# Affine and Euclidean Geometry by Shahzad Idress

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These are short notes containing topics related to Affine and Euclidean Geometry. The main sections includes “Vector Space and Affine Geometry”, “Euclidean Geometry”, “Orthogonal Transformations” and “Platonic Polyhedra”.

Name | Affine and Euclidean Geometry |
---|---|

Provider | Shahzad Idress |

Pages | 41 pages |

Format | PDF (see Software section for PDF Reader) |

Size | 1.44 mB |

### Contents & Summary

- Linear & Affine Subspaces
- Linear Spaces & Subspaces
- Affine Subspaces: Affine Combination, Convex Combination, Dimension of an Affine Subspace, Affine Span, Affine Independence, Affine Basis, Barycentric or Affine Coordinates, Hyperplane in $R^n$

- Inner Product and Euclidean Geometry
- Inner Product Spaces: Inner Product, Euclidean Inner Product, Norm of a Vector, Distance Between Two Points, Cauchy-Schwarz Inequality, Angle Between Two Vectors.
- The Laws of Cosine and Sines: The Law of Cosine, Pythagoras Theorem, Parallelogram Law, The Law of Sines,
- Euclidean Constructions: The Euclidean Tools, The Method of Loci

- Classical Theorems in Affine Geometry
- Sensed Magnitudes, Positive and Negative Segments, Range of Points and Complete Range, Basic Theorems.

- Menelaus, Ceva and Desargues Theorems: The ratio 𝑨𝑷/𝑷𝑩, Angles Associated with Parallel Lines, Thales’ Theorem, Menelaus Point, Menelaus’ Theorem, Cevian Line, Ceva’s Theorem, Copolar Triangles, Coaxial Triangles, Desargues’ Theorem.
- Platonic Polyhedra
- Platonic Solids, Convex Set, Convex Polyhedron, Regular Polyhedron, Classification of Platonic Solids, Euler’s Formula, Duality.

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