# Affine and Euclidean Geometry by Shahzad Idress

These notes are sent by shahzad-idress. We acknowledged his efforts to published these notes on MathCity.org.

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.

### Download

### Notes of other subjects

- Advance Analysis by Ms. Iqra Liaqat
- Advanced Analysis: Handwritten Notes
- Affine and Euclidean Geometry by Shahzad Idress
- Algebra II by Syed Sheraz Asghar
- Complex Analysis (Easy Notes of Complex Analysis)
- Complex Analysis (Notes) by Ms. Iqra Liaqat
- Complex Analysis (Quick Review)
- Complex Analysis by M Usman Hamid
- Differential Geometry (Notes) by Ms. Kaushef Salamat
- Differential Geometry by M Usman Hamid
- Differential Geometry by Syed Hassan Waqas
- Differential Geometry: Handwritten Notes
- Fluid Dynamics I by Muhammad Usman Hamid
- Fluid Mechanics I by Dr Rao Muzamal Hussain
- Fluid Mechanics II by Dr Rao Muzamal Hussain
- Functional Analysis by M Usman Hamid and Zeeshan Ahmad
- Functional Analysis by Mr. Tahir Hussain Jaffery
- Functional Analysis by Prof Mumtaz Ahmad
- Fundamental of Complex Analysis (Solutions of Some Exercises)
- Fuzzy Sets Theory by Umar Saeed Bunarai
- General Topology by Raheel Ahmad
- Group Theory by Mr. Muhammad Iftikhar
- Group Theory: Important Definitions and Results
- Groups (Handwritten notes)
- Handwritten Notes of Real Analysis by Asim Marwat
- History of Mathematics by Muhammad Usman Hamid
- Linear Algebra: Important Definitions and Results
- Mathematical Method by Khalid Latif Mir (Solutions)
- Mathematical Method by Muhammad Usman Hamid
- Mathematical Method by Sir Muhammad Awais Aun
- Mathematical Statistics by Ms. Iqra Liaqat
- Mathematical Statistics I by Muzammil Tanveer
- Mathematical Statistics II by Sir Haidar Ali
- Measure Theory by M Usman Hamid & Saima Akram
- Measure Theory Notes by Anwar Khan
- Mechanics (Easy Notes of Mechanics)
- Mechanics by Sir Nouman Siddique
- Mechanics I (Statics) by Dr Babar Ahmad
- Method of Mathematical Physics by Mr. Muhammad Usman Hamid
- Metric Spaces (Notes)
- Multiple Choice Questions (BSc/BS/PPSC) by Akhtar Abbas
- Number Theory by Dr Muhammad Umer Shuaib
- Number Theory by Ms. Iqra Liaqat
- Number Theory: Handwritten Notes
- Number Theory: Notes by Anwar Khan
- Numerical Analysis by M Usman Hamid
- Numerical Analysis II
- Operation Research by Sir Haidar Ali
- Operation Research: Handwritten Notes
- Partial Differential Equations
- Partial Differential Equations by M Usman Hamid
- Real Analysis (Notes by Prof. Syed Gul Shah)
- Ring (Notes) by Prof. M. Dabeer Mughal
- Rings & Modules by Ms. Iqra Liaqat
- Rings (Handwritten notes)
- Special Functions by Dr. Muhey-U-Din
- Theoretical Mechanics by Khalid Latif Mir (Solutions)
- Theory of Optimization by Ma'am Iqra Razzaq
- Theory of Relativity & Analytic Dynamics: Handwritten Notes
- Topology and Functional Analysis Solved Paper by Noman Khalid
- Topology Notes by Azhar Hussain
- Topology: Handwritten Notes
- Vector & Tensor Analysis by Dr Nawazish Ali (Solutions)
- Vector Space (Review) by Rashad Wattu
- Vector Spaces (Handwritten notes)