Fundamentals of Geometry
Considers areas of Euclidean and non-Euclidean geometries, axiomatic systems, synthetic and analytic representations, relationships with algebra, and selected topics and applications.
- Evaluate and contrast projective geometry as generalizations of Euclidean geometry.
- Evaluate projective geometry as developed from a set of axioms or from groups of transformations.
- Analyze the various attempts to prove the Fifth Postulate and the social climate of the times and countries.
- Analyze Euclidean, hyperbolic geometry and elliptic geometry.
- Elaborate straightedge and compass constructions and the geometric constructions of arithmetic operations.
- Discuss the concepts in Euclid’s elements, Euclidean geometry and proofs of the theorems of Thales and Pythagoras.
- Elaborate definition of geometry as study of invariants of groups of transformation, introduction to transformation groups, quaternion field, and operations on spherical spaces.
- Elaborate the concept of parallax and describe how modern scientists use non-Euclidean geometry to attempt to describe the physical nature of the universe.
Why Choose National University?
We’re proud to be a veteran-founded, San Diego-based nonprofit. Since 1971, our mission has been to provide accessible, achievable higher education to adult learners. Today, we educate students from across the U.S. and around the globe, with over 200,000 alumni worldwide.
Focus on one subject at a time — one month at a time — and finish your degree faster.
75+ Degree Programs
Choose from associate, bachelor’s, and master’s degrees, plus credentials and certificates.
On Campus or Online
Study when and where it’s convenient for you with evening, weekend, and 100% online classes.
Apply or transfer any time. Classes start monthly, and applications are accepted year round.
Attend class and learn onsite at one of over 20 locations in California.
As a Yellow Ribbon school, we offer tuition discounts to servicemembers and dependents.
School of Arts, Letters, and Sciences
“Our faculty are established scholars and creators in their own fields. They are dedicated to making your entry into their disciplines a successful one, preparing you for your career as well as graduate study.”School of Arts, Letters, and Sciences