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Deposit #89
Greg Frederickson
Purdue University
gnf@cs.purdue.edu
A
Penrose Sampler
____________

Wadham College,
Oxford, one of the newest in the 17th century. Recently Sir Roger
Penrose retired there.
In a garden in the back of the College, a
patio has been tiled with a design based on Sir Roger's work.

Computer animations now
enhance centuries old mathematical constructions.
Tartaglia's
stellated truncated hexahedron from his 1543 edition of Euclid's
"Elements."



Polygonal Geometry
Penrose Tilings ~ Hinged Dissections
This section . . . .
Greg
Frederickson illustrates the classic hinged dissection of a
triangle turned into a square.
Click on the RealPlayer to see his animation. 

More
Animations
(The
animations are under copyright by Greg Frederickson and may not be
copied, electronically or otherwise, without his express written
permission.)

On
catching a first glimpse of the "Water Cube" at the Beijing Summer
Olympics in 2008, students remarked they thought they had seen Penrose
Tilings. The National Aquatic Center, located in the Olympic
Green, became the focal point of American viewers watching Michael
Phelps win his record setting eight gold medals. The design by
ARUP was not inspired by Sir Roger Penrose but by the somewhat more
relevant
geometric structures of soap bubbles. Nevertheless the
translucent recyclable panels provided a fascinating visual impact,
especially at night.





Almost
simultaneously
other students read Greg Frederickson's article in The College Mathematics Journal
on
hinged dissections. His opening sentence was prophetic:
"Some mathematical ideas are just
so nifty that people can't resist finding a physical realization for
them."

Frederickson discusses the history of several
mathematicians who have investigated dissections including the above
realPlayer animation.
He has also gone on
to apply his carpentry skills to construct models of Penrose Tilings. 


Howard Eves and others
have built sets of four tables based on the hinged design.


A brief list of
references that should
be in most university libraries.

From the
author of Deposit # 89 . . .
Frederickson, Greg N., Designing a Table Both Swinging
and Stable, The College Mathematics
Journal, 39 (4) September 2008, pp. 258266.
Frederickson, Greg N., Dissections: Plane and Fancy,
Cambridge University Press, 1997.

Weisstein,
E. W., CRC Concise Encyclopedia of Mathematics, CRC Press,
1999, pp. 471  473. See Dissection.

and from The College Mathematics Journal, 40(1) January, 2009, p. 71,
Julie Rehmeyer on the mathematics of the "Water Cube" in Beijing, 2008
Olympics:
< http://www.sciencenews.org/view/generic/id/34283/description/A_building_of_bubbles
>

