Transcript CS Scholars Program, October 20, 2014 The Power & Beauty of Geometry and the Secret of a Happy Life Carlo H.

CS Scholars Program, October 20, 2014
The Power & Beauty of Geometry
and the Secret of a Happy Life
Carlo H. Séquin
University of California, Berkeley
Important Questions

Why are you in College ?
Important Questions
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Why in EECS ?
Important Questions
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What do you hope to get out of
your four college years ?
Important Questions
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What is the secret of a happy life ?
Another Important Task
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Broaden your horizon !
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Find out what you really like to do.
Basel, Switzerland
MNG
Jakob Bernoulli (1654‒1705)
Logarithmic Spiral
Leonhard Euler (1707‒1783)
Imaginary Numbers
Geometry !
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Descriptive Geometry – love since high school
Descriptive Geometry
Geometry in every assignment . . .
CCD TV Camera (1973)
Soda Hall (1992)
RISC 1 MicroChip (1982)
Octa-Gear (2000)
Recent Designs and Models
What came first: Art or Mathematics ?

Question posed Nov. 16, 2006 by Dr. Ivan Sutherland
“father” of computer graphics (SKETCHPAD, 1963).
Early “Free-Form” Art
Cave paintings, Lascaux
Venus von Willendorf
Regular, Geometric Art
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Early art: Patterns on bones, pots, weavings...
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Mathematics (geometry) to help make things fit:
Another Question:
What came first: Art or Science?
What is Art ? -- What do artists do ?
What is Science ? -- What do scientists do ?
ART  SCIENCE
Scientists are model-builders.
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They carefully observe a domain of interest.
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Then they cast their findings into a predictive model
(which may be refined over time).
Artists also start with observations of the world,
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then they render it from their own perspective,
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emphasizing certain aspects to make some statement,
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or projecting an alternate vision of the world.
Aurora Sculptures
Inspired by the curtain- or ribbon-like Northern Lights
Torus-Knot_5,3
Inspired by a well defined type of mathematical knot
Torus-Knot_5,3
Brent Collins: Hyperbolic Hexagon
Inspired by the shape of soap films suspended in wire frame.
Scherk-Collins Toroids
Collaboration with sculptor Brent Collins:
 “Hyperbolic Hexagon”, 1994
 “Hyperbolic Hexagon II”, 1996
 “Heptoroid”, 1998
6-story “Scherk-tower” wound into a toroidal loop.
Scherk’s 2nd Minimal Surface (1834)
2 planes
 bi-ped saddles
the central core
= “Scherk tower”
4 planes
 4-way saddles
Scherk’s 2nd Minimal Surface
Normal
“biped”
saddles
“Scherk Tower”
Generalization to
higher-order saddles
(monkey saddle)
V-art
(1999)
Virtual
Glass
Scherk
Tower
with
Monkey
Saddles
(Radiance
40 hours)
Jane Yen
Closing the Loop
straight
or
twisted
“Scherk Tower”
“Scherk-Collins Toroids”
Sculpture Generator 1, GUI
Shapes from Sculpture Generator 1
The Finished
Heptoroid
 at
Fermi Lab
Art Gallery (1998).
2003: “Whirled White Web”
12:40 pm -- 42° F
12:41 pm -- 42° F
“WWW” Wins Silver Medal
12-Story Scherk-Collins Toroid
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branches = 4
storeys = 11
height = 1.55
flange = 1.00
thickness = 0.06
rim_bulge = 1.00
warp = 330.00
twist = 247.50
azimuth = 56.25
mesh_tiles = 0
textr_tiles = 1
detail = 8
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bounding box:
xmax= 6.01,
ymax= 1.14,
zmax= 5.55,
xmin= -7.93,
ymin= -1.14,
zmin= -8.41
12 Signs of the Zodiac
David Lynn, Nova Blue Studio Arts
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http://sites.google.com/site/novabluestudioarts/
Master Module for “Millennium Arch”
Fabrication of “Millennium Arch”
The mold for the key module
A polyester segment cast
Two Times Three Modules
Merging the Two Half-Circles
Brent Collins and David Lynn
“Millennium” Arch by Night
Millennium Man
Vitruvian Man
by Leonardo
Yet Another Medium:
Stone
“The Three Pillars of Engineering”
Math – Materials – Physics(Science)
Sponsored by Paul Suciu (EECS alum)
Spring, 2012
ART  MATH
Inspiring Sculptures
by Brent Collins
Procedural Capture in
Sculpture Generator
MATH  ART
Making a Single-Sided Surface
Twisting a ribbon into a Möbius band
Simple Möbius Bands
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A single-sided surface with a single edge:
A closed ribbon
with a 180°flip.
A closed ribbon
with a 540°flip.
Twisted Möbius Bands in Art
Web
Max Bill
M.C. Escher
M.C. Escher
Deformations of Möbius Bands
Sue-Dan-ese
Möbius band
Boy-Cap
Mӧbius Band into Boy Cap
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Credit: Bryant-Kusner
Classical “Inverted-Sock” Klein Bottle
Felix Klein (1849-1925)
Fancy Klein Bottles
Cliff Stoll
Klein bottles by Alan Bennett
in the Science Museum in South Kensington, UK
How to Construct a Klein Bottle
(2)
(1)
(3)
(4)
2 Möbius Bands Make a Klein Bottle
KOJ
=
MR
+
ML
Limerick
A mathematician named Klein
thought Möbius bands are divine.
Said he: "If you glue
the edges of two,
you'll get a weird bottle like mine."
Split Klein-Bottle Model
 Made
on an FDM machine
Klein Bottle made from two Boy-Caps
A Boy-Cap is a Möbius band !
+
=
Two Möbius bands make a Klein bottle !
Klein Bottle from Mirrored Boy-Caps
Polyhedron
Subdvision
Gridded
Actual Sculpture Model
S6 Klein Bottle Rendered by C. Mouradian
http://netcyborg.free.fr/
More Complex Single-sided Surfaces
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To make a surface of genus h ,
punch h holes into a sphere and
close them up with Boy-Caps.
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A Klein bottle is of genus 2,
it uses two Boy-Caps.
Construction of a Genus-4 Surface
4 Boy caps grafted onto a sphere with tetra symmetry
Octa-Boy Sculpture
Granny-Knot-Lattice (Séquin, 1981)
Metal Sculpture at SIGGRAPH 2006
The Bridges Conference
Mathematical Connections
in Art, Music, and Science
the largest, best-established, annual
Math / Art conference in the world
www.BridgesMathArt.org
My Favorite Annual Conference: 2014
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BRIDGES Art …
Glimpses of My Portfolio
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20 talks at the “Bridges” Math-Art conferences
Assets Beyond Course Credits
Stellar grades are not everything!
(But keep GPA above 3.0).
What recruiters are looking for:
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Demonstrable achievements
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Strong recommendation letters
 Get involved in research early !
 Do more than one project;
get to know more than one professor.
Look for Posted URAP Projects
Some of my recent URAP projects
(spanning Art and Science):
Building
Proper
“The
a “LEGO-Knot” system
rendering of the RCO in Pacioli painting
Beauty of Knots”
Inspiration for “LEGO-Knots”
Henk van Putten
“LEGO-Knot” Realization of “Borsalino”
E R=1.0
C R=2.4142
Two modular components can form the Borsalino
Initial Parts Catalog
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types of end-caps; 3 curved connectors
“Pas de Deux”
Making Sculptures Glow …
Proper rendering of the RCO
in Pacioli painting (1495)
Physical RCO & CG Rendering
Model by Claude Boeringer
Rendering by Raymond Shiau
“The Beauty of Knots”
Presenting Your Accomplishments
Build up a Portfolio:
Course
project reports;
Demonstrations
Photos
of creative work;
of things you built.
Prepare your “Elevator-Speech”:
– 2 minute summary of your work
interesting enough that a listener wants to hear more,
and perhaps wants to see your portfolio!
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Chinese
Button Knot
(Knot 940)
Bronze, Dec. 2007
Carlo Séquin
cast & patina by
Steve Reinmuth
Figure-8 Knot
Bronze, Dec. 2007
Carlo Séquin
2nd Prize, AMS Exhibit 2009
“Volution’s Evolution”
(Patina’d Bronze, 2013)
“Pax Mundi” (Bronze, 2007)
Team effort: Brent Collins, Steve Reinmuth, Carlo Séquin
Music of the Spheres, MWSU 2013
Photo by Phillip Geller
Evolving Trefoil
(polyester resin, 2013)
Inauguration Sutardja Dai Hall 2/27/09
Pillar of Engineering (2012)
QUESTIONS ?
?
http://www.cs.berkeley.edu/~sequin/TALKS/