming white tetrahedral form, quietly showing how to map the fundamental domain onto the tetrahedron. Run a finger along any groove or ridge, alternating left and right turns at each corner, and in eight pivots, you'll return to your starting point.
Dimensions: 27" x 27" x 9" (enveloping torus)
Weight: 100 lbs
Surface: surface filling hilbert-peano curve
Materials: Silicon bronze with antique verde patina
1/12 The Mathematical Association of America
2/12 Syracuse University, Department of Mathematics, Syracuse, New York
3/12 The University of California at San Francisco, Medical School Library, Parnassus, San Francisco, California
4/12 Mitchell and Robin Melamed, Chicago, Illinois;
5/12 David and Karen Stoutemeyer, Soft Warehouse, Honolulu, Hawaii;
6/12 Roland E. Larson, Larson Texts, Inc., Erie, Pennsylvania;
7/12 Ron Graham and Fan Chung, San Diego, California;
8/12 Beckman Institute, University of Illinois, Urbana-Champaign;
9/12 Dean Morehouse, MTM, Pennsylvania Avenue, Upper Marlboro, Maryland
10/12 private collection
11/12 private collection
12/12 private collection, Zeist, The Netherlands
The form of Umbilic Torus NC is a continuous donut-shaped surface patterned with a space-filling curve. It stands as a monument to the timelessness of human creativity as though it had just been unearthed with painstaking care from a Chinese tomb or an Egyptian pyramid--its Faience-tinted bronze corroded by centuries of silent waiting. The space filling curve, mysterious as the Chinese calligraphic script or Egyptian hieroglyphics-- flows over the surface, defining it, by beginning at any point and meticulously returning to that point after traversing every inch of its area. The form of the space filling curve is universal, known from the earliest architecture and ornament. The angles of the space filling curve play a harmonious counterpoint to the torus, or ring, which has always signified unbroken love.
Provenance: This Jaime Escalante Award was commissioned by David Bilotti of Arco, 40 were made with two types of bases and awarded to outstanding California High School Mathematics teachers, one was stolen from the Los Angeles School District offices. Arco was bought out by BP and the award fell through the cracks.
Collections: Lots of outstanding high school teachers; Professor William Summerfield, Mathematics, University of Newcastle, New South Wales, Australia
Nature of Edition: indefinite
Dimensions: 4 1/2" x 5" x 2 1/4"
Material:silicon bronze, natural bronze patina, negro monterray stone base
Special Engraving: surface filling hilbert-peano curve
Weight: 1 lb
Related Sculpture: Ariadne Torus
Installation: National Council of Teachers of Mathematics, Reston, Virginia
Dimensions: 18" x 24" x 12"
Weight: 100 lbs
Materials: White Carrara Marble
Natural Number Bridge crosses divisions between the numerical world and nature. Among other numerical patterns, the Fibbonacci Sequence plays out on the surface of this sculpture through the riges, horns, and textures to illustrate the natural numbers. By tracing the ridges on the sculpture, and summing actions, the viewer can derive the complete Fibbonacci Sequence.
Installed at the National Council of Teachers of Mathematics, as a gift from the Mathematical Association of America, this piece celebrates the thrill of learning by discovery, and urges mathematics teachers to connect the abstract beauty of mathematics with nature.
Installation: Brekenridge, Colorado, USA, 13-27 January 1999
Dimensions: 14' x 10' x 10'
Weight: 30-35 lbs / cubic foot (~20 Tons)
Materials: Artificial Snow (Psudomonas Syringae)
The images shown here were taken by Claire Ferguson on site in Breckenridge, Colorado in January 19-24, 1999 at the International Snow Sculpture Championships. This piece was entitled "Invisible Handshake" because it is the negative space of two hands just before the two hands clasp. Two such wye forms about to couple succinctly describes the topology of the Costa surface itself and suggests the differential geometry of negative Gaussian curvature. I carved this work with the assistance of Stan Wagon, Dan Schwalbe, Tomas Nemeth, and posthumously Alfred Gray. We began with a 12'x10'x10' 20 ton block of dense artificial snow; we were given four days to complete it, no power tools were allowed. Cf., Barry Cipra, "Minimal Till It Melts", SIAM News, March 1999, two photos, page 20; "Melting Minimalist", SCIENCE, volume 283, 5 February 1999, one photo, page 787; also, forthcoming articles in MiER and the Mathematical Intelligencer.
I choose this negative Gaussian curvature geometric form specifically because of the material properties of snow. Snow with its fair compressive strength and poor tensile strength is a caricature of stone. But negative Gaussian curvature, even in snow, presents a fabric of saddle points everywhere. Each point of the surface is the keystone of a pair of principle arches. There were 14 other snow sculptures completed at the Breckenridge affair; a week later they all completely imploded in the heat wave. Our negative Gaussian curvature snow carving stood, retained its structure, sublimed, thinned, gracile.
Installation: University of St. Thomas, St. Paul, Minnesota, USA
Dimensions: 9' x 7' x 9' (standing aspect) 21' x 20' (plaza tiling)
Weight: 9 tons
Materials: Red and black granite, quarried and cut by Cold Spring Granite, MN.
Helaman Ferguson sculpted Four Canoes as the keystone outdoor piece located in the quadrangle bordered by two new "wet" and "dry" science and engineering buildings at the University of St. Thomas in St. Paul, Minnesota.
Installed in September 1997, this granite sculpture includes a plaza of alternating red and black hexagonal tiles, two hexagonal prisms rising from the plaza, and two three dimensional non-orientable double cross cap toroidal forms resting on the prisms.
Six feet in diameter, the toroidal forms weigh three tons each, and stand linked upon the prisms, as if to span the gap between. Each toroid can be thought of as two canoes sewn together and bent round. Translated past and rotated through one another, these two double canoe Klein bottle forms– solid granite toroids with double cross-caps, couple inextricably– mysteriously.
Twenty-eight serrated-edge hexagons, each three feet in diameter, tile the plaza. Whether or not the double canoe hexagonal tiles cover the plane in an aperiodic tiling in the sense of Penrose, is an unsolved problem, this intensifies the mystery of the sculpture.
Cold Spring Granite quarried and cut the granite.
Installation of Four Canoes occured in September 1997. The piece presented a tremendous technical challenge: how to marry the two Klein Bottles. Moving a three ton object, which has a built-in tendency to roll, is no trivial matter.
Collection: two sets with the Maryland Science Center, Inner Harbor, Baltimore, Maryland
Nature of Edition: direct casting from prepared waxes
Availability: immediately, if that one is gone, then twelve weeks
Material:Silicon bronze with school-kid patina, the 28 pieces are arranged in a circle on an oak turntable
Dimensions: 6" x 32" x 32"
Weight: 120 lbs
School-kid patina I hear you cry? What is that? I brought the 28 double tori up for a summer-long tryout to the Maryland Science Center and 40,000 school kids were encouraged to put their hands all over the pieces. It didn't take any encouragement at all. Now this regular isogeny is as familiar to those little tykes as the phases of the moon.
A regular isogeny, homotopy, or smooth deformation of a double torus in linked form to and unlinked form. This piece is a theorem and proof, in fact, contains the germ of the proof for the classification of surfaces by handles and cross-caps.