Euclidean and Affine Geometry, Assignments of Analytical Geometry and Calculus

This document provides a comprehensive study of **Euclidean and Affine Geometry**, covering the fundamental concepts, definitions, properties, and applications of geometric structures. It explores Euclidean geometry, including points, lines, planes, angles, triangles, circles, distance, congruence, similarity, and coordinate geometry. It also introduces Affine Geometry, focusing on affine spaces, affine transformations, parallelism, vectors, translations, and geometric invariants. The document includes theoretical explanations, mathematical proofs, worked examples, diagrams, and practice problems to strengthen understanding. It is designed as a university-level resource for students studying Mathematics, Graph Theory, Geometry, Computer Science, or related engineering courses, making it suitable for exam preparation, assignments, and academic reference.

Typology: Assignments

2024/2025

Available from 06/29/2026

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Assignment of
Euclidean and Affine Geometry
Group members
Name Roll No
Sania Bibi 70
Eman Fatima 10
Asma Bibi 61
Question # 01
Take three different examples that are homomorphic but not
isomorphic give reasons as well
Solution
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Assignment of

Euclidean and Affine Geometry

Group members

Name Roll No

Sania Bibi 70

Eman Fatima 10

Asma Bibi 61

Question # 01

Take three different examples that are homomorphic but not isomorphic give reasons as well

Solution

Question # 02

Explain the isometries of the plane using different AI tools such as ChatGPT, Deep Seek, and Gemini or identify the differences in the data produced by these AI tools.

Solution