By René K. Müller, Switzerland

http://housing.byrene.com/Polyhedra_Notes
http://housing.byrene.com/Geodesic_Polyhedra
http://housing.byrene.com/Geodesic_Dome_Notes

Kirby Urner gives a talk at the London Knowledge Lab. This talk explores an alternative technical track through maths which intersects with Fuller's synergetics more successfully. The approach is called Pythonic Mathematics, meaning it elects to impart math savvy in the context of a particular object oriented computer language.


» Click here to view the talk

» Click here to see the Synergetics Teaching Website also by Kirby Urner

Quantum computing holds great promise for solving difficult problems that would take classical computers an infinitely long time. But working out the algorithms to solve these problems efficiently remains a major hurdle. According to a Report in the 24 Feb 2006 Science, help lies in the realm of geometry. In essence, a quantum computer designer wants to figure out the shortest path from the input data of a problem to its output solution without having the number of calculations grow out of hand along the way. Using that logic, Nielsen et al., showed that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry — a geodesic, which also represents a path that a freely falling object would take.In making this analogy, the researchers open up the possibility of using the mathematical tools of Riemannian geometry (which involves the study of curved surfaces and spaces) to suggest new and efficient quantum algorithms or to reveal limitations of the power of quantum computers. An accompanying Perspective by J. Oppenheim (sciencemag.org) highlighted the study.

» Click here to view the entire article

Submitted by ricardo sandoval

Richardo writes: I had assembly my dome for unique time in december of 2005 in Tatacoa desert, Huila Colombia, we had a thunder storm, a lot of side wind but no rain, 8 more tents suffer damages some of them were unattached from the ground, the dome tent was the only one straight after the storm, and it wasnt attached to the ground, not even tied by ropes. it was just amazing. Now im working in a project called Olive City, its the ideal city made by domes.

Pillowdome presentation

Kirby addresses the Wanderers to talk about Buckminster Fuller, Geodesic Domes and Pillow-domes. Jay Baldwin also makes an appearance.



Click read more to view two other videos on Hypertoons (dynamic geometry modeling) and an OSCON presentation ...

Hypertoons!

Kirby Urner talks about how to generate Hypertoons using the Python programming language. Hypertoons involve geodesic models that generate and modify themselves.



OSCON 2005

Kirby Urner talking about some of his work done in Python, Synergetics and other Open Source related ideas.



» Read Kirby Urner's blog

By Jay Salsburg



Geodesic Math is a document representing a very good beginning for the novice investigator. This document is not simple but an elegant and reliable treatment of Geodesic Math in a scientific and geometrically graphic way without mathematical complexity.

» Click here to view the original document (PDF)

MatheMagical Resources by Jeff Hrdlicka
List of Books

Abbott, Edwin A. Flatland. New York: Dover Books, 1952.

Banchoff, Thomas. Beyond The Third Dimension: Geometry, Computer Graphics, and Higher Dimensions. New York: Scientific American Library, 1990.
Burger, Dionys. Sphereland. New York: Thomas Y. Crowell, 1965.

Clifford, William Kingdon. The Common Sense of the Exact Sciences. New York: Dover Books, 1955.
Coxeter, H. S. M. Introduction to Geometry: Second Edition. New York: John Wiley & Sons, 1989.
Cundy, H. Martyn, and Rollet, A. P. Mathematical Models. Oxford: Oxford University Press, 1961.

Davis, Philip, & Hersch, Reuben. The Mathematical Experience. Boston: Houghton Mifflin, 1981.
Devlin, Keith. Mathematics, The Science of Patterns: The Search for Order in Life, Mind and the Universe. New York: Scientific American Library, 1994.
Doczi, Gyögy. The Power of Limits: Proportional Harmonies in Nature, Art & Architecture. Boulder, CO: Shambhala, 1981.
Downs, J. W. Practical Conic Sections. Palo Alto: Dale Seymour Publications, 1993.
Dunham, William. Journey Through Genius: The Great Theorems of Mathematics. New York: John Wiley & Sons, 1990.

Gardner, Martin. “A game in which standard pieces composed of cubes are assembled into larger forms [Soma Cubes].” Mathematical Games, Scientific American, September 1958, p. 182.
Gullberg, Jan. Mathematics: From the Birth of Numbers. New York: W. W. Norton, 1997.
Hargattai, Istvan, and Hargattai, Magdolna. Symmetry: A Unifying Concept. Bolinas, CA: Shelter Press, 1994.

Hilbert, David and Cohn-Vossen, S. Geometry and the Imagination. New York: Chelsea Publishing, 1952.
Hilton, Peter, and Pedersen, Jean. Build Your Own Polyhedra. Menlo Park, CA:Addison-Wesley, 1988.
Hoffman, Paul. Archimedes’ Revenge: The Joys and Perils of Mathematics. New York: W. W. Norton, 1988.
Hofstadter, Douglas R. Gödel, Escher, Bach: an Eternal Golden Braid. New York: Basic Books, 1979.
Holden, Alan. Shapes, Space and Symmetry. New York: Columbia University Press, 1971.

Kaku, Michio. Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension. New York: Oxford University Press, 1994.
Kappraff, Jay. Connections: The Geometric Bridge between Art and Science. New York: McGraw-Hill, 1991.

Liusternik, L. A. Convex Figures and Polyhedra. New York: Dover Books, 1963.

Mathematics. Life Science Library. New York: Time, Inc., 1963.
Miyazaki, Koji. An Adventure in Multidimensional Space: The Art and Geometry of Polygons, Polyhedra and Polytopes. New York: John Wiley & Sons, 1986.

Oglivy, C. Stanley. Excursions in Geometry. Oxford: Oxford University Press, 1967.
Pappas, Theoni. The Joy of Mathematics: Discovering Mathematics All Around You. San Carlos, CA: World Wide Publishing/Tetra, 1989.

Pearce, Peter. Structure in Nature is a Strategy for Design. Cambridge, Mass.: The MIT Press, 1978.
Pearce, Peter and Susan. Polyhedra Primer.(1) New York: Van Nostrand Reinhold, 1978.
Pearce, Peter and Susan. Experiments in Form: a Foundation Course in Three-Dimensional Design.(2) New York: Van Nostrand Reinhold, 1980.
Pedoe, Dan. Geometry and The Visual Arts. New York: Dover Publications, 1983.
Peterson, Ivars. The Mathematical Tourist: Snapshots of Modern Mathematics. New York: W. H. Freeman, 1988.
Peterson, Ivars. Islands of Truth: A Mathematical Mystery Cruise. New York: W. H. Freeman, 1990.
Pugh, Anthony. Polyhedra: a Visual Approach. Berkeley: University of California Press, 1976.

Ranucci, Ernest R., and Rollins, Wilma E. Curiosities of the Cube. New York: Thomas Y. Crowell, 1977.
Rucker, Rudy. Geometry, Relativity, and the Fourth Dimension. New York: Dover Books,1977.
Rucker, Rudy. The Fourth Dimension. Boston:Houghton Mifflin, 1984.

Salem, Lionel; Testard, Frédéric, and Salem, Coralie. The Most Beautiful Mathematical Formulas. New York: John Wiley & Sons, 1992.
Schattschneider, Doris, and Walker, Wallace. Kaleidocycles. New York: Ballantine Books, 1977.
Seymour, Dale, and Britton, Jill. Introduction to Tessellations. Palo Alto, CA: Dale Seymour Publications, 1989.
Steen, Lynn Arthur, ed. Mathematics Today. New York: Vintage Books, 1980.
Stewart, B. M. Adventures Among The Toroids. Published by the author, 4494 Wausau Road, Okemos, MI 48864 ($11.00), 1980.
Stewart, Ian. The Problems of Mathematics. New York: Oxford University Press, 1987.
Stewart, Ian. Nature’s Numbers: The Unreal Reality of Mathematics. New York: Oxford University Press, 1995.
Stewart, Ian. Flatterland: Like Flatland, Only More So. Cambridge, MA: Perseus Books, 2001.

Wenninger, Magnus. Polyhedron Models. Cambridge: Cambridge University Press, 1974.
Wenninger, Magnus. Spherical Models. Cambridge: Cambridge University Press, 1979.


References on the Web


Mathematics

Mathworld
History of Mathematics
Math Forum
Nerd World: MATHEMATICS


Geometry

The Geometry Junkyard
The Geometry Center Welcome Page
Geometry, Art and Abstract Sculpture
Gallery of Mathematical Images
Geometry Games
World of Escher
Mark Newbold’s Java Stuff


Polyhedra

George W. Hart
Father Magnus Wenninger
Tom Lechner’s Time Well Spent
Paper Models of Polyhedra
Polyhedron Models
Pedagoguery Software Inc.
http://www.peda.com/poly/Welcome.html Polyhedra
Eric Swab Polyhedra
Richard Hawkins’ Digital Archive
Hoberman Sphere
Roger’s [Magnetic] Connection
Lesson Plans


Polytopes

Eric Swab Hyperspace

You can find more Websites by using any of the following terms in your favorite search engine: geometry, polygons, tessellations, polyhedra, polytopes, hyperspace

This list was compiled by Jeff Hrdlicka, MatheMagician
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