Honeycomb Conjectures
*This course is intended for upper elementary students
Class Schedule
Mondays 5:30-6:20 pm PST
January 6, January 13, January 20, January 27, February 3
Note: Classes are listed in PST, click below to convert time to your time zone.
Course Overview
Small Group Advanced Math
5 week course, 3 students max.
In this course, we will look at arranging with colored interlocking blocks shapes resembling honeycombs and explore in our own way the exciting math behind tessellating hexagons. We will start by looking at Euclid’s proposition 1 in which he poses the problem of how to construct an equilateral triangle. Using a compass and straightedge we will construct equilateral triangles which we can arrange and tesselate into overlapping hexagons. From here our voyage of discovery begins.
The honeycomb was also the inspiration for the ‘Honeycomb Conjecture’, proved by Thomas Hale in 1998 which states that a hexagon produces the greatest area with the least perimeter. We can get an idea if this is the case by comparing the hexagons we make with other polygonal shapes. The James Webb telescope was inspired by the honeycomb. The telescope containing 18 tessellated hexagonal gold plated mirrors, delicately aligned and working as a single mirror was launched into space on December 25, 2021. The concept of tessellated hexagons is a beautiful piece of number theory which curious and enthusiastic elementary students can discover.
*Materials Required:
- 1cm graph paper
- blank paper
- colored pencils
- cm/inch ruler
- scissors
- scotch tape
- colored markers
- interlocking blocks sold as Omnifix blocks that Peter recommends. Please let us know if you have trouble accessing the materials!
**Please Note: Our Mysteries in Math sessions are part of an ever changing revolving door of topics- it is unlikely that a student repeating the course would encounter the same topic twice because the field is so rich and wide.
Student Experience
Pattern Seeker
Mathematician
Researcher
Inventor
Your Teacher: Dr. Peter Koehler
Peter Koehler holds a PhD in theoretical and elementary particle physics from Royal Holloway College, University of London; a master’s degree from Imperial College of Science, Technology and Medicine, London; and carried out post-doc studies in the theory group at Stanford Linear Accelerator Center before becoming a math enrichment teacher at Nueva, where he has been teaching for over 20 years. At Nueva, Peter has become particularly interested in encouraging and fostering mathematical creativity in his students and was awarded a fellowship from Johns Hopkins University for excellence in teaching in 2012. He enjoys showing his students the surprising ways in which math can be used to describe aspects of the natural world. Inspired by the work of the Pythagoreans, he has developed an approach to elementary math teaching where the students use colored interlinking blocks and follow a few simple rules to visualize numbers; look for patterns, shapes, and sequences; make their own mathematical creations; and develop a sense of the more general principles of mathematics. He has found that this approach stimulates interest and enthusiasm for math, is a great motivator, and can spark mathematical creativity, originality, and a joy in the subject, and can lead to more intriguing and advanced aspects of math.
Peter has been a regular presenter at the Nueva ILC conferences and will be presenting a paper at the 11th International Conference on Mathematical Creativity and Giftedness in Hamburg, Germany, in 2019. He has taught independent enrichment programs at several Bay Area schools and the University of Santa Cruz extension. A painter in his spare time, Peter has run visual arts summer camps throughout the Bay Area for the past 25 years. He has also written plays for children.
