Math 490, Spring 2021

Kellie Evans, 2021. 1. 28.

GeoGebra demos for Spring 2021

차례

  1. Triangles, Trig, and Tech
    1. Construct a triangle with the given side lengths
    2. Triangle Side Lengths (visualize Triangle Inequality)
    3. Triangle with given side lengths
    4. Angle sum triangle
    5. Triangle Angle Sum Theorem
    6. Angle sum triangle explanation
    7. Pythagorean theorem
    8. Law of Cosines
    9. Law of Sines
    10. Inscribed and central angles of a circle.
    11. Ptolemy
    12. Outline of proof of Ptolemy's theorem
    13. Graphs of cosine and sine from unit circle
  2. Congruence
    1. ASA Triangle Congruence
    2. SAS Triangle Congruence
    3. SSS Triangle Congruence
    4. SAS Triangle Congruence
    5. Are the parallelograms congruent?
  3. Similarity
    1. Are the triangles similar? (Given: AA)
  4. Golden Rectangles and Golden Triangles
    1. Use transformations to show the rectangle is golden.
    2. Golden Triangle
    3. Golden Triangle and Similarity
  5. pi
    1. Area of Circles
    2. Archimedes' polygons
    3. Digits of pi
    4. Approximate pi Newton's way
    5. Estimate Pi
    6. Monte Carlo method to approximate pi.
    7. Pi Turtles
    8. Visualize regular n-gon and 2n-gon
    9. Pi Data Math 490 S21
  6. e
    1. What is e?
  7. Probability
    1. Monty Hall Problem: Simulation
    2. (Generalized) Birthday Problem Calculator
    3. Pascal's triangle
  8. De Moivre's formula
    1. Pascal's triangle
    2. De Moivre's formula calculator
    3. Straightedge and Compass Constructions
  9. Geometric Transformations
    1. Matrix Transformation
    2. Rotate standard basis vectors in counterclockwise direction
    3. Reflection of standard basis vectors about a given line
    4. ASA Triangle Congruence Theorem
    5. SSS Triangle Congruence
  10. Sample Activities
    1. Warm-up Activity
  11. Straightedge and Compass Constructions
    1. What CAN you construct with straightedge and compass only?
    2. Student Construction: What length does it give?

1.

Triangles, Trig, and Tech

  • 1. Construct a triangle with the given side lengths
  • 2. Triangle Side Lengths (visualize Triangle Inequality)
  • 3. Triangle with given side lengths
  • 4. Angle sum triangle
  • 5. Triangle Angle Sum Theorem
  • 6. Angle sum triangle explanation
  • 7. Pythagorean theorem
  • 8. Law of Cosines
  • 9. Law of Sines
  • 10. Inscribed and central angles of a circle.
  • 11. Ptolemy
  • 12. Outline of proof of Ptolemy's theorem
  • 13. Graphs of cosine and sine from unit circle

1.1.

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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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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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2.

Congruence

  • 1. ASA Triangle Congruence
  • 2. SAS Triangle Congruence
  • 3. SSS Triangle Congruence
  • 4. SAS Triangle Congruence
  • 5. Are the parallelograms congruent?

2.1.

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2.2.

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2.3.

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2.4.

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2.5.

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3.

Similarity

  • 1. Are the triangles similar? (Given: AA)

3.1.

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4.

Golden Rectangles and Golden Triangles

  • 1. Use transformations to show the rectangle is golden.
  • 2. Golden Triangle
  • 3. Golden Triangle and Similarity

4.1.

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4.2.

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4.3.

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5.

pi

  • 1. Area of Circles
  • 2. Archimedes' polygons
  • 3. Digits of pi
  • 4. Approximate pi Newton's way
  • 5. Estimate Pi
  • 6. Monte Carlo method to approximate pi.
  • 7. Pi Turtles
  • 8. Visualize regular n-gon and 2n-gon
  • 9. Pi Data Math 490 S21

5.1.

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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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6.

e

  • 1. What is e?

6.1.

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7.

Probability

  • 1. Monty Hall Problem: Simulation
  • 2. (Generalized) Birthday Problem Calculator
  • 3. Pascal's triangle

7.1.

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7.2.

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7.3.

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8.

De Moivre's formula

  • 1. Pascal's triangle
  • 2. De Moivre's formula calculator
  • 3. Straightedge and Compass Constructions

8.1.

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8.2.

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8.3.

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9.

Geometric Transformations

  • 1. Matrix Transformation
  • 2. Rotate standard basis vectors in counterclockwise direction
  • 3. Reflection of standard basis vectors about a given line
  • 4. ASA Triangle Congruence Theorem
  • 5. SSS Triangle Congruence

9.1.

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9.2.

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9.3.

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9.4.

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9.5.

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10.

Sample Activities

  • 1. Warm-up Activity

10.1.

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11.

Straightedge and Compass Constructions

  • 1. What CAN you construct with straightedge and compass only?
  • 2. Student Construction: What length does it give?

11.1.

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11.2.

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정보