Calculus and GeoGebra 3D

Andreas Lindner, May 22, 2015

[b]Talk at Global Gathering 2015 July 2015 Linz, Austria[/b]

Table of Contents

  1. Differential calculus
    1. Juice box
    2. Cone and inscribed cylinder - part 1
    3. Cone and inscribed cylinder - part 2
    4. Tangent plane to an area (animation)
  2. Integral calculus
    1. Cavalieri's Principle
    2. Volume of a Pyramid
    3. Dome of Speyer Cathedral
    4. Volume of a Dam
    5. Solid of Revolution
    6. Volume of Solids of Revolution

1.

Differential calculus

  • 1. Juice box
  • 2. Cone and inscribed cylinder - part 1
  • 3. Cone and inscribed cylinder - part 2
  • 4. Tangent plane to an area (animation)

1.1.

Juice box

The base of a juice box with a volume of 1 liter (1000 ml) is a square.[br]Find the height of the juice box when the surface is to have minimum value?[br][br][b]Exercise[/b][br]a) Move [color=#c51414]point B[/color] either in [i]Graphics View[/i] or in [i]Graphics 3D View[/i] and try to identify the minimum.[br]b) Solve the problem using the CAS of GeoGebra.
Juice box
– Andreas Lindner

1.2.

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1.3.

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1.4.

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2.

Integral calculus

  • 1. Cavalieri's Principle
  • 2. Volume of a Pyramid
  • 3. Dome of Speyer Cathedral
  • 4. Volume of a Dam
  • 5. Solid of Revolution
  • 6. Volume of Solids of Revolution

2.1.

Cavalieri's Principle

[b]Cavalieri's Principle[/b][br]The volumes of two objects are equal if the areas of their corresponding cross-sections are equal in all cases.[br][br][b]Exercise[/b][br]Change the height h of the intersections for both pyramids.[br]Move point [math]S_2[/math] and make sure that the cross section areas of both pyramids are equal in all cases.[br]Show the plane intersecting the vertices of the pyramids.
Andreas Lindner
– Andreas Lindner

2.2.

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2.4.

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2.5.

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2.6.

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