Geometric Proofs and Logic

Mathematics & Statistics - Geometric Proofs and Logic - 19 slides

Explore Geometric Proofs and Logic, covering This lecture on Geometry provides an overview of its fundamental concepts, history, basic shapes, and essential.

Topics Covered

  • Introduction to Geometry
  • History of Geometry
  • Basic Geometric Shapes
  • Circumference and Area of Circles
  • Polygons: Definition and Types
  • Regular vs. Irregular Polygons
  • Midpoint Formula
  • Slope of a Line
  • Symmetry in Geometry
  • Introduction to Non-Euclidean Geometry
  • Key Theorists in Geometry
  • Properties of Triangles
  • Types of Triangles
  • Coordinate Geometry Basics
  • Distance Formula
  • Equations of Lines
  • Case Study: Geometry in Nature
  • Worked Example: Solving Geometric Problems
  • Summary and Conclusion

References

  • Euclid's Elements translated by Heath, T.L. (1956). Dover Publications.
  • Greenberg, M.J. (1993) Euclidean and Non-Euclidean Geometries: Development and History. W.H. Freeman & Company.
  • OpenStax (2023) Elementary Geometry Textbook.
  • Smith, G. (2018) Geometry Explained. 2nd edn. Boston: McGraw Hill.
  • OpenStax (2023) Geometry Basics. Available at: https://openstax.org.
  • Robinson, D. (2016) Introduction to Polygons. 1st edn. Cambridge: Cambridge Publications.
  • Khan Academy (2023) Polygons: Types and Properties. Available at: https://khanacademy.org.
  • Adams, T. (2019) Advanced Geometry Studies. 3rd edn. Pearson Education.
  • Stewart, J. (2016) Calculus: Early Transcendentals. 8th edn. Boston: Cengage Learning.
  • CK-12 Foundation (2023) Coordinate Geometry.
  • Larson, R. and Edwards, B.H. (2020) Calculus. 11th edn. Boston: Cengage Learning.
  • OpenStax Geometry (2023)
  • Khan Academy Symmetry (2023)
  • Euclidean and Non-Euclidean Geometries (2023)
  • Geometry History (Oxford Press, 2023)
  • OpenStax Geometry (2021). Available at: https://openstax.org/details/books/geometry
  • CK-12 Foundation (2022). CK-12 Geometry. Available at: https://www.ck12.org/geometry
  • Stewart, J. (2016). Calculus: Concepts and Contexts. 4th ed. Belmont: Brooks/Cole.
  • Larson, R., Hostetler, R.P., and Edwards, B.H. (2015). Precalculus: Real Mathematics, Real People. 8th ed. Boston: Cengage Learning.
  • Stewart, I. (2017) Geometry in Nature. Oxford University Press.
  • Abbott, E.A. (2020) Natural Fractals: Mathematical Biology Applications. Cambridge University Press.
  • OpenStax (2022) Algebra and Geometry. OpenStax.
  • Khan Academy (2023) Geometry Course. Available at: https://www.khanacademy.org/
  • Euclid (300 BCE) Elements. Translated by Proclus.
  • OpenStax (2022) Geometry Principles. Available at: https://www.openstax.org/
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