Purpose: The goal of the projects is to investigate a geometric idea in greater depth, to understand the connections between different topics, and to develop skill in writing and speaking about math. Please listen carefully to all the presentations.

Possible Topics: Here's a starting point. I'm happy to help anyone figure out a good project.

Great extra credit topics:
Constructible numbers and impossible constructions.
Triangles: Euler line and Morley triangle theorem.
Circles: Nine Point Circle and Feuerbach's theorem.
Hexagons: Pascal Mystic Hexagon and Brianchon's theorem.
Penrose tilings.
Bezier curves.
Apollonian circles.
Symmetries of Platonic solids.
Triangular model of the hyperbolic plane.
Sphere packing.
Projective geometry.

Here are some other possibilities:
3-D: volume, surface area, coordinates, etc
X Spheres
X Pyramids (square base)
X Tetrahedron (plus symmetries or containing sphere)
X Dodecahedron
X Icosahedron

Axiomatic geometry: (V6)
X Godel's incompleteness theorem
Clairaut's axiom on rectangles 6.7
Parallel postulates #6.37-6.40
Parallel projection theorem 7.3
X Similar triangles theorem 7.4

Quadrilaterals:
X Rhombus #6.32 #6.33
Trapezoids #6.28, #9.11
Saccheri and Lambert quadrilaterals V6.7

Geometry of triangles: (V7.7)
Median concurrence theorem
X Euler line theorem
X Ceva's theorem
X Theorem of Menelaus
X Theorem of Ceva
X Morley triangle theorem

Geometry of circles: (V10)
X Nine point circle theorem
Miquel's theorem
X Pascal's theorem
Quadrilaterals in circles #10.16, #10.17, #10.19
Brianchon's theorem (conic in hexagon)
X History of Pi

Symmetries:
X Symmetries of cube and octahedron
X Isometries of plane tilings
Semi-regular polyhedra
X Frieze patterns
Wallpaper designs
Semi-regular tilings

Spherical geometry:
X Spherical law of sin and cosine
Spherical theorem of Menelaus
Spherical theorem of Heron
Projective geometry

Construction Projects:
Many on ruler and compass constructions V11.2,V11.3,V11.5
Construction of egg
X Construction project CP2 pg 444
Construction project CP3 pg 444
X Construction project CP4 pg 444
Construction project CP5 pg 444

Discrete topics:
X Pythagorean triples
X Golden ratio
Pick's theorem on lattice points
X Finite geometries and error-correcting codes
X Taxi-cab geometry

Topological topics:
X Mobius band
X Klein bottle
X Hypercubes
X Sierpinski's carpet
X Apollonian packing
X Sphere packing
X Euler characteristic

Analytic topics:
Curvature of cones #14.7
Mean curvature #14.8
X Bezier curves
Or choose your own!

Guidelines:
Grading: Your project is worth up to 10 points towards your grade in the class. This grade will be based on the accuracy, clarity, and motivation in your project.

Format: The handout should be 2-4 pages (single space, 1 inch margins, standard font) and be as well-written as an English paper.


Content: The project should include: an introduction with motivation; mathematical content (the relevant definitions, theorems, proofs); an explanation; a picture (figure, diagram, etc); and a bibliography with at least 3 references (including web pages).

Warning: Do not cut and paste from a webpage or copy from a book without quoting your source. Avoid plagarism at all costs. Make sure your handout is written in your own words.

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