Math 445 Projects

Will give more details soon but here are the main points.

Purpose of the project is for the authors to learn a topic in depth and consider carefully how to teach it to others.
Topic will be chosen from a list of geometry topics relevant to the course.
Project will be a written exposition of the topic plus a short teaching unit for the class.
Project will also include some questions for the class that will be part of the course.
Project will go through at least 2 drafts with consultation, practice presentation before presenting to the class.

Organization and Timeline

It is suggested that you work in teams of 3. Teams of 2 are also possible. Teams and topics should be chosen by Friday 1/14 or by the next Wed at the latest.

There will be a due date for the first draft and at least a week or two before the final delivery so that the team can get feedback and make changes.

Topic List

This is an initial list of suggested topics. There may be more later. It is possible to suggest a topic, but these are topics that we want in the course, so there is a strong bias towards them.

Topic	Some info	Timeline
Centers of Mass in Geometry	Gives new results and powerful tools for barycentric topics. Physical models with weights recommended.	Should be early topic
Bezier Curves	How computer science draws curves, from fonts to figures. A coordinate topic with some interesting polynomials..	Middle
Fermat point in the triangle	This point shows up in amazing figures with equilateral triangles. Possible phyical models with weights.	Can be early
Symmetries of the cube	Starts with simple hands-on activity. Mark axes. Find orientation reversing symmetries. includes surprising rotation relationships.	Middle
Maps and spheres 1: Surface area	Explain facts about the surface area of the sphere. Relate to area-preserving maps.	Middle or late
Maps and spheres 2: Mercator	What is the mercator projection mathematically. How is it good? How is it not so good?	Middle or late
Logarithmic Spiral	This is the nautilus shell, approximately.	Any time
Star Polygons	A simple shape with some nice angle and integer properties.	Any time
Paper models of non-Euclidean geometry	Tape together annuli to get a very curvy plane. Anyone for pentagons with all angles = 90 degrees?	Latish.
Cathedral windows	Advanced constructions with circles and arcs. Be medieval.	Middle
Origami Math	Some beautiful models can be part of this but there must be a big math component also (i.e., why does the folding work?).	Any time
Conic Sections	Several possible projects here, from 3D intersections of cones to constructions from perspective geometry	Middle or late
Euclidean tessellations	Several possible projects here. But must be math-y and not just prett-y.	Any time
Spherical tessellations	Integrate polyhedra and tiling of the sphere.	Middle to late.
Hyperbolic Non-Euclidean tessellations	Many tilings of the non-Euclidean plane.	Late