OMT - Tessellations

OntarioMathTeacher, Jun 9, 2016

A collection of Geogebra Applets to allow students to learn more about tessellations.

Table of Contents

  1. Escher's Tessellations
    1. Escher's Dog Tessellation
    2. Escherized Tessellation
    3. Escher's Lizard Tessellation
  2. Polygon Tessellations
    1. Two Right Tessellation
    2. A Tessellation
  3. Make your own tessellations
    1. Tessellation
    2. Triangle Tessellation
    3. Kite Tessellation
    4. Hexagon Tessellation
  4. Tessellations - from scratch
    1. Step 1: Deciding on a Tessellation Shape
    2. Step 2: Creating Midpoints and Line Segments
    3. Step 3: Creating a Star in the Middle
    4. Step 4: Starting to create the outer part of the tesselation
    5. Step 5: Completing Translations

1.

Escher's Tessellations

  • 1. Escher's Dog Tessellation
  • 2. Escherized Tessellation
  • 3. Escher's Lizard Tessellation

1.1.

Escher's Dog Tessellation

Escher's Dog Tessellation
– Duke

1.2.

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1.3.

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2.

Polygon Tessellations

  • 1. Two Right Tessellation
  • 2. A Tessellation

2.1.

Two Right Tessellation

Playing around with another Christopher Danielson tiling... His 60-90-120-90 kite has this neat overlapping squares tessellation with congruent squares for gaps... so nice! I realized playing with it that you just needed opposite 90 degree corners to get the effect. Such a sweet pattern. Do you see any other ways to generalize it?
– John Golden

2.2.

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3.

Make your own tessellations

  • 1. Tessellation
  • 2. Triangle Tessellation
  • 3. Kite Tessellation
  • 4. Hexagon Tessellation

3.1.

Tessellation

Drag the red points to change the shape of the square. Then slide the slider and observe what happens.
– Steve Phelps

3.2.

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3.3.

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3.4.

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4.

Tessellations - from scratch

  • 1. Step 1: Deciding on a Tessellation Shape
  • 2. Step 2: Creating Midpoints and Line Segments
  • 3. Step 3: Creating a Star in the Middle
  • 4. Step 4: Starting to create the outer part of the tesselation
  • 5. Step 5: Completing Translations

4.1.

Step 1: Deciding on a Tessellation Shape

Step 1 [br]Decide on a shape for your tessellation. In this procedure, we are going to use a regular hexagon. [br]To create this shape, click the box labeled "Polygon", and access the drop-down menu to find "Regular Polygon". [br]Click two places on the screen to create the bottom side of your shape. [br][br]When you complete this, move on to the next step.
Step 1: Deciding on a Tessellation Shape
– brittanyrowe

4.2.

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4.3.

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4.4.

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4.5.

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