Volume: 7; 2017; 157 pp; Softcover
MSC: Primary 00;
Print ISBN: 978-1-4704-4064-0
Product Code: SSTP/7
List Price: $29.00
AMS Member Price: $23.20
MAA Member Price: $26.10
Electronic ISBN: 978-1-4704-4340-5
Product Code: SSTP/7.E
List Price: $29.00
AMS Member Price: $23.20
MAA Member Price: $26.10
Fractions, Tilings, and Geometry
Share this pageBowen Kerins; Darryl Yong; Al Cuoco; Glenn Stevens; Mary Pilgrim
A co-publication of the AMS and IAS/Park City Mathematics Institute
Designed for precollege teachers by a
collaborative of teachers, educators, and mathematicians,
Fractions, Tilings, and Geometry is based on a course offered
in the Summer School Teacher Program at the Park City Mathematics
Institute.
The overall goal of the course is an introduction to non-periodic
tilings in two dimensions and space-filling polyhedra. While the
course does not address quasicrystals, it provides the underlying
mathematics that is used in their study. Because of this goal, the
course explores Penrose tilings, the irrationality of the golden
ratio, the connections between tessellations and packing problems, and
Voronoi diagrams in 2 and 3 dimensions. These topics all connect to
precollege mathematics, either as core ideas (irrational numbers) or
enrichment for standard topics in geometry (polygons, angles, and
constructions).
But this book isn't a “course” in the traditional
sense. It consists of a carefully sequenced collection of problem sets
designed to develop several interconnected mathematical themes. These
materials provide participants with the opportunity for authentic
mathematical discovery—participants build mathematical structures by
investigating patterns, use reasoning to test and formalize their
ideas, offer and negotiate mathematical definitions, and apply their
theories and mathematical machinery to solve problems.
Fractions, Tilings, and Geometry is a volume of the book
series “IAS/PCMI—The Teacher Program Series”
published by the American Mathematical Society. Each volume in this
series covers the content of one Summer School Teacher Program year
and is independent of the rest.
Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.
Readership
Teachers of middle and high school mathematics.
Reviews & Endorsements
This is exactly the sort of experience to invigorate in-service mathematics teachers in summer seminars.
-- Paul J. Campbell, Mathematics Magazine
Very well designed to offer participants an authentic experience of discovery through an orderly succession of motivation and revelation through guided, hands-on investigation of patterns. The finished material can be directly applied to aid students in honing reasoning, learning to formalize ideas, and grow in mathematical sophistication while having fun solving problems.
-- Tom Schulte, MAA Reviews