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Sculpture Design and Models in Mathematical Geometry at University of California, Berkeley

Explore the innovative world of sculpture design linked to mathematical geometry at the University of California, Berkeley. Discover the intricate details of various sculptures, including the Hyperbolic Hexagon and Scherk Towers. Delve into the process of creating these unique pieces using modular geometry and precision techniques. Immerse yourself in the fusion of art and mathematics as showcased by talented artists and designers.

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Sculpture Design and Models in Mathematical Geometry at University of California, Berkeley

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  1. “d m m d i” 2015 “I made the data” Carlo H. Séquin University of California, Berkeley

  2. Basel, Switzerland

  3. Logarithmic Spiral Jakob Bernoulli (1654‒1705)

  4. Leonhard Euler (1707‒1783) Imaginary Numbers

  5. Descriptive Geometry

  6. Who Am I ? I don’t like “BIG DATA”! I am more of an engineer than a statistician. I like small, relevant info – under my control. Then I let the computer generate the needed detailed data derived from my specifications. I like to keep things simple and concise.

  7. Keep It Simple, Stupid!applied to microcomputersReduced Instruction Set Computers

  8. Geometry in every assignment . . . CCD TV Camera (1973) Soda Hall (1992) RISC 1 MicroChip (1982) Octa-Gear (2000)

  9. Recent Designs and Models Hilbert-Cube_3D Double-Boy Klein-bottle Pax Mundi Evolving Trefoil

  10. Brent Collins (1997) “Hyperbolic Hexagon II”

  11. Brent Collins: Stacked Saddles All photos by Phillip Geller

  12. The Math in Collins’ Sculptures • Collins works with rulers and compasses;any math in his early work is intuitive. • He is inspired by nature,e.g. soap films (= minimal area surfaces). • Prof. George Francis:“Connection to math. Minimal Surfaces!”

  13. Scherk’s 2nd Minimal Surface (1834) • The central part of this is a “Scherk Tower.”

  14. Generalizing the “Scherk Tower” Normal “biped” saddles Generalization to higher-order saddles(“Monkey saddle”) “Scherk Tower”

  15. Closing the Loop straight or twisted “Scherk Tower” “Scherk-Collins Toroids”

  16. Brent Collins: Hyperbolic Hexagon Six balanced saddles in a circular ring. Inspired by the shape of a soap filmsuspended in a wire frame. = Deformed “Scherk Tower”.

  17. Sculpture Generator 1, GUI

  18. Shapes from Sculpture Generator 1

  19. Some Scherk-Collins FDM Models

  20. Hyper-sculpture: Family of 12 Trefoils W=2 W=1 B=1 B=2 B=3 B=4

  21. “Hyperbolic Heptagon” (1997)

  22. Profiled Slice through “Heptoroid” • One thick slicethru sculpture,from which Brent can cut boards and assemble a rough shape. • Traces represent: top and bottom,as well as cuts at 1/4, 1/2, 3/4of one board.

  23. Emergence of the Heptoroid (1) Assembly of the precut boards

  24. Emergence of the Heptoroid (2) Forming a continuous smooth edge

  25. Emergence of the Heptoroid (3) Smoothing the whole surface

  26. The Finished Heptoroid • at Fermi Lab Art Gallery (1998).

  27. Snowsculpting Championships 2003 Silver Medal Winner: “Whirled White Web”(C. Séquin, S. Wagon, D. Schwalbe, B. Collins, S. Reinmuth)

  28. 12:40 pm -- 42° F

  29. 12:41 pm -- 42° F

  30. V-art VirtualGlassScherkTowerwith MonkeySaddles(Radiance 40 hours) Jane Yen

  31. Yet Another Medium: Stone Progress picture from Dingli Stone Carving Art Co., SE China

  32. Spring, 2012

  33. An Evolution of Ideas and Forms

  34. “Evolving Trefoil”

  35. Modular Geometry 6 inches

  36. Three FDM Modules Assembled

  37. Master Module and Mold 8 fiberglass pieces bolted together Milled foam core coated with clay

  38. More on Mold Construction Framework of steel rebar gives overall rigidity, stability

  39. Formation of a Main Sculpture Module

  40. Sealed-off Mold (Catalyzed Matrix Inside)

  41. Fabricate 6 Identical Pieces Nova Blue Studio Arts, Seymour, MO 6 identical pieces had to be fabricated in this very labor-intensive way!

  42. Tentative Assembly of Three Units

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