Fractions, Tilings, and Geometry
( IAS/PCMI--The Teacher Program Series )
Publication series ： IAS/PCMI--The Teacher Program Series
Author： Bowen Kerins;Darryl Yong;Al Cuoco
Publisher： American Mathematical Society
Publication year： 2018
E-ISBN: 9781470443405
P-ISBN(Paperback): 9781470440640
Subject： O1 Mathematics
Keyword： 数学
Language： ENG
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Fractions, Tilings, and Geometry
Description
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 America
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