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.

Frequently Asked Questions (FAQ)

When/how is the professor available outside of class?

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 other commitments.

My drop-in schedule and sign-up for Zoom appointments are posted at

What is the attendance policy?

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 (e.g., taking a group quiz individually).

If you are absent, please check the course schedule then meet with the instructor via drop-in hours, Zoom, or email to make sure you are caught up. Graded work that occurs during an authorized absence (school functions, emergencies or illness) may be made up for full credit. Other absences may complete graded assignments late for 90% credit or early for full credit. Late work is expected to be completed within two weeks of the return date or by the last day of classes, whichever occurs first. In situations where a makeup cannot occur, the final exam score may be used as a proxy for a missing assignment. Students missing a week or more of class should contact the Dean of Students Office to get extra support.

What if the class is too easy or too difficult?

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.

How does grading work?

Final scores (rounded up to the nearest whole number) are compared to the grading scale given in the syllabus to determine a final grade. Individual scores or grades will not be modified because they represent a student's progress in the class throughout the semester. If there is a mistake in scoring, please contact the instructor as soon as possible to get the error fixed.

Midterm grades do not have a score table so are based on the percentage of points completed at the time of midterm submission.

Note: I dislike the University's scale of "F" because I have never once felt that a student has "failed" a class. Instead, I prefer to think of this as a "not pass" where insufficient evidence has been demonstrated by a student to move on to the next level.

What if I need accommodations (like extra time on tests)?

Any student who is in need of classroom accommodations should contact the Services for Students with Disabilities Office in Centennial Hall 2106 at the beginning of the semester.

What else do I need to know?