Spring 2022


Listed in: Mathematics and Statistics, as MATH-255


Aamir Rasheed (Section 01)


About 2300 years ago, Euclid introduced the axiomatic method to mathematics in his geometry textbook, the Elements. In this book, Euclid deduced the theorems of geometry from a small number of simple axioms about points, lines, and circles. Among his axioms is the parallel axiom, which asserts that if we are given a line and a point not on the line, then there is a unique line through the given point that is parallel to the given line.

Over 2000 years after Euclid, mathematicians discovered that by replacing Euclid's parallel axiom with its negation, we can develop a different kind of geometry in which we still have geometric objects like triangles and circles, but many of the theorems and formulas are different. For example, the sum of the angles of a triangle will always be less than 180 degrees, and this sum will determine the area of the triangle.

In this course we will study both Euclidean and non-Euclidean geometry. We will also consider the fascinating history of how non-Euclidean geometry was discovered. Four class hours per week.

Requisite: MATH 121. Spring semester. Professor Contreras. 

Students who enroll in this course will likely encounter and be expected to engage in the following intellectual skills, modes of learning, and assessment: Problem sets, In-class group work or exams, Take-home exams, Oral presentations. Students with documented disabilities who will require accommodations in this course should be in consultation with Accessibility Services and reach out to the faculty member as soon as possible to ensure that accommodations can be made in a timely manner.


2023-24: Not offered
Other years: Offered in Fall 2011, Fall 2015, Fall 2017, Fall 2018, Fall 2020, Spring 2022