http://www.phoenix.edu
Modern Geometry –
mth405
(3 credits)
This course explores geometry from heuristic, axiomatic, and computational angles. Students examine ancient results, Euclid, non-Euclidean geometry via the Poincaré disk, and transformational geometry.
This undergraduate-level course is 5
weeks.
To enroll, speak with an Enrollment Advisor.
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Symmetry and Fractal Geometry
- Calculate the similarity dimension of geometric objects.
- Identify characteristics of self-similar geometric objects.
- Prove elementary results involving finite plane symmetry groups.
- Demonstrate properties of types of finite plane symmetry groups.
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Non-Euclidean Geometry
- Summarize contributions of pivotal geometers.
- Prove Simple theorems of hyperbolic geometry.
- Calculate distances, angle measures, and areas in the Poincaré Disk.
- Construct objects in the Poincaré Disk.
- Explain the significance of denying the fifth axiom of Euclid's Playfair's Postulate.
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Transformational Geometry
- Represent direct and indirect isometries using matrix methods.
- Represent geometric objects and linear transformations using matrices.
- Identify the invariants of matrix transformations.
- Analyze the compositions of linear transformations.
- Demonstrate properties of isometries: reflections, rotations, translations, and glide reflections.
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Euclidean Plane Geometry and Constructions
- Perform basic constructions with straight-edge and compass.
- Prove theorems in Euclidean Geometry.
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Axiomatic Systems and Ancient and Neutral (Finite) Geometries
- Prove elementary theorems in neutral geometry.
- Demonstrate properties of components of axiomatic systems.
- Solve elementary problems from Western and Non-Western sources.
- The University of Phoenix reserves the right to modify courses.
- While widely available, not all programs are available in all locations or in both online and on-campus formats. Please check with a University Enrollment Advisor.
- Transferability of credit is at the discretion of the receiving institution. It is the student’s responsibility to confirm whether or not credits earned at University of Phoenix will be accepted by another institution of the student’s choice.
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