## Beauty, Rigor, Surprise

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### Elementary Euclidean Geometry

 Course ResourcesWhy Geometry?SyllabusCourse Contents, and Course Contents with Commentary (intended primarily for teachers)CalendarChapter 1. The Language of GeometryChapter 2. ProofChapter 3. CongruenceChapter 4. ParallelsChapter 5. InequalityChapter 6. QuadrilateralsChapter 7. SimilarityChapter 8. Right TrianglesChapter 9. CirclesChapter 10. Triangle CentersChapter 11. AreaChapter 12. Surface Area and VolumeChapter 13. Analytic Geometry (Expected roll-out date: 1/1/2014.)Postulates and TheoremsFinal ReviewsLecturesInstructions to access the Online Text.The Old Text. Better than the new text. (A pattern that's been repeated many times in current textbook history.) Occasionally I'll send you there for problems.Self-StudyMath Open Reference. An excellent if basic resource. Highly recommended for its illustrations of geometrical results. But don't expect proofs. They're few and far between.Software ToolsGeoGebra. Our primary software tool.NonEuclid. "For the creation of ruler and compass constructions in both the Poincaré Disk and the Upper Half-Plane Models of hyperbolic geometry." You probably don't know what that means. I barely do. But I do know this: NonEuclid allows us to model the variety of non-Euclidean geometry in which, through a point not on a given line, there are many lines parallel to that given line.Spherical Easel. What NonEuclid is to hyperbolic geometry, Spherical Easel is to elliptical geometry. It allows us to model the variety of non-Euclidean in which there are no parallels.A clean, quick Triangle Solver. For those times when you just want to know the answer.Proofs, Derivations, IllustrationsA Derivation of Heron's Formula. You might find it ugly. I might agree.A Derivation of the Pyramid Volume Formula. My take on a Euclidean classic.A Dynamic Illustration of Archimedes' Derivation of the Sphere Volume Formula. Sphere Cross-Section = Cylinder Cross-Section - Bicone Cross-Section. By Cavalier's Principle, Sphere Volume = Cylinder Volume - Bicone Volume. Cylinder Volume = 2πr3. Bicone Volume = (2/3)πr3. Thus Sphere Volume = (4/3)πr3.Solidssolids 1.0. Simple, clean models of common polyhedra.MatHSoliD. An in-browser demonstration of how polyhedra fold up from their nets.Stella. Download and install the demo. You'll be astounded by the power of Stella. One reviewer calls it "the greatest program ever devised for the use of polyhedron model makers". I agree. Paper Models of Polyhedra. Truly a labor of love. Particularly useful for its examples of how pyramids of equal area can be fitted together to form a prism.