Geometr

Tim Brzezinski, Алтангэрэлийн Ууганбаяр, Apr 16, 2021

Table of Contents

  1. Perimeter, Area, Volume
    1. Unit Squares: Multipurpose Template
    2. Constructing Rectangles: Open Middle Problem
    3. Composite Figure Template
    4. TRUE MEANING of π
    5. Circumference = ? (Animation)
    6. Animation 66
    7. Circumference = ? (Animation II)
    8. Animation 70
    9. Animation 65
    10. Parallelogram: Area
    11. Building Parallelograms with Given Area: Quick Formative Assessment
    12. Animation 202
    13. Area of a Rhombus
    14. Triangle Area Action! (V1)
    15. Triangle Area Action!!! (V2)
    16. Animation 175
    17. Create a Triangle with Given Area: Quick Formative Assessment
    18. Create a Triangle with Given Area (V2)
    19. Open Middle: Area of a House
    20. Open Middle: Trapezoid Area Problem
    21. Open Middle Trapezoid Area Problem: Choose Your Own Fixed Perimeter
    22. Create a Trapezoid with Given Area: Quick Formative Assessment
    23. Circle Area (by Peeling)
    24. Circle Area (By Peeling!)
    25. Area of a Circle - without words (Animation 38)
    26. Area of a Circle (III)
    27. Area of a Circle (by Peeling)
    28. Area of a Circle II
    29. Classic Cow Grazing Problem
    30. Build a Circle: Radius, Diameter, Circumference, Area
    31. Segment Area: Quick Investigation
    32. Cavalieri's Principle
    33. Cavalieri's Principle
    34. Figure 6.7 Cavalieri's principle
    35. Mailbox? Backpack? (Composite Solid)
    36. Washer Action!!! (1)
    37. Animation 169
    38. Trisecting the Cube into 3 Pyramids
    39. Volume of Pyramids
    40. Volume of Pyramids - Chinese Proof
    41. SolveMyMaths Action 3A!
    42. SolveMyMaths Action 3B!
    43. Animation 203
    44. SolveMyMaths Action 4!
    45. Animation 204
    46. 4 Triangles Action!!!
    47. Animation 179
    48. Open Middle: Maximizing Rectangular Prism Surface Area
    49. Maximizing Surface Area: Open Middle Cube Problem (V1)
    50. Maximizing Surface Area: Open Middle Cube Problem (V2)
    51. Open Middle (Revamped): Creating Rectangular Prisms with a Given Surface Area
  2. More with volume
    1. Unwrapping a Cylinder
    2. Unwrapping a Cylinder: REVAMPED!
    3. Volume of Spheres
    4. Volume of Spheres with Proof
    5. A sphere in a cylinder.
    6. Surface Area of Spheres
    7. Volumes and Surface Areas of Similar Cuboids
    8. Square Pyramid: Underlying Anatomy
    9. Cone Anatomy
    10. oblique and right pyramid - Cavalieri
    11. Build Your Own Right Triangular Prism (V2)!
    12. Build Your Own Right Triangular Prism!
    13. Right Triangular Prism!
    14. Adjustable Triangular Prism
    15. Sphere Peeling: Volume
    16. Net of a Cone
    17. Curved Surface Area of Cones (Combined Version)
    18. Volume of a Rectangular Prism
  3. 2D to 3D and Cross Section
    1. Rotating 2D Graphs about Lines to Create 3D Surfaces of Revolution in GeoGebra AR
    2. Surface of Revolution: GeoGebra Augmented Reality Template
    3. Sphere + Plane = ?
    4. Sections of Rectangular Prisms (Cuboids)
    5. Sections of Triangular Prisms
    6. Sections of Cylinders
    7. Sections of Rectangular Pyramids
    8. Sections of Triangular Pyramids
    9. Sections of Cones
    10. Sections of Spheres
    11. Exploring Sections of Cubes
    12. 11 Nets of the Cube
    13. Cube Geometry: Shortest Path Between Points - A Net
    14. Cube Dissection Problem
    15. Rotating a Triangle Around a Coordinate Axis
    16. Box with Open Top
    17. Cross Section? (1)
    18. Surface of Revolution Template
    19. Surface with Square Cross Sections
  4. Forming Surfaces of Revolution (V1)
    1. Creating Surfaces of Revolution
    2. Part 1
    3. Part 2
    4. Part 3
  5. Forming Surfaces of Revolution (V2)
    1. 2D to 3D: What's Going On? (Part 1)
    2. 2D to 3D: What's Going On? (Part 2)
    3. 2D to 3D: What's Going On? (Part 3)
    4. 2D to 3D: What's Going On? (Part 4)
    5. 2D to 3D: What's Going On? (Part 5)
    6. 2D to 3D: What's Going On? (Part 6)
  6. Other Geometry Resources
    1. Geometry Resources

1.

Perimeter, Area, Volume

  • 1. Unit Squares: Multipurpose Template
  • 2. Constructing Rectangles: Open Middle Problem
  • 3. Composite Figure Template
  • 4. TRUE MEANING of π
  • 5. Circumference = ? (Animation)
  • 6. Animation 66
  • 7. Circumference = ? (Animation II)
  • 8. Animation 70
  • 9. Animation 65
  • 10. Parallelogram: Area
  • 11. Building Parallelograms with Given Area: Quick Formative Assessment
  • 12. Animation 202
  • 13. Area of a Rhombus
  • 14. Triangle Area Action! (V1)
  • 15. Triangle Area Action!!! (V2)
  • 16. Animation 175
  • 17. Create a Triangle with Given Area: Quick Formative Assessment
  • 18. Create a Triangle with Given Area (V2)
  • 19. Open Middle: Area of a House
  • 20. Open Middle: Trapezoid Area Problem
  • 21. Open Middle Trapezoid Area Problem: Choose Your Own Fixed Perimeter
  • 22. Create a Trapezoid with Given Area: Quick Formative Assessment
  • 23. Circle Area (by Peeling)
  • 24. Circle Area (By Peeling!)
  • 25. Area of a Circle - without words (Animation 38)
  • 26. Area of a Circle (III)
  • 27. Area of a Circle (by Peeling)
  • 28. Area of a Circle II
  • 29. Classic Cow Grazing Problem
  • 30. Build a Circle: Radius, Diameter, Circumference, Area
  • 31. Segment Area: Quick Investigation
  • 32. Cavalieri's Principle
  • 33. Cavalieri's Principle
  • 34. Figure 6.7 Cavalieri's principle
  • 35. Mailbox? Backpack? (Composite Solid)
  • 36. Washer Action!!! (1)
  • 37. Animation 169
  • 38. Trisecting the Cube into 3 Pyramids
  • 39. Volume of Pyramids
  • 40. Volume of Pyramids - Chinese Proof
  • 41. SolveMyMaths Action 3A!
  • 42. SolveMyMaths Action 3B!
  • 43. Animation 203
  • 44. SolveMyMaths Action 4!
  • 45. Animation 204
  • 46. 4 Triangles Action!!!
  • 47. Animation 179
  • 48. Open Middle: Maximizing Rectangular Prism Surface Area
  • 49. Maximizing Surface Area: Open Middle Cube Problem (V1)
  • 50. Maximizing Surface Area: Open Middle Cube Problem (V2)
  • 51. Open Middle (Revamped): Creating Rectangular Prisms with a Given Surface Area

1.1.

Unit Squares: Multipurpose Template

Choose any number of squares from 1-60. You can move these squares around.
Choose any number of squares from 1-60. You can move these squares around.
Choose any number of squares from 1-60. You can move these squares around.
Choose any number of squares from 1-60. You can move these squares around.
– Tim Brzezinski

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2.

More with volume

  • 1. Unwrapping a Cylinder
  • 2. Unwrapping a Cylinder: REVAMPED!
  • 3. Volume of Spheres
  • 4. Volume of Spheres with Proof
  • 5. A sphere in a cylinder.
  • 6. Surface Area of Spheres
  • 7. Volumes and Surface Areas of Similar Cuboids
  • 8. Square Pyramid: Underlying Anatomy
  • 9. Cone Anatomy
  • 10. oblique and right pyramid - Cavalieri
  • 11. Build Your Own Right Triangular Prism (V2)!
  • 12. Build Your Own Right Triangular Prism!
  • 13. Right Triangular Prism!
  • 14. Adjustable Triangular Prism
  • 15. Sphere Peeling: Volume
  • 16. Net of a Cone
  • 17. Curved Surface Area of Cones (Combined Version)
  • 18. Volume of a Rectangular Prism

2.1.

Unwrapping a Cylinder

– Tim Brzezinski

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3.

2D to 3D and Cross Section

  • 1. Rotating 2D Graphs about Lines to Create 3D Surfaces of Revolution in GeoGebra AR
  • 2. Surface of Revolution: GeoGebra Augmented Reality Template
  • 3. Sphere + Plane = ?
  • 4. Sections of Rectangular Prisms (Cuboids)
  • 5. Sections of Triangular Prisms
  • 6. Sections of Cylinders
  • 7. Sections of Rectangular Pyramids
  • 8. Sections of Triangular Pyramids
  • 9. Sections of Cones
  • 10. Sections of Spheres
  • 11. Exploring Sections of Cubes
  • 12. 11 Nets of the Cube
  • 13. Cube Geometry: Shortest Path Between Points - A Net
  • 14. Cube Dissection Problem
  • 15. Rotating a Triangle Around a Coordinate Axis
  • 16. Box with Open Top
  • 17. Cross Section? (1)
  • 18. Surface of Revolution Template
  • 19. Surface with Square Cross Sections

3.1.

Rotating 2D Graphs about Lines to Create 3D Surfaces of Revolution in GeoGebra AR

Students & Teachers with ARCore by Google Installed on Your Devices:
Here's how you can create a 3D surface by rotating the graph of ANY function about the xAxis within [url=https://play.google.com/store/apps/details?id=org.geogebra.android.g3d]GeoGebra's 3D Graphing Calculator app[/url]. (This screencast was recorded on an ACER Chrome Tab 10.) [br][br]For more information re: getting started with GeoGebra Augmented Reality, [url=https://www.geogebra.org/m/jhcywuqw]click here[/url].
Quick Demo
Now, press the [b]AR [/b]button (lower right) to explore this within GeoGebra Augmented Reality! [br][br]Once viewing in Augmented Reality, slide the slider slowly. You should see a surface of revolution form!
Here's what this surface looks like in GeoGebra Augmented Reality!
For further exploration:
[b]Note[/b]:[br][br]If interested, you can use this pre-made template [url=https://www.geogebra.org/m/qbxbcmqw#material/yt22anmh]that can be found here[/url]. [br]Follow the directions on this page to open in the [color=#1e84cc]GeoGebra 3D Graphing Calculator[/color] on your device. [br][br]1) Instead of f(x) = 3, try typing [math]f\left(x\right)=x,0\le x\le4[/math] (just the way you see it). Spin this graph about the [br] xAxis. What kind of solid do you get? [br][br]2) Same direction as in (1), but do this time for [math]f\left(x\right)=x,2\le x\le4[/math]. What do you get now? [br][br]3) Same direction as in (1), but do this time for [math]f\left(x\right)=0.5x^2,0\le x\le2[/math] . What does this look like? [br][br]4) What other kinds of 3D surfaces of revolution can we create this way? [br] Let your creativity take you places!
Another demo: Modeling a bowl
– Tim Brzezinski

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4.

Forming Surfaces of Revolution (V1)

  • 1. Creating Surfaces of Revolution
  • 2. Part 1
  • 3. Part 2
  • 4. Part 3

4.1.

Creating Surfaces of Revolution

[b]Exploring Surfaces of Revolution: Exploration (in 3 parts):[/b][br][list][*][url=https://www.geogebra.org/m/tcnajqm2]2D to 3D: What Can You Create?[/url][/*][/list]
– Tim Brzezinski

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5.

Forming Surfaces of Revolution (V2)

  • 1. 2D to 3D: What's Going On? (Part 1)
  • 2. 2D to 3D: What's Going On? (Part 2)
  • 3. 2D to 3D: What's Going On? (Part 3)
  • 4. 2D to 3D: What's Going On? (Part 4)
  • 5. 2D to 3D: What's Going On? (Part 5)
  • 6. 2D to 3D: What's Going On? (Part 6)

5.1.

2D to 3D: What's Going On? (Part 1)

In the app below, the 2D figure you see on the left is the same as the 2D figure you see on the right.
Slide the slider (lower left) all the way to the right.
What do you see happening here? Describe as best you can in your own words.
– Tim Brzezinski

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6.

Other Geometry Resources

  • 1. Geometry Resources

6.1.

Geometry Resources

[list][*][b][url=https://www.geogebra.org/m/z8nvD94T]Congruence (Volume 1)[/url][/b][/*][*][b][url=https://www.geogebra.org/m/munhXmzx]Congruence (Volume 2)[/url][/b][/*][*][b][url=https://www.geogebra.org/m/dPqv8ACE]Similarity, Right Triangles, Trigonometry[/url][/b][/*][*][b][url=https://www.geogebra.org/m/C7dutQHh]Circles[/url][/b][/*][*][b][url=https://www.geogebra.org/m/K2YbdFk8]Coordinate and Analytic Geometry[/url][/b][/*][*][b][url=https://www.geogebra.org/m/xDNjSjEK]Area, Surface Area, Volume, 3D, Cross Section[/url] [/b][/*][*][b][url=https://www.geogebra.org/m/NjmEPs3t]Proof Challenges[/url]  [/b][/*][/list]
What phenomenon is dynamically being illustrated here? (Vertices are moveable.)
What phenomenon is dynamically being illustrated here? (Vertices are moveable.)
– Tim Brzezinski

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