Park City Mathematics Institute
Algebraic and Analytic Geometry
Project Abstract

Drafts of Project Files (password required)

Exploring the Real Projective Line
Marcy Conn*, Mark Sawula, Todd Vawdrey
How do you add points of infinity to lines? Why would you want to? Projective geometry adds infinity to lines, planes, and spaces in such a way that algebraic geometers can see all conics as spheres and all cubics as tori. In this activity we examine the simplest projective extension, that of the real projective line. We try to understand the distinctive properties of the real projective line by comparing it to a variety of projections of lines, including nomographs (function graphs in which the x- and y- axes are parallel).
Projections, Projections, Wherefore Art Thou Projections?
Chris Border, Dan Willms, Haley Woods*
When a light source is incident on a two- or three-dimensional object, what geometric properties are preserved in its projected image? In a lab-style activity, high school geometry students will investigate which properties (length, angle measure, etc.) are preserved under which conditions. In particular, students will examine the projections of two- and three-dimensional objects under different light sources as well as the stereographic projection of points on a sphere. The lesson will culminate with a video showing the stereographic projection of the earth.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.