Making Mathematics Visible: Forty-Sixth Annual Conference

Steve Phelps, Sep 8, 2018

This is the GeoGebra Book for my presentation Visualizing Modular Multiplication Tables Through Curve Stitching at Miami University in Oxford, Ohio, USA. [url]http://miamioh.edu/cas/academics/departments/mathematics/about/events/annual-mathematics-conference/index.html [/url] https://tinyurl.com/miamimmv

Table of Contents

  1. Motivation
    1. The Vortex
    2. A New Way to Knit
    3. Emmanuel Maths Curve Stitching
    4. The Haze
    5. Rings and Strings
    6. A Look into Heaven
    7. The Art of Problem Posing
    8. This Presentation
  2. Simple curve stitching
    1. The Simplest Curve Stitch
    2. Curve Stitching and Transformations 1
    3. Curve Stitching and Transformations 2
    4. Curve Stitching and Transformations 3
    5. Curve Stitching and Transformations 4
    6. Curve Stitching and Transformations 5
    7. Curve Stitching with Variable Spacing
    8. Curve Stitching With Semicircles
    9. Curve Stitching with Polygons
  3. Modular addition curve stitching
    1. Curve Stitching mod 13
    2. Curve Stitching mod 17
    3. Modular Addition for Selected Mods
    4. Modular Addition in 3D
    5. Modular Addition for Selected Mods and Inversion
    6. Modular Addition in a Triangle
  4. Modular multiplication curve stitching
    1. Curve Stitching mod 13
    2. Curve Stitching mod 17
    3. Curve Stitching mod 24
  5. Modular multiplication: The doubling map
    1. The Doubling Map for Selected Mods
    2. Rolling Circle
    3. Reflecting Light Rays
    4. Complex Numbers Squaring Map
  6. Modular multiplication: The tripling map
    1. The Tripling Map for Selected Mods
    2. Rolling Circle Tripling Map
    3. Reflecting Light Rays Tripling Map
    4. Complex Number Tripling Map
  7. What-If-Not Modular Curve Stitching
    1. Different Maps for Selected Mods
    2. Continuous Multiples for Selected Mods
    3. Different Multiples, Selected Mods, with Inversion
    4. Different Functions for mod 360

1.

Motivation

  • 1. The Vortex
  • 2. A New Way to Knit
  • 3. Emmanuel Maths Curve Stitching
  • 4. The Haze
  • 5. Rings and Strings
  • 6. A Look into Heaven
  • 7. The Art of Problem Posing
  • 8. This Presentation

1.1.

The Vortex

– Steve Phelps

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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2.

Simple curve stitching

  • 1. The Simplest Curve Stitch
  • 2. Curve Stitching and Transformations 1
  • 3. Curve Stitching and Transformations 2
  • 4. Curve Stitching and Transformations 3
  • 5. Curve Stitching and Transformations 4
  • 6. Curve Stitching and Transformations 5
  • 7. Curve Stitching with Variable Spacing
  • 8. Curve Stitching With Semicircles
  • 9. Curve Stitching with Polygons

2.1.

The Simplest Curve Stitch

– Steve Phelps

2.2.

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2.3.

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2.4.

–

2.5.

–

2.6.

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2.7.

–

2.8.

–

2.9.

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3.

Modular addition curve stitching

  • 1. Curve Stitching mod 13
  • 2. Curve Stitching mod 17
  • 3. Modular Addition for Selected Mods
  • 4. Modular Addition in 3D
  • 5. Modular Addition for Selected Mods and Inversion
  • 6. Modular Addition in a Triangle

3.1.

Curve Stitching mod 13

– Steve Phelps

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

4.

Modular multiplication curve stitching

  • 1. Curve Stitching mod 13
  • 2. Curve Stitching mod 17
  • 3. Curve Stitching mod 24

4.1.

– Steve Phelps

4.2.

–

4.3.

–

5.

Modular multiplication: The doubling map

  • 1. The Doubling Map for Selected Mods
  • 2. Rolling Circle
  • 3. Reflecting Light Rays
  • 4. Complex Numbers Squaring Map

5.1.

The Doubling Map for Selected Mods

– Steve Phelps

5.2.

–

5.3.

–

5.4.

–

6.

Modular multiplication: The tripling map

  • 1. The Tripling Map for Selected Mods
  • 2. Rolling Circle Tripling Map
  • 3. Reflecting Light Rays Tripling Map
  • 4. Complex Number Tripling Map

6.1.

The Tripling Map for Selected Mods

– Steve Phelps

6.2.

–

6.3.

–

6.4.

–

7.

What-If-Not Modular Curve Stitching

  • 1. Different Maps for Selected Mods
  • 2. Continuous Multiples for Selected Mods
  • 3. Different Multiples, Selected Mods, with Inversion
  • 4. Different Functions for mod 360

7.1.

Different Maps for Selected Mods

– Steve Phelps

7.2.

–

7.3.

–

7.4.

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Information