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Fractions, Tilings, and Geometry
 
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
A co-publication of the AMS and IAS/Park City Mathematics Institute
Fractions, Tilings, and Geometry
Softcover ISBN:  978-1-4704-4064-0
Product Code:  SSTP/7
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $36.00
eBook ISBN:  978-1-4704-4340-5
Product Code:  SSTP/7.E
List Price: $35.00
MAA Member Price: $31.50
AMS Member Price: $28.00
Softcover ISBN:  978-1-4704-4064-0
eBook: ISBN:  978-1-4704-4340-5
Product Code:  SSTP/7.B
List Price: $80.00 $62.50
MAA Member Price: $72.00 $56.25
AMS Member Price: $64.00 $50.00
Fractions, Tilings, and Geometry
Click above image for expanded view
Fractions, Tilings, and Geometry
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
A co-publication of the AMS and IAS/Park City Mathematics Institute
Softcover ISBN:  978-1-4704-4064-0
Product Code:  SSTP/7
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $36.00
eBook ISBN:  978-1-4704-4340-5
Product Code:  SSTP/7.E
List Price: $35.00
MAA Member Price: $31.50
AMS Member Price: $28.00
Softcover ISBN:  978-1-4704-4064-0
eBook ISBN:  978-1-4704-4340-5
Product Code:  SSTP/7.B
List Price: $80.00 $62.50
MAA Member Price: $72.00 $56.25
AMS Member Price: $64.00 $50.00
  • Book Details
     
     
    IAS/PCMI--The Teacher Program Series
    Volume: 72017; 157 pp
    MSC: Primary 00;

    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.

  • Table of Contents
     
     
    • Contents
    • Preface
    • Chapter 1: Problem Sets
    • Chapter 2: Facilitator Notes
    • Chapter 3: Solutions
  • Additional Material
     
     
  • Reviews
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 72017; 157 pp
MSC: Primary 00;

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.

  • Contents
  • Preface
  • Chapter 1: Problem Sets
  • Chapter 2: Facilitator Notes
  • Chapter 3: Solutions
  • 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.