Use Cases of GeoGebra

Guillermo Bautista, Mar 3, 2023

Table of Contents

  1. Demonstrations
    1. Multiplication of Fractions
    2. (a + b) cubed
    3. Inscribed and Circumscribed Polygons
    4. Amplitude, Period, and Midline
  2. Interactive Exercises
    1. Representing Fractions Part 1
    2. Prime and Composite Numbers
    3. Write Down the Coordinates
    4. Find the Equation of the Line
  3. Fun and Games
    1. Pop that Balloon 1
    2. Sink that Ship (Large Screen)
  4. Visual Proofs
    1. Making Conjectures and Proofs in GeoGebra
    2. Sum of First n Odd Numbers
    3. Pythagorean Theorem Proof Without Words
  5. AR and 3D Models
    1. Incandescent Light Bulb
    2. 3D Three-Fold Umbrella (version 2)
    3. Hilbert's Cube
    4. 3d Drone Version 2
    5. Desk Fan (3D)
  6. Art and Aesthetics
    1. Multicolored Butterfly
    2. GeoGebra Gown
    3. Butterfly Curve
  7. Simulations
    1. Dice Roll Simulation
    2. Projectile Motion
    3. Revolution of Planets (3D)
  8. Lessons
    1. Forming Rectangles with Squares
    2. Factors and Factorization
    3. Searching for Factorizations
    4. Prime and Composite Numbers
    5. Summary and Practice Exercise

1.

Demonstrations

  • 1. Multiplication of Fractions
  • 2. (a + b) cubed
  • 3. Inscribed and Circumscribed Polygons
  • 4. Amplitude, Period, and Midline

1.1.

Multiplication of Fractions

Inspired by: https://www.geogebra.org/m/kyaj6M7r
– Guillermo Bautista

1.2.

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1.3.

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1.4.

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2.

Interactive Exercises

  • 1. Representing Fractions Part 1
  • 2. Prime and Composite Numbers
  • 3. Write Down the Coordinates
  • 4. Find the Equation of the Line

2.1.

Representing Fractions Part 1

– Guillermo Bautista

2.2.

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2.3.

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2.4.

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3.

Fun and Games

  • 1. Pop that Balloon 1
  • 2. Sink that Ship (Large Screen)

3.1.

Pop that Balloon 1

Pop the balloon by locating its coordinates.
Concept: Truls Cronberg
– Guillermo Bautista

3.2.

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4.

Visual Proofs

  • 1. Making Conjectures and Proofs in GeoGebra
  • 2. Sum of First n Odd Numbers
  • 3. Pythagorean Theorem Proof Without Words

4.1.

Making Conjectures and Proofs in GeoGebra

Move points A, C, B, and slider [math]\alpha[/math] to investigate the figure.
Credit. Dr. Soledad Ulep
– Guillermo Bautista

4.2.

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4.3.

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5.

AR and 3D Models

  • 1. Incandescent Light Bulb
  • 2. 3D Three-Fold Umbrella (version 2)
  • 3. Hilbert's Cube
  • 4. 3d Drone Version 2
  • 5. Desk Fan (3D)

5.1.

Incandescent Light Bulb

The light bulb below was created mainly using elementary functions. The curves in the 2D view are functions except for the three vertical line segments. All the components of the light bulb (except the filament) were created in the 2D view and then rotated about the x-axis in the 3D view. The filament was created in the 3D view using a helix.
Inspired by this [url=https://i1.wp.com/edisonlightglobes.com/120V/wp-content/uploads/2013/06/80mm-spiral-round.jpg?fit=800%2C800&ssl=1]l[/url][url=https://i1.wp.com/edisonlightglobes.com/120V/wp-content/uploads/2013/06/80mm-spiral-round.jpg?fit=800%2C800&ssl=1]ight bulb[/url].
– Guillermo Bautista

5.2.

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5.3.

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5.4.

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5.5.

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6.

Art and Aesthetics

  • 1. Multicolored Butterfly
  • 2. GeoGebra Gown
  • 3. Butterfly Curve

6.1.

Multicolored Butterfly

Reference
Inspired by: https://qph.fs.quoracdn.net/main-qimg-0d772d5a5ab4573c6630b03c33dece05[br]Ellipse Equation: https://math.stackexchange.com/questions/426150/what-is-the-general-equation-of-the-ellipse-that-is-not-in-the-origin-and-rotate
– Guillermo Bautista

6.2.

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6.3.

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7.

Simulations

  • 1. Dice Roll Simulation
  • 2. Projectile Motion
  • 3. Revolution of Planets (3D)

7.1.

Dice Roll Simulation

– Guillermo Bautista

7.2.

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7.3.

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8.

Lessons

  • 1. Forming Rectangles with Squares
  • 2. Factors and Factorization
  • 3. Searching for Factorizations
  • 4. Prime and Composite Numbers
  • 5. Summary and Practice Exercise

8.1.

Forming Rectangles with Squares

A [b]unit square[/b] is a square with a side length of 1 unit. The rectangle below was formed using 6 unit squares. Its dimensions are 1 unit × 6 units or simply 1 × 6.[br]
TASK
Using the [b][color=#93c47d]Square tool[/color][/b], form as many rectangles as you can using [b]exactly[/b] 6 unit squares.[br]
Question 1
What are the dimensions of the rectangles that you have formed?
Question 2
We know that a 1 × 6 and a 6 × 1 rectangle are just the same rectangle (Why?), so we can count them as [b]one rectangle[/b]. Now that we know this, how many rectangles can we form if we use exactly 6 unit squares?
Question 3
How many rectangles can we form if we only use exactly 5 squares?
– Guillermo Bautista

8.2.

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8.3.

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8.4.

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8.5.

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Information