Mathematics

SeriousMax, Jan 14, 2025

Table of Contents

  1. Calculus
    1. Integration (Discrete)
    2. Integration (Continuous)
    3. Integration (Antiderivative Approximation)
    4. Derivative Approximation
    5. Derivative Approximation v2
    6. Derivative of Exponential Function
  2. Linear Algebra
    1. Linear Transformation
  3. Plane Geometry
    1. Van Aubel's Theorem
    2. Pythagorean Theorem
  4. Projective Geometry
    1. Desargues's Theorem
    2. Pappus's Hexagon Theorem

1.

Calculus

  • 1. Integration (Discrete)
  • 2. Integration (Continuous)
  • 3. Integration (Antiderivative Approximation)
  • 4. Derivative Approximation
  • 5. Derivative Approximation v2
  • 6. Derivative of Exponential Function

1.1.

Integration (Discrete)

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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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2.

Linear Algebra

  • 1. Linear Transformation

2.1.

Linear Transformation

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3.

Plane Geometry

  • 1. Van Aubel's Theorem
  • 2. Pythagorean Theorem

3.1.

Van Aubel's Theorem

[b]Van Aubel's theorem[/b] describes a relationship between squares constructed on the sides of a quadrilateral. Starting with a given convex quadrilateral, construct a square, external to the quadrilateral, on each side. Van Aubel's theorem states that the two line segments between the centers of opposite squares are of equal lengths and are at right angles to one another.
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3.2.

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4.

Projective Geometry

  • 1. Desargues's Theorem
  • 2. Pappus's Hexagon Theorem

4.1.

Desargues's Theorem

In projective geometry, [b]Desargues's theorem[/b] states: if the three straight lines joining the corresponding vertices of two triangles all meet in a point (the [i]perspector[/i]), then the three intersections of pairs of corresponding sides lie on a straight line (the [i]perspectrix[/i]).
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4.2.

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