Fractions, Tilings, and Geometry
āļĄ.āļ. 2018 · IAS/PCMI--The Teacher Program Series āļŦāļāļąāļāļŠāļ·āļāđāļĨāđāļĄāļāļĩāđ 7 · American Mathematical Soc.
eBook
157
āļŦāļāđāļē
reportāļāļ°āđāļāļāđāļĨāļ°āļĢāļĩāļ§āļīāļ§āđāļĄāđāđāļāđāļĢāļąāļāļāļēāļĢāļāļĢāļ§āļāļŠāļāļāļĒāļ·āļāļĒāļąāļ Â āļāļđāļāđāļāļĄāļđāļĨāđāļāļīāđāļĄāđāļāļīāļĄ
āđāļāļĩāđāļĒāļ§āļāļąāļ eBook āđāļĨāđāļĄāļāļĩāđ
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 âcourseâ 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 discoveryâparticipants 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 âIAS/PCMIâThe Teacher Program Seriesâ 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.
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 âcourseâ 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 discoveryâparticipants 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 âIAS/PCMIâThe Teacher Program Seriesâ 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.
āđāļāļĩāđāļĒāļ§āļāļąāļāļāļđāđāđāļāđāļ
Bowen Kerins: Education Development Center, Inc., Waltham, MA,
Darryl Yong: Harvey Mudd College, Pomona, CA,
Al Cuoco: Education Development Center, Inc., Waltham, MA,
Glenn Stevens: Boston University, Boston, MA,
Mary Pilgrim: Colorado State University, Fort Collins, CO
āđāļŦāđāļāļ°āđāļāļ eBook āļāļĩāđ
āđāļŠāļāļāļāļ§āļēāļĄāđāļŦāđāļāļāļāļāļāļļāļāđāļŦāđāđāļĢāļēāļĢāļąāļāļĢāļđāđ
āļāđāļāļĄāļđāļĨāđāļāļāļēāļĢāļāđāļēāļ
āļŠāļĄāļēāļĢāđāļāđāļāļāđāļĨāļ°āđāļāđāļāđāļĨāđāļ
āļāļīāļāļāļąāđāļāđāļāļ Google Play Books āļŠāļģāļŦāļĢāļąāļ Android āđāļĨāļ° iPad/iPhone āđāļāļāļāļ°āļāļīāļāļāđāđāļāļĒāļāļąāļāđāļāļĄāļąāļāļīāļāļąāļāļāļąāļāļāļĩāļāļāļāļāļļāļ āđāļĨāļ°āļāđāļ§āļĒāđāļŦāđāļāļļāļāļāđāļēāļāđāļāļāļāļāļāđāļĨāļāđāļŦāļĢāļ·āļāļāļāļāđāļĨāļāđāđāļāđāļāļļāļāļāļĩāđ
āđāļĨāđāļāļāđāļāļāđāļĨāļ°āļāļāļĄāļāļīāļ§āđāļāļāļĢāđ
āļāļļāļāļāļąāļāļŦāļāļąāļāļŠāļ·āļāđāļŠāļĩāļĒāļāļāļĩāđāļāļ·āđāļāļāļēāļ Google Play āđāļāļĒāđāļāđāđāļ§āđāļāđāļāļĢāļēāļ§āđāđāļāļāļĢāđāđāļāļāļāļĄāļāļīāļ§āđāļāļāļĢāđāđāļāđ
eReader āđāļĨāļ°āļāļļāļāļāļĢāļāđāļāļ·āđāļāđ
āļŦāļēāļāļāđāļāļāļāļēāļĢāļāđāļēāļāļāļāļāļļāļāļāļĢāļāđ e-ink āđāļāđāļ Kobo eReader āļāļļāļāļāļ°āļāđāļāļāļāļēāļ§āļāđāđāļŦāļĨāļāđāļĨāļ°āđāļāļāđāļāļĨāđāđāļāļĒāļąāļāļāļļāļāļāļĢāļāđāļāļāļāļāļļāļ āđāļāļĢāļāļāļģāļāļēāļĄāļ§āļīāļāļĩāļāļēāļĢāļāļĒāđāļēāļāļĨāļ°āđāļāļĩāļĒāļāđāļāļĻāļđāļāļĒāđāļāđāļ§āļĒāđāļŦāļĨāļ·āļāđāļāļ·āđāļāđāļāļāđāļāļĨāđāđāļāļĒāļąāļ eReader āļāļĩāđāļĢāļāļāļĢāļąāļ
