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MAT 131 – Course Topics​


Axiomatic System of Reasoning * * *

  • What is geometry and how has it developed in history, art and science?
  • What is the historical literature for a system of geometry? We will examine Euclid’s Elements, Book I.
  • Changing our axiomatic system for geometry: what happens without the fifth Euclidean postulate? Or what is taxicab geometry? (Non-Euclidean systems in contrast)
  • Categorizing our knowledge of 2D objects allows us to classify cases of shapes by essential, remarkable characteristics.

Connecting Representations of Shapes: old and new ways to draw with tools

  • Use a variety of representations for geometric ideas (drawings, text, software, objects);
  • Exploring dynamic computer sketches of geometric ideas helps support argumentation and explanation of our generalizations about 2D space objects and relations.


  • What does it mean to measure paths or regions of the plane, or regions of space? What is a metric space?
  • How can we analyze geometric plane objects in the Cartesian Coordinate Plane?
  • How do we apply geometry to measure the earth and in astronomy more broadly?
  • How does geometry promote navigation and way-finding on the surface of Earth?

Symmetry of Structure: Mappings that preserve structure

  • ​What is symmetry (point/axis and line/plane symmetries)? 
  • What is an isometry (a structure preserving operation)? 
  • What types of projections allow us to portray 3D objects on a 2D mapping? 
  • What happens when we combine symmetric operations or other transformations?​
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