This workshop featured Gord Hamilton and Dani Alvarez-Gavela.
Professional development credit certificates and stipends were offered for this workshop. If you have questions reach out to us at navajomath@gmail.com or 785 473 0273 (call or text).
Funding for this workshop is provided by MIT and Math for America.
The workshop featured mathematical activities/explorations led by Dave Auckly, and Gabriella Pinter.
Full session descriptions are posted below.
Schedule
(All times valid for Crownpoint, NM.)
9:00 Welcome.
9:15 – 10:30 (Dave Auckly) Math Circle Session 1
Title: Altered symmetries
10:30 – 10:50 Introductions/Discussion – Brookhaven, NYU, MoMath atmosphere
10:50 – 12:05 (Gord Hamilton) Math Circle Session 2
Title: The Infinite Pickle
12:05 – 12:30 Sanity Break
12:30 – 1:45 (Dani Alvarez-Gavela) Math Circle Session 3
Title: What is the color of my hat?
1:45 – Whenever math circle discussion/suggested resources
Sessions
Altered symmetries
We will see how to build sculptures using straws and then use the sculptures to discuss what symmetry is.
Symmetry Talk Notes.
One topic that was not covered in these notes and in the video is how functions play a role in symmetry. Here is one example that should be enough to give the idea. The rotation of the triangle is completely captured by the function rot(red) = blue, rot(blue) = green, rot(green) = red. Now students can explore function composition and inverse functions in a geometric context.
The complicated sculpture featured is a compound of five tetrahedra having icosahedral symmetry. A possible Diné name for it is Ashdlaʼ Dį́į́ʼ Tsé. There are several ways to make one. Doubling each edge gives Zachary Abel’s straw thingy.
You can make your own small version of the sculpture by following the “straw thingy” instructions.
If you just want the template, you can print two copies of straws-thingy-scaffold, cut along the solid lines (including the small ellipses — perhaps with a hole punch) and start inserting straws. If you have access to a laser cutter you can use the SVG version: SVG scaffold.
Alternately, you may make your own sculpture put of paper oragami compound of tetrahedra version.
You can read much more about the math related to Ashdlaʼ Dį́į́ʼ Tsé and see two other ways of constructing one at Altered Symmetry.
The Infinite Pickle
Gord demonstrated two puzzles from his recent “Infinite Pickle” book. These were a challenge to make floor plans for buildings with sets of rooms of given areas and a minimal number of walls, and a challenge to make a seating chart for some rather funky students who follow strict logical rules.
The book is currently freely available
Infinite Pickle PDF
One resource that assists this is grid paper. The following is a link to virtual grid paper.
Virtual Graph Paper
The second activity used the following slides. Make a copy if you wish to make large edits/changes.
Pinocchio slides
What color is my hat?
Dani ran the hat color puzzles from the “Camp Logic” book. There are many options to get this book and many other interesting books of math activities (including a “name your price” option) from Natural Math.
Connecting to the Virtual Meeting
We will open the meeting 15 minutes before the official start. If you have trouble connecting you may call (785) 473-0273 and we will help as we can.
Join Zoom Meeting
https://ksu.zoom.us/j/91404514920
Meeting ID: 914 0451 4920
Can be e-mailed navajomath@gmail.com, sent via text (785) 473-0273, or mailed to:
Dave Auckly
Math Department
Kansas State University
Cardewll 138
1228 N MLK Drive
Manhattan, KS 66505
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