Math 131 - Geometrical Inference and Reasoning

• Prerequisites: Math 130 or consent of instructor.
• Frequency: Fall (I) and Spring (II)
• Student Body: Open only to students in Education and Frcs.
• Credits: 3. Does not count toward degree requirements in L&S.
• Recent Texts: Geometry: an Investigative Approach, by O'Daffer and Clemens.
• Course Coordinator: Steffen Lempp
• Background and Goals: Discovery, conjecture, and proof through geometric explorations in the following areas: lines; polygons; formal constructions; tesselations; polyhedra; symmetry; rigid motions; length; area and volume.
• Alternatives: n/a
• Subsequent Courses: Math 132 (Mathematical Models)

Content coverage:

• Pythagorean theorem
  • proofs
  • uses
  • golden ratio
• Lines, polygons, and construction
  • examples of axioms
  • lines on a geoboard
  • possible symmetries of triangles, quadrilaterals, and other polygons
  • angles of polygons
  • ruler and compass constructions: copying, bisecting, perpendiculars
• Discovering theorems: medians, altitudes, circumcenter, orthocenter, centroid, incenter, Cevians, Euler line.
• Tesselations, polyhedra, and symmetry
  • regular and semiregular tessellation
  • symmetries of a tesselation
  • which shapes tessellate
  • types of regular and semiregular polyhedra
  • Euler's formula
• Rigid motions and similarities: translations, reflections, rotations, magnifications, products of these
• Length, area, and volume
  • lengths and areas on geoboards
  • maps, projections, and their properties
  • effects of scale on length, area, volume, and angle
  • effects of affine maps