Henri Picciotto’s Math Education Page

Some of the work will be based on material that is available elsewhere on my Web site. Relevant pages for additional materials and ideas:

    • Transformational Geometry (this page includes many links, including to a logically tight formal introduction to transformational proof for teachers and curriculum developers, and to most of the content covered in this workshop.)

    • Introduction to isometries and dilations (worksheets)

    • Introduction to isometries and dilations (online, using GeoGebra applets)

On some of those topics, there are many more documents available on the site than you have in your handout. You'll also find teacher notes, some answers / solutions, and pedagogical / philosophical comments.

Geometry Labs

Some of the symmetry work is from Section 5 of my book Geometry Labs. The book includes many more labs, plus answers and abundant teacher notes about all the labs. It is available for free download on my Web site.


Many teachers enthusiastically recommend Euclid: The Game. It guides students step by step to more and more complicated constructions, and gradually gives them more and more tools. It is simultaneously an introduction to construction, and an introduction to GeoGebra. I have not used it, but I have played Euclidea, an excellent app for mobile devices, which seems to be along the same lines.

Not as comprehensive, and not as directly useful in teaching: Science vs. Magic (?) offers a fantastic Web applet to do pure compass and straightedge construction without the challenges of physical compasses and straightedges, and without having to learn GeoGebra. It provides specific construction goals, which are fun and challenging, but you have no control over what is given. The puzzles always start with two given points, and that's it. There is no way to create your own points, so even something as simple as "bisect an angle" is not possible. However it would be great for a math club.

Transformational Geometry

by Richard G. Brown

Out of print, but probably findable on the Web. Solid introduction to the topic, based on pre-Common Core approaches. This was a major tool in my Space course, and an inspiration for some of this workshop's content.

Handbook of Regular Patterns

An Introduction to Symmetry in Two Dimensions

by Peter S. Stevens

An amazing multicultural resource from MIT Press, with an accessible presentation of some of the math underlying symmetry and tiling, and hundreds of black and white images from all over the world.


A blog post about Miras (see-through plexiglas mirrors).

Robert Hasson's matrices site at the College of San Mateo. (No longer works for me, but try it.)

My vacation blog post and photos, mostly of wallpaper symmetry at the Alhambra in Spain.