# Mathematics Galore! The First Five Years of the St. Mark's Institute of Mathematics

### By James Tanton

Catalog Code: MAG
Print ISBN: 978-0-88385-776-2
Electronic ISBN: 978-1-61444-103-8
286 pp., Hardbound, 2012
List Price: $50.00 Member Price:$40.00
Series: Classroom Resource Materials

Mathematics Galore! showcases some of the best activities and student outcomes of the St. Mark’s Institute of Mathematics and invites you to engage in more! Revel in the true delight of intellectually deep mathematical play. Marvel at the heights to which young scholars can rise when given the freedom to soar and help others rise to such heights too. See some great mathematics explained and proved via natural and accessible means.

Based on 26 essays (“newsletters”) and eight additional pieces, Mathematics Galore! examines a wide variety of mathematical tidbits, teasers and treasures, each immediately enticing, and each serving as a gateway to layers of surprising depth and conundrum. This is a book for teachers, student teachers, math club leaders, math circle organizers, professional development leaders, mathematicians, math majors, and general math enthusiasts.

### Table of Contents

Introduction
Newsletters and Commentaries
1. Arctangents
2. Benford’s Law
3. Braids
4. CLIP Theory
5. Dots and Dashes
6. Factor Trees
7. Folding Fractions and Conics
8. Folding Patterns and Dragons
9. Folding and Pouring
10. Fractions
11. Integer Triangles
12. Lattice Polygons
13. Layered Tilings
14. The Middle of a Triangle
15. Partitions
16. Personalized Polynomials
17. Playing with Pi
18. Pythagoras’s Theorem
19. On Reflection
20. Repunits and Primes
21. The Stern-Brocot Tree
22. Tessellations
23. Theon’s Ladder and Squangular Numbers
24. Tilings and Theorems
25. The Tower of Hanoi
26. Weird Multiplication
Appendices
I: Numbers that are the Sum of Two Squares
II: Pick’s Theorem
III: The Möbius Function
IV: The Borsuk-Ulam Theorem
V: The Galilean Ratios
VI: A Candy-Sharing Game
VII: Bending Buffon’s Needle
VIII: On Separating Dots
Indexes
Index of Topics
Classic Theorems Proved
About the Author

### About the Authors

Born in Adelaide, Australia, James Tanton received his PhD from Princeton University in 1994 and worked at the college level a number of years before developing a deep interest in secondary mathematics education. He is committed to sharing the beauty of the subject to all, especially at the formative teenage years. James is the founding director of the St. Mark’s Institute of Mathematics, an outreach program designed to promote joyful and effective mathematics education. He is a full-time high school teacher at St.Mark’s School, Southborough, MA, and he conducts mathematics graduate courses for teachers through Northeastern University’s School of Education. James is the author of Solve This: Math Activities for Students and Clubs (MAA, 2001), The Encyclopedia of Mathematics (Facts on File, 2005), and ten self-published texts. He is the 2001 and the 2002 recipient of the Trevor Evans Award, the 2005 recipient of the Beckenbach Book Prize, the 2006 recipient of the Kidder Faculty Prize at St. Mark’s School and a 2010 recipient of the Raytheon Math Hero Award for excellence in school teaching. He was also just nominated for a Presidential Teaching Award.

James continues to publish research and expository articles, and through his St. Mark’s Institute of Mathematics research classes has helped high-school students pursue research projects and publish their results too.