BJH Geogebra Book

bjhenders88, Apr 7, 2014

Table of Contents

  1. Chapter 1
    1. Complex Mapping of Parametric Curve
    2. Sequences in GeoGebra
    3. Matrices Used To Generate Fibonacci Sequence
    4. Triangle de Sierpinski.
    5. Fractales lineales
    6. Penrose -Escher Triangle
    7. Graphing Complex Solutions
    8. Complex analysis: equations
    9. A complex thing made simple with GeoGebra
    10. Transform Fourier 3
    11. Transform Fourier 1
    12. Transform Fourier 2
    13. Pythagoras Waves
    14. Complex Numbers and Transformations
    15. Copy of zentangle
    16. Copy of Locus Examples
    17. Pythagoras Waves
    18. Polar Cartesian Comparison
  2. Geometry of Euclidian Space
    1. Addition of vectors
    2. Scalar multiplication
    3. Vector product
    4. Plotting 3D surfaces
    5. Parametric surfaces
    6. Klein bottle
  3. Vector-Valued Functions
    1. Vector fields in 2D
    2. Vector field 3D
    3. Dynamic Frenet-Serret frame
    4. Vector Fields
    5. Divergence and Curl calculator
  4. Integrals over paths and surfaces
    1. Path integral for planar curves
    2. Area of fence Example 1
    3. Line integral: Work

1.

Chapter 1

  • 1. Complex Mapping of Parametric Curve
  • 2. Sequences in GeoGebra
  • 3. Matrices Used To Generate Fibonacci Sequence
  • 4. Triangle de Sierpinski.
  • 5. Fractales lineales
  • 6. Penrose -Escher Triangle
  • 7. Graphing Complex Solutions
  • 8. Complex analysis: equations
  • 9. A complex thing made simple with GeoGebra
  • 10. Transform Fourier 3
  • 11. Transform Fourier 1
  • 12. Transform Fourier 2
  • 13. Pythagoras Waves
  • 14. Complex Numbers and Transformations
  • 15. Copy of zentangle
  • 16. Copy of Locus Examples
  • 17. Pythagoras Waves
  • 18. Polar Cartesian Comparison

1.1.

Complex Mapping of Parametric Curve

Image of the parametric curve [math]x(t) + iy(t)[/math] under the complex mapping [math]u(x,y) + i v(x,y)[/math]. Drag the time slider and input the appropriate functions. The blue curve is the parametric and the red curve is the image under the complex mapping. The arrow shows there the leading point of the parametric curve is mapping to.
– Carroll College Math Department

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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1.14.

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1.15.

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1.16.

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1.17.

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1.18.

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2.

Geometry of Euclidian Space

  • 1. Addition of vectors
  • 2. Scalar multiplication
  • 3. Vector product
  • 4. Plotting 3D surfaces
  • 5. Parametric surfaces
  • 6. Klein bottle

2.1.

Addition of vectors

Addition of two vectors.
Drag the vectors around. You can change the magnitude and direction of the vectors too. To show the parallelogram rule, place the vectors at the origin.
– Juan Carlos Ponce Campuzano

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.

Vector-Valued Functions

1. Vectors fields. 2. Frenet-Serret frame.

  • 1. Vector fields in 2D
  • 2. Vector field 3D
  • 3. Dynamic Frenet-Serret frame
  • 4. Vector Fields
  • 5. Divergence and Curl calculator

3.1.

Vector fields in 2D

– Juan Carlos Ponce Campuzano

3.2.

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3.3.

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3.4.

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3.5.

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4.

Integrals over paths and surfaces

  • 1. Path integral for planar curves
  • 2. Area of fence Example 1
  • 3. Line integral: Work

4.1.

Path integral for planar curves

This worksheet shows a geometrical representation of the path integral for planar curves. [br]If [math]c:[a,b]\rightarrow \mathbb R^2[/math] is of class [math]C^1[/math] and the composite function [math]t\rightarrow f(x(t),y(t))[/math] is continuous, then we define[br][math]\quad \quad\quad\int_c fds=\int_a^bf(x(t),y(t))||c'(t)||dt[/math][br]When [math]f(x,y)\geq0[/math], this integral has a geometric interpretation as the [b]area of a fence[/b].
Path integral for planar curves
Move the points in the plane to change the shape of the curve. You can change the surface as well.
– Juan Carlos Ponce Campuzano

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4.3.

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