Art & Practice of Math

Kristen Beck, Apr 15, 2016

Table of Contents

  1. Geometric Constructions
    1. Square Roots
    2. Compass & Straightedge Tools
    3. Vertices of a Regular n-sided Polygon
    4. Visualizing Sine and Cosine
  2. Dimension
    1. Circular Cross-Sections
  3. Fractals
    1. Mandelbrot Iteration Orbits
    2. Mandelbrot Function Iteration
    3. The Hilbert Curve
    4. Circle Fractal
  4. The Golden Ratio
  5. Miscellaneous

1.

Geometric Constructions

  • 1. Square Roots
  • 2. Compass & Straightedge Tools
  • 3. Vertices of a Regular n-sided Polygon
  • 4. Visualizing Sine and Cosine

1.1.

Square Roots

Drag the slider to adjust the value of x. Which triangles are similar?
– Kristen Beck

1.2.

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1.3.

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1.4.

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2.

Dimension

  • 1. Circular Cross-Sections

2.1.

Circular Cross-Sections

This worksheet illustrates three different solid objects having circular cross-sections (disks).
– Kristen Beck

3.

Fractals

  • 1. Mandelbrot Iteration Orbits
  • 2. Mandelbrot Function Iteration
  • 3. The Hilbert Curve
  • 4. Circle Fractal

3.1.

Mandelbrot Iteration Orbits

Simple exploration of the Mandelbrot Set (and the orbits of the iteration with different 'c' values).[br][br]This is the iteration: [math]z_{n+1} = z_{n}^{2}+c[/math][br][br]Try moving 'c' around to see the orbits change.[br][br]Stable orbits are coloured black. The colours 'outside' the set are determined by how quickly the iteration diverges...
Mandelbrot Iteration Orbits
– Ben Sparks

3.2.

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3.3.

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3.4.

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4.

The Golden Ratio


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5.

Miscellaneous


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