Transformations

John Golden, Feb 18, 2018

Euclidean motions and dilations.

Table of Contents

  1. Introduction
    1. Handy Intro to Motions
    2. Motion Introduction
    3. Jump Turn
    4. Motion Control
    5. Wallpaper Groups
    6. Transformations With Coordinates
  2. Reflection
    1. Face Symmetry
    2. Flip Flop
    3. Make a Flake
  3. Translation
  4. Rotation
    1. Escherized Tessellation
    2. Two Rotations
    3. Escherized Double Rotations
    4. Escherized Pentagons
  5. Glide Reflection
    1. Tessellation
  6. Dilation
    1. Pantograph
    2. Gigantotron
    3. Dilation Game
    4. Trapezoidal Dilation Tessellation

1.

Introduction

  • 1. Handy Intro to Motions
  • 2. Motion Introduction
  • 3. Jump Turn
  • 4. Motion Control
  • 5. Wallpaper Groups
  • 6. Transformations With Coordinates

1.1.

Handy Intro to Motions

There are four basic motions. Three that everyone knows about and a fourth neglected colleague. This sketch shows the motions and the information needed to describe the motion. How would you describe each motion? What do you notice about them? What do you wonder about if it might be true?

More GeoGebra at [url]mathhombre.blogspot.com[/url]
– John Golden

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1.4.

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1.5.

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1.6.

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2.

Reflection

  • 1. Face Symmetry
  • 2. Flip Flop
  • 3. Make a Flake

2.1.

Face Symmetry

Face Symmetry. Inspired by a Mathalicious lesson, developed with help from Jennifer Silverman, Audrey McLaren and Jed Butler. In preparation for GeoGebra Chat 3; #ggbchat on Twitter. http://ggbchat.wordpress.com/ How symmetrical is Jennifer Lawrence's face?

#ggbchat 3 More GeoGebra at [url]mathhombre.blogspot.com/p/geogebra.html[/url]
– John Golden

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3.

Translation


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4.

Rotation

  • 1. Escherized Tessellation
  • 2. Two Rotations
  • 3. Escherized Double Rotations
  • 4. Escherized Pentagons

4.1.

Escherized Tessellation

What can you tell about this tessellation?[br]What motions move one tile onto its neighbor?[br]What is the underlying shape before it was modified? How do you know?
Escherized Tessellation
More GeoGebra at [url]mathhombre.blogspot.com[/url].[br]Base tessellation at [url]http://www.geogebratube.org/material/show/id/28859[/url]
– John Golden

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5.

Glide Reflection

  • 1. Tessellation

5.1.

Tessellation

What will happen as you move the vertices? What are the motions? What is the base shape?[br][br]What can you make the tiles look like?
– John Golden

6.

Dilation

  • 1. Pantograph
  • 2. Gigantotron
  • 3. Dilation Game
  • 4. Trapezoidal Dilation Tessellation

6.1.

Pantograph

This sketch is inspired by a lesson taught by Keegan Ferris and Becky Simon working with Paul Yu.[br]See:[br][url]http://gvsujenison.weebly.com/[/url][br][url]http://beckysimon23.wordpress.com/2014/03/20/teaching-technology-lessons/[/url][br][url]http://ferrisksite.wordpress.com/2014/03/28/incorporating-technology-into-math-ed-lessons/[/url][br]and the pantograph sketch they used from LingguoBu[br][url]http://www.geogebratube.org/material/show/id/1515[/url][br][br]Like LingguoBu's sketch, this lets you change the proportions in the pantograph. (Click on the Settings checkbox) Does the pantograph always draw similar figures? How can you tell? How do the settings relate to scale factor or magnitude?
Pantograph
More GeoGebra at [url]mathhombre.blogspot.com[/url]
– John Golden

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Information