For 17 years, from 2001 to 2018, I created, developed and taught an original course called “Mathematical Ideas for Artists” at the California College of the Arts in San Francisco and Oakland, California.

My intent for the course was to introduce young, creative art students to the similarly recurring patterns and proportions found throughout nature and which were intentionally applied to worldwide arts, crafts and architecture in great and small creations since the dawn of civilization. I also felt it important that these students get solid hands-on experience creating geometric constructions using a compass and straightedge as their artistic forebears did, and as some creative people still do today. There is wisdom and great psychological power in the visual designs of nature and in art which makes intelligent use of these proportions.

I built this course after years studying mathematics (with a Bachelor of Science degree in pure mathematics and a Master’s degree in mathematics and science education). Helpful also has been the longtime study of the histories and philosophies of mathematics and art. By the time I retired in 2018 I had taught for 45 years.

My students represented a wide and wonderful range of creative interests: painting and drawing, illustration, graphic design, fashion design, glass, jewelry and metal arts, film, furniture, comics, animation, architecture, industrial design, photography, sculpture, textiles and writing. I wanted to see what would result from putting this knowledge into their heads and hands.

There were 16 class sessions in a semester. Each session lasted 3 hours and was divided into distinct parts with flexible timings:

Introduction to the topic (5 minutes)
PowerPoint presentation with discussions (45-60 minutes)
Workbook activities (30-45 minutes)
Break (30 minutes)
Finish Workbook activities (0-15 minutes)
Homework presentations by students (45-60 minutes)

I always began each class with a brief introduction to the day’s topic, given in the context of previous ideas when appropriate. I projected the PowerPoint presentation and spoke about each slide, welcoming questions from students at any time to help clarify ideas. Sometimes I paused the presentation so that students could do geometric constructions with a compass, and sometimes the hands-on activities were saved until after the PowerPoint show. But it was always important to have enough time for active, hands-on experiences with the ideas and not just passively watching a screen. A Workbook was created for this purpose, also available below.

Along with seeing my students’ fascination with the topics, and their delight in doing geometric constructions in the Workbook upon images of nature and art, the most interesting part of each class for me was having each student present and describe their homework to the class, including the class ideas which inspired them. Students and I could ask questions and make constructive comments. (After each presentation the entire class applauded.) The homework assignment for each class was always the same: take any idea from the day’s presentation and create something original in any medium to make us all say “wow!” What they’d come in with each week always amazed and impressed me with their interpretations and applications of the ideas into concrete works of art in their major. I encouraged them to make creations which they could also use as homework in other classes, and when this happened I usually heard back that their other teacher was very impressed with their knowledge of the ideas and principles behind their work, as well as its execution.

I’ve decided to make the course’s PowerPoint (.pptx) presentations (and one .pdf Workbook document) available for educators and others to view or download for your own classes, or for your personal study. It also includes exams and their answers. They are presented here free and may not be used for any commercial or financial purposes. Be sure to view in Presentation mode to enjoy the essential transitions.

If you need a free PowerPoint viewer, you can download one here.


1 - Introduction class.pptx

2 - Unity and Polarity.pptx

3 - Ad Triangulum Symmetry.pptx

4 - Ad Quadratum Symmetry Part 1.pptx

5 - Ad Quadratum Symmetry Part 2.pptx

6 - Root Rectangle Symmetry.pptx

7a - Miderm study guide.pptx

7b - Midterm 2018 answers.pptx

8 – Tessellation.pptx

9 - Mystery of Seven.pptx

10 - Pentagonal Symmetry.pptx

11 - Fibonacci Numbers.pptx

12 - Golden Rectangle Symmetry wo Fib Phi.pptx

12 - Golden Rectangle Symmetry.pptx

13 - Platonic Solids.pptx

14 - Finals Study topics.pptx

15 - Final answers full.pptx

15 - Final answers wo Fib.pptx

16 - Final answers 2.pptx

Mathematical Ideas for Artists Workbook.pdf


There is no audio recorded with these presentations but the slides develop in a logical sequence and are generally self-evident and speak for themselves with the teacher’s assistance. It would be helpful if the presenter is familiar with my book “A Beginner’s Guide to Constructing the Universe” and to have some familiarity with the ideas and activities presented in my Activity Books and DVDs. The Activity Books and DVDs are actually greatly expanded versions of the ideas in the class Workbook.

I hope you have great success and fun in presenting any of these classes or the entire course!

If anyone uses this material for teaching, or for your own creative work, I’d like to know how it goes, so email me:

Michael S. Schneider
15 January 2022

© Michael S. Schneider 2022