Geometry 2: Geometry since 1800

Introduces more recent Euclidean geometry, such as Feuerbach’s nine-point circle, the Euler line, and Morley’s theorem. Looks at geometry on the surface of the spherical earth and the passage to elliptic geometry and some features of hyperbolic geometries. Uses the Geometer’s Sketchpad to study transformations of friezes and to visualize the geometry in the above paragraph, including pictures of the geometry of the hyperbolic plane. Introduces the six regular polytopes in four-dimensional space. Abbott’s Flatland and Dewdney’s The Planiverse are among the readings and are suitable for secondary classrooms.

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