Midterm Review Outline

The midterm will cover the work of the course up through the polyhedral unit. There will be constructions, definitions, explanations, and some problem solving.

• Learn definitions of important terms, such as harmonic division, Apollonian circles, inversion, orthogonal, power, radical axis, inversive plane, DWEG plane, names of and nature of regular polyhedra (Platonic solids), dihedral angle, prisms, antiprisms, etc. Also, be able to construct important objects in examples.
• Review relationships among the basic concepts above, especially all the guises in which orthogonal circles and inversion appear. The inversive plane is the most general picture, with both the Euclidean plane and the DWEG model resulting from picking out some special points.
• Be able to construct and/or visualize inversion images. Also be able to construct circles of inversion that will transform one figure to another, e.g., two non-intersecting circles into concentric circles.
• Review interpretation of lines and circles and basic figures in various models and how to construct them.
• Be familiar with the Platonic solids. Know how to compute dihedral angles, distances, and volumes. Know how to find, name and count the symmetries of simple polyhedra. Be prepared to work with volumes, either by formula or by comparison, dilation, subtraction of pieces, etc.