Geometry in action

Geometry in action

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Geometry in action

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Presentation Transcript

1. Bicycle Tracks Geometry in action Which way did the bicycle go?

2. Geometry and Symmetry Class 1

3. A geometer sees … and dreams Some of my wildest dreams are about geometry!

4. Why is a point in the middle not moving? Balance of forces: symmetry Hang a weight on a string What do you expect to see? Why? Geometry with ... symmetry Pierre Curé’s Law: The symmetry of the input matches the symmetry of the output.

5. Geometry with symmetry Some dynamic images • Use dynamic geometry in my own work Geometer’s SketchPad (GSP) • Mix visual and kinesthetic: • Exploring ‘equal lengths’, and ‘folding’ in GSP GSP Exploration • ‘Equal length’ is about transformation to superimpose end points!

6. Geometry with symmetry Symmetry as the core of geometry. • Ways of testing a proposed straight line: • Carpenter’s test: Gaps means the two boards are curved. Does no gaps mean the two boards are straight?

7. Quotes on Proof and the practice of Mathematics Goemetry not proof! • Axioms and proofs differ from mathematics as medicine differs from food. Paraphrase ofGian-Carlo Rota, 1997 • Only professional mathematics learn anything from proofs. Other people learn from explanations. Raol Boas, 1980 • Any fool can know. The point is to understand. Albert Einstein