History of Maths

Simona Riva, Jun 8, 2024

Collection of worksheets about History of Mathematics: classical constructions, curves as loci of points, envelopes...

Table of Contents

  1. Classical Curves - Loci
    1. Astroid - A Classical Construction
    2. Limaçon / Cardioid as a Locus - A Classical Construction
    3. Rose Curve - A Classical Construction
    4. Witch of Agnesi - A Classical Construction
  2. Envelopes
    1. Ellipse as Envelope - Correspondence Method
    2. Ellipse, Hyperbola and Circle as Envelopes
    3. "Compressed" Astroid as Envelope
  3. Plane Curves and Surfaces
    1. Pelecoid
  4. 3D Curves and Surfaces
    1. Viviani's Window

1.

Classical Curves - Loci

  • 1. Astroid - A Classical Construction
  • 2. Limaçon / Cardioid as a Locus - A Classical Construction
  • 3. Rose Curve - A Classical Construction
  • 4. Witch of Agnesi - A Classical Construction

1.1.

Astroid - A Classical Construction

Classical construction of the astroid as a locus.[br][br]To generate the locus, move point [math]A[/math] along the circle, or use the animation button on top right of the app.
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1.2.

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1.3.

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1.4.

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2.

Envelopes

  • 1. Ellipse as Envelope - Correspondence Method
  • 2. Ellipse, Hyperbola and Circle as Envelopes
  • 3. "Compressed" Astroid as Envelope

2.1.

Ellipse as Envelope - Correspondence Method

Consider the function [math]f\left(x\right)=\frac{1}{x}[/math] . [br]Represent domain and range of this function respectively over two parallel reference axes.[br]The segments that join each point of the domain with the corresponding point of the range are the envelope of an ellipse.[br][br]Use the sliders [i][color=#a64d79]distance[/color][/i] and [math]O'[/math] to change the distance between axes and the relative position of the Origin points on the two axes.
– Simona Riva

2.2.

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2.3.

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3.

Plane Curves and Surfaces

  • 1. Pelecoid

3.1.

Pelecoid

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4.

3D Curves and Surfaces

  • 1. Viviani's Window

4.1.

Viviani's Window

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