My Geometry

Jila, Jun 5, 2017

This book contains a series worksheet that I used and will be using in teaching Geometry for Middle school teachers and History of Mathematics. Another free resource that accompanies this book is a Free Geometry for Middle school teachers' book that can be found at [url]https://drive.google.com/file/d/1Vrgtp_2TirYxz3qVDHa6uY-QwRgJyQvm/view [/url] Also available, only to Educators, is a series of iClicker type questions to match chapters of the Geometry book.

Table of Contents

  1. Euclidean
    1. Coming up with the definition of a circle.
    2. Pythagorean
    3. Pythagorean Proof Construction
  2. Transformations
    1. Three Reflection Lemma for Transformations
    2. Homework, Symmetries of different shapes.
    3. Homework, Symmetries of points and lines.
    4. Reflection over two intersecting lines.
    5. Composition of reflection with 90 degree rotation
    6. Two Reflection Transformations
  3. Tiling
    1. Tiling
    2. Regular Tessellations and Why Not Regular Pentagon?
    3. Interior Angles of Polygons
    4. Sum of the Angles
    5. Any Quadrilateral tiles the plane.
    6. Pentagonal Tilling Type 4, four equal side. (Most common type 4)
    7. Type 4 Pentagonal Tiling (General)
    8. Pentagonal Tiling Type I
    9. Quadrilateral Tiling
    10. Tile the plane with this Quadrilateral
    11. The triangle tiling
    12. Triangle-reflection-tiling
  4. Fun Projects
    1. Smiley, Move the slider back and forth.
  5. History
    1. Estimating the area of a circle using Hexagons
    2. Estimating the area of a circle, using squares
    3. Interactive Estimator
    4. Interactive estimator
    5. Trisection of an angle
    6. Drawing Limacons using Ancient Tools
    7. Drawing parabolas using ancient tools
    8. Drawing Hyperbola Using ancient tools
    9. Ellipse, Constructions with ancient tools
    10. Gerrymandering
    11. Khayyam Equation Calculator
    12. Khayam (possible changes)
    13. Infinite Cardinalities, N times N

1.

Euclidean

  • 1. Coming up with the definition of a circle.
  • 2. Pythagorean
  • 3. Pythagorean Proof Construction

1.1.

Coming up with the definition of a circle.

What is length of the radius? The distance between the center and a point on the circle. The distance stays the same. Try for a few circles by moving the slider. For each circle, try a few points on the circle (move X).
– Jila

1.2.

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1.3.

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2.

Transformations

  • 1. Three Reflection Lemma for Transformations
  • 2. Homework, Symmetries of different shapes.
  • 3. Homework, Symmetries of points and lines.
  • 4. Reflection over two intersecting lines.
  • 5. Composition of reflection with 90 degree rotation
  • 6. Two Reflection Transformations

2.1.

Three Reflection Lemma for Transformations

Find the three reflections that takes the first triangle to the second triangle.[br]Make sure that your construction is not distructable easily. (If I move the triangles, the construction should still work.)[br]Write out the proof of lemma. (You will need the three points transformation lemma.)
– Jila

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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3.

Tiling

  • 1. Tiling
  • 2. Regular Tessellations and Why Not Regular Pentagon?
  • 3. Interior Angles of Polygons
  • 4. Sum of the Angles
  • 5. Any Quadrilateral tiles the plane.
  • 6. Pentagonal Tilling Type 4, four equal side. (Most common type 4)
  • 7. Type 4 Pentagonal Tiling (General)
  • 8. Pentagonal Tiling Type I
  • 9. Quadrilateral Tiling
  • 10. Tile the plane with this Quadrilateral
  • 11. The triangle tiling
  • 12. Triangle-reflection-tiling

3.1.

Tiling

– Jila

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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3.12.

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4.

Fun Projects

  • 1. Smiley, Move the slider back and forth.

4.1.

Smiley, Move the slider back and forth.

Move the slider to see the animation.
– Jila

5.

History

  • 1. Estimating the area of a circle using Hexagons
  • 2. Estimating the area of a circle, using squares
  • 3. Interactive Estimator
  • 4. Interactive estimator
  • 5. Trisection of an angle
  • 6. Drawing Limacons using Ancient Tools
  • 7. Drawing parabolas using ancient tools
  • 8. Drawing Hyperbola Using ancient tools
  • 9. Ellipse, Constructions with ancient tools
  • 10. Gerrymandering
  • 11. Khayyam Equation Calculator
  • 12. Khayam (possible changes)
  • 13. Infinite Cardinalities, N times N

5.1.

Estimating the area of a circle using Hexagons

– Jila

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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5.9.

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5.10.

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5.11.

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5.12.

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5.13.

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