Project Suggestions

Choose a specific topic for your project. Below is a list of possible ideas. If you do not find a topic that is of interest to you or have another one not listed, please let me know.
The project must be either in the form of a web site which uses the Java Sketchpad applet to explain a specific idea, OR a PowerPoint presentation. If you are doing a PowerPoint presentation, send it to me, so that I can create a small web site for you. These web sites will be linked through a class links page. (20%)

The project must cover:
1. the history behind the ideas of your topic

2. the ideas in the topic
3. the geometrical or theoretical implications of the topic

Possible Topics

1. Cyclic quadrilaterals
2. Projective geometry

3. Taxicab Geometry

4. Heron's Theorem

5. Ceva's Theorem

6. Gergonnne Point

7. The Brocard Circle and Brocard Point

8. Orthogonal Circles

9. Menelaus' Theorem

10. The Fermat Point

11. Reuleaux Triangle

12. Napolean's Theorem

13. Simson's Theorem

14. Locus of centers of circles passing through two points, OR tangent to a line m at point T, OR tangent to a circle at point T, OR with radius r and tangent to line m, OR tangent to two lines m and n intersecting at O

15. Star polygons

16. Kaleidoscopes

17. Penrose Tessellations

18. Construction of Pythagorean Triplets

19. Constructible Numbers

20. Constructible Polygons

21. Golden Rectangle and its related Spiral

22. Platonic and Archimedean Polyhedra, OR Stellations OR Non-Convex Uniform Polyhedra

23. Regular Spherical Models (such as a spherical octahedron) Or semi-regular spherical models OR any category of the variations

24. Birkoff's Axioms for Geometry

25. Hilbert's Axioms for Geometry

26. Klein-Beltrami Model for non-Euclidean Geometry

27. A self-dual Finite Geometry

28. Pick's Theorem

29. Sphere Packing Problem

30. Three Famous Greek Construction Problems - Trisection of an Angle, Doubling a cube, OR Squaring the Circle

31. Mascheroni Constructions

32. Transformations using Matrices

33. Transformations in 3-Space with Invariant Points

34. Geometry of Fractals and their dimensions

35. Problem of Appolonius

36. Power of a Point wtih respect to a Circle

37. Tomahawk Method for Trisecting an angle (can be done in Sketchpad)

38. Coordinate Geometry

Choose a specific topic for your project. Below is a list of possible ideas. If you do not find a topic that is of interest to you or have another one not listed, please let me know. The project must be either in the form of a web site which uses the Java Sketchpad applet to explain a specific idea, OR a PowerPoint presentation. If you are doing a PowerPoint presentation, send it to me, so that I can create a small web site for you. These web sites will be linked through a class links page. (20%) The project must cover: 1. the history behind the ideas of your topic 2. the ideas in the topic 3. the geometrical or theoretical implications of the topic

Possible Topics
1. Cyclic quadrilaterals 2. Projective geometry 3. Taxicab Geometry 4. Heron's Theorem 5. Ceva's Theorem 6. Gergonnne Point 7. The Brocard Circle and Brocard Point 8. Orthogonal Circles 9. Menelaus' Theorem 10. The Fermat Point 11. Reuleaux Triangle 12. Napolean's Theorem 13. Simson's Theorem 14. Locus of centers of circles passing through two points, OR tangent to a line m at point T, OR tangent to a circle at point T, OR with radius r and tangent to line m, OR tangent to two lines m and n intersecting at O 15. Star polygons 16. Kaleidoscopes 17. Penrose Tessellations 18. Construction of Pythagorean Triplets 19. Constructible Numbers 20. Constructible Polygons 21. Golden Rectangle and its related Spiral	22. Platonic and Archimedean Polyhedra, OR Stellations OR Non-Convex Uniform Polyhedra 23. Regular Spherical Models (such as a spherical octahedron) Or semi-regular spherical models OR any category of the variations 24. Birkoff's Axioms for Geometry 25. Hilbert's Axioms for Geometry 26. Klein-Beltrami Model for non-Euclidean Geometry 27. A self-dual Finite Geometry 28. Pick's Theorem 29. Sphere Packing Problem 30. Three Famous Greek Construction Problems - Trisection of an Angle, Doubling a cube, OR Squaring the Circle 31. Mascheroni Constructions 32. Transformations using Matrices 33. Transformations in 3-Space with Invariant Points 34. Geometry of Fractals and their dimensions 35. Problem of Appolonius 36. Power of a Point wtih respect to a Circle 37. Tomahawk Method for Trisecting an angle (can be done in Sketchpad) 38. Coordinate Geometry