At the end of this course you will be able to:
- Develop a deep understanding of geometry and create your own geometric questions, conjectures, and projects.
- Take core geometric concepts, (point, line, angle, sum of angle in a triangle, congruency, similarity, transformations) and ‘unpack’ the concepts through presentations with multiple representations and appropriate examples on different geometric surfaces.
- Explain the primitive terms (objects, relations, and functions), common notions, and axioms used in different axiomatic geometries.
- Construct, analyze, and interpret different geometric axiomatic models and understand the value and limitations of these models, such as Euclidean and non-Euclidean (Lobachevski’s Hyperbolic Geometry Model, Spherical, Cylindrical, Poincare disk, etc.,).
- Work with transformations such inversion, reflections, rotations, projections of a sphere and a cylinder onto a plane.
- Develop a deep understanding of congruency and similarity of two geometrical objects on different geometrical surfaces such as Euclidean plane, Sphere, cylinder, Hyperbolical plane, etc.
- Critically analyze the fifth postulate and develop a supporting argument of equivalent statements with the fifth postulate, i.e., Parallel transport postulate.
- Join in group work regularly in class and some group work outside of class.
- Work with and build physical models in class (such as plastic spheres for spherical geometry, plastic "polydron" for polyhedral models, kaleidoscopes), and use these for reasoning and communication.
- Work with a dynamic plane and spherical geometry program, i.e., Geometer's Sketchpad, GeoGebra 3D, GeoGebra Geometry, Desmos, MatLab, Maple, etc.
- Explore the use of visual material in the learning and communication of mathematics (including geometry);
- Prepare and present some material in class, and in a written project; while the topic of this project must be discussed with the instructor, we encourage you to take your own questions and ideas seriously. Propose a project that is significant to your own learning and possible career plans.
