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1 General Links

Big Ideas

Here is a page (under construction) which is gathering and exploring some reflecions on 'big ideas' in geometry / geometry for teaching: Big Ideas in Geometry: procedures, concepts, patterns

I (Walter whiteley@mathstat.yorku.ca) welcome suggestions / alternatives / expansions. I hope to develop additional linked pages for each of the big ideas that emerges.

A companion page on Geometry for Teaching will also be developed.

General Links

Some interesting geometry web sites: http://www.math.yorku.ca/~whiteley/geometrysites.html

An annotated bibliography of related to Geometry: http://www.math.cornell.edu/~dwh/biblio/

Information and papers from the ICME Topic Study Group 16: Visualisation in the teaching and learning of mathematics can be found at: http://www.icme-organisers.dk/tsg16/

Geometers Sketchpad Users Group activities: http://www.dynamicgeometry.com/general_resources/user_groups/index.php

One activity (by Walter Whiteley and Lily Moshe) we may follow up is at the bottom of the page: http://www.dynamicgeometry.com/general_resources/user_groups/jmm_2006/index.php with a sketch, a lab sheet and instructors notes.

An on-line book on symmetry is: Slavik V. Jablan "Theory of Symmetry and Ornament": http://www.emis.de/monographs/jablan/index.html

Math Forum site on Symmetry/Tessellations: http://mathforum.org/library/topics/sym_tess/

George Hart's pages on polyhedra, with instructions to build some of the objects: http://www.georgehart.com/pavilion.html

A web site with links related to the recent Biography of Donald Coxeter: http://www.math.yorku.ca/dcoxeter/

Creative Geometry: some activities - including hands on activities - from a teacher, mounted on the Math Forum website. http://mathforum.org/~sanders/creativegeometry/

Symmetry in Physics

Symmetry is central to modern geometry and more generally to modern science.

Teaching symmetry in introductory physics and mathematics courses: Here is a catchy phrase: The answer to the question "Why teach symmetry?" is simply an equation: Physics = Symmetry = Beauty. http://ed.fnal.gov/samplers/hsphys/people/Hill.html.

Underlying this is Noether's Principle: http://en.wikipedia.org/wiki/Noether's_theorem See also the pdf papers to download at: http://xxx.lanl.gov/abs/physics/9807044 and http://xxx.lanl.gov/abs/physics/0001061. An associated web site with a one week module for teaching symmetry and physics in high school is found at: http://www.emmynoether.com/

In general Symmetry is crucial to Modern Physics. Here is one link: http://en.wikipedia.org/wiki/Symmetry_in_physics For an introductory paper by Francois Giere: About Symmetries in Physics: http://xxx.lanl.gov/abs/hep-th/9712154 Here is another link (higher level): http://courses.theophys.kth.se/5A1335/intro.html


One other physics/geometry principle is Cure's Principle: that the symmetry of the input of a physical situation should appear as symmetry of the output. See Ian Stewart + Martin Golubitsky: Fearful Symmetry: Is God a Geometer? Penguin 1992

Symmetry in Biology

Symmetry in Biology: http://en.wikipedia.org/wiki/Symmetry_(biology)

T. L. Blundell: Symmetry, Stability and Motion in Molecular Biology and in the Visual Arts Leonardo, Vol. 14, No. 4 (Autumn, 1981), pp. 311-313

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