Geometry: An Interactive Journey to Mastery

Overview

Experience an intuitive and fun approach to learning the subject of geometry in this course taught by an award-winning educator. “Geometry: An Interactive Journey to Mastery” dives deep into foundational concepts while emphasizing logic and reasoning, essential for success in various fields.

Course Instructor

The course is led by Professor Arthur T. Benjamin, who combines his vast knowledge with an engaging style to present the complexity and beauty of geometry in 36 lectures.

Video Lessons

1. Geometry—Ancient Ropes and Modern Phones
   • Duration: 33 min
   • Description: Explore the origins and practical applications of geometry in modern contexts.

2. Beginnings—Jargon and Undefined Terms
   • Duration: 28 min
   • Description: Lay the foundation by examining basic geometric terms and principles.

3. Angles and Pencil-Turning Mysteries
   • Duration: 28 min
   • Description: Investigate the relationship between angles in triangles and explore flat versus spherical geometry.

4. Understanding Polygons
   • Duration: 31 min
   • Description: Define polygons mathematically and examine their properties.

• The Pythagorean Theorem
  • Duration: 29 min
  • Description: Discover an intuitive understanding of this fundamental theorem.

6. Distance, Midpoints, and Folding Ties
   • Duration: 29 min
   • Description: Learn how geometry connects with algebra through distance calculations.

• The Nature of Parallelism
  • Duration: 35 min
  • Description: Explore methods to determine parallel lines using foundational postulates.

8. Proofs and Proof Writing
   • Duration: 29 min
   • Description: Learn the process of constructing valid proofs through logical deduction.

9. Similarity and Congruence
   • Duration: 34 min
   • Description: Understand the differences between similar and congruent shapes through geometric applications.

10. Practical Applications of Similarity
    • Duration: 31 min
    • Description: Use similarity principles to solve real-world examples.

11. Making Use of Linear Equations
    • Duration: 29 min
    • Description: Connect algebra to geometry through the study of lines and their equations.

12. Equidistance—A Focus on Distance
    • Duration: 33 min
    • Description: Explore the concept of equidistance and its geometric implications.

13. A Return to Parallelism
    • Duration: 31 min
    • Description: Study transversal properties and their geometric applications.

• Exploring Special Quadrilaterals
  • Duration: 30 min
  • Description: Classify different quadrilaterals and analyze their properties.

15. The Classification of Triangles
    • Duration: 30 min
    • Description: Discover various types of triangles and their characteristics.

16. Circle-ometry—On Circular Motion
    • Duration: 32 min
    • Description: Investigate the connection between angle measurement and circular motion.

• Trigonometry through Right Triangles
  • Duration: 28 min
  • Description: Learn about trigonometric ratios and their applications in measurements.

18. What Is the Sine of 1°?
    • Duration: 32 min
    • Description: Learn how to calculate sine values for angles using geometric principles.

19. The Geometry of a Circle
    • Duration: 29 min
    • Description: Explore the definitions and properties associated with circles.

• The Equation of a Circle
  • Duration: 33 min
  • Description: Derive the algebraic equation for a circle.

21. Understanding Area
    • Duration: 28 min
    • Description: Study how to calculate the area of different geometric shapes.

• Explorations with Pi
  • Duration: 31 min
  • Description: Discover the relevance of pi and its applications in geometry.

23. Three-Dimensional Geometry—Solids
    • Duration: 32 min
    • Description: Classify common three-dimensional shapes and their properties.

• Introduction to Scale
  • Duration: 30 min
  • Description: Learn about the concept of scale and its implications in geometry.

• Playing with Geometric Probability
  • Duration: 30 min
  • Description: Unite geometry and probability to solve practical problems.

26. Exploring Geometric Constructions
    • Duration: 29 min
    • Description: Discover classic geometric constructions using simple tools.

27. The Reflection Principle
    • Duration: 31 min
    • Description: Understand the principles of reflection in geometric applications.

28. Tilings, Platonic Solids, and Theorems
    • Duration: 32 min
    • Description: Explore geometric tiling and the properties of platonic solids.

29. Folding and Conics
    • Duration: 29 min
    • Description: Investigate the properties of conic sections through folding techniques.

30. The Mathematics of Symmetry
    • Duration: 28 min
    • Description: Study symmetries in various geometric forms and their applications.

31. The Mathematics of Fractals
    • Duration: 30 min
    • Description: Discover the beauty and complexity of fractals in nature.

32. Dido’s Problem
    • Duration: 31 min
    • Description: Explore a historical problem using geometric principles.

33. The Geometry of Braids—Curious Applications
    • Duration: 29 min
    • Description: Examine the intersection of geometry and mechanics using braids.

34. The Geometry of Figurate Numbers
    • Duration: 32 min
    • Description: Analyze relationships between geometric shapes and figurate numbers.

35. Complex Numbers in Geometry
    • Duration: 32 min
    • Description: Explore the application of complex numbers in solving geometric problems.

36. Bending the Axioms—New Geometries
    • Duration: 32 min
    • Description: Investigate non-Euclidean geometries and their implications.