Modern Geometry

Professor Hlas
hlascs (@)
Drop-in times

Each problem I solved became a rule, which served afterwards to solve other problems.
—Rene Descartes

Course Information

This course focuses on axiomatic thinking in Euclidean and non-Euclidean geometries. Emphasis will be on proof techniques, finite geometries, Euclidean constructions, transformations, spherical geometry, hyperbolic geometry, and geometry software.

More course information is posted on Canvas.




  1. Geometry & Symmetry by Kinsey, Moore, & Prassidis, 2011
  2. Euclid Elements (with applets)
  3. Geometry software

Research background


It is important to accurately show your mathematical thinking and to communicate clearly. If any concerns arise regarding grading, contact the instructor outside of class time. Students earn "math points" (MP) for demonstration of mathematical thinking in their solutions.

Warm-up activities

Warm-up activities is often assigned to prepare students for in-class activities. These activities are more effective when everyone attends class fully prepared. "Eyeglasses" in the calendar will indicate warm-up activities.

Recommended practice

Explicit homework is usually not given to practice course material. Instead it is recommended to:

Wikibook author (3 × 10 MP)

Most class activities will require updating the wikibook. A student from each group will volunteer for that class's updates. See the score sheet for more information.

Group quizzes (8 × 10 MP)

Each group will submit one quiz and each member of that group will receive the same score. Students are expected to fully contribute to quiz solutions and quiz items may appear on examinations. Quizzes will typically have an application problem and require a proof.

Projects (2 × 20 MP)

Student projects will extend what is discussed in class. The first project will be as a group, the second project will be individual. More details will be discussed when appropriate.

Exams (2 × 25 MP)

"To assess conceptual knowledge, researchers often use novel tasks … Because children do not already know a procedure for solving the task, they must rely on their knowledge of relevant concepts to generate methods for solving the problems." (Rittle-Johnson, Seigler, Alibali, 2001, p. 347). A such, assessments are a part of the learning experience and will not only require mastery of class material, but will also require the ability to apply class material to new situations.

For each exam, one page of notes (one-sided, handwritten) is allowed.

Final exam (30 MP)

Cumulative final exam following same structure as in-class exams.

Bonus (? MP)

Homework, quizzes, or examination points may be assigned beyond those indicated above.

Fine print

Email is the best way to reach me. I typically respond within 24 hours, but do not check email in the evenings or on Saturdays due to family commitments.

Attendance A record of attendance is required by the University to maintain accurate class rosters. Attendance is not graded but poor attendance may impact participation in group activities.

Absences If you are absent, please check the course schedule then meet with me (drop-in hours, Zoom, or email) so I can make sure you are caught up. Authorized absences (school functions, emergencies or illness) may be made up for full credit. Other absences may be completed early for full credit, or late for 90% credit. Late work is expected to be completed within two weeks of the original due date or by the last day of classes, whichever occurs first.

Entry-level switching The Department of Mathematics allows students within entry-level mathematics courses (i.e., 010, 020, 104, 109, 112, 114, or 246) to move up to a higher numbered course during the first two weeks of a semester or move down during the first three weeks. Please contact the instructor for more details.


Student Accommodations Any student who has a disability and is in need of classroom accommodations should contact the instructor and the Services for Students with Disabilities Office in Centennial Hall 2106 at the beginning of the semester.

Academic Integrity Any academic misconduct in this course will be submitted to the Dean of Students.

Mandatory Reporter As a Wisconsin State employee, the instructor is obligated to report any crimes to the Dean of Students, including claims of sexual harassment or sexual assault. The Dean of Students office may reach out to you to offer resources and support.

Community As members of this class we are members of a learning community that values all people with all backgrounds. Please remember that our words and actions affect everyone within our community and remember a little positivity can go a long way.