This is an excerpt from a complete course on Differential Geometry.
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The Analysis of the Unit Circle as a Planar Curve in Differential Geometry.
Kinematic Analysis of a Rigid Bar
Classical Euclidean Geometry Is Limited to Three Dimensions
Differentiation of Vectors: What It Actually Means to DIfferentiate a Vector-Valued Function!
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The Medians of a Triangle Are Concurrent, A Vector-Based Proof - As Straightforward as It Gets!
A Simple Solution to an Otherwise Challenging Problem - Algebra and Geometry Working Together!
The Diagonals of a Rhombus Intersect at a Right Angle - A Dot Product Proof
The SIMPLEST proof ot the Pythagorean Theorem - a visual approach even a kindergartener would get!
What Is a Vector? It depends! Geometric perspective vs Linear Algebra vs ℝⁿ
Mr. Tibbs, the Queen's butler in BFG made a math mistake. Did the Movie Get It Right? We Investigate
A Lesson in Daring, Flair, and Beauty: Archimedes' Incredible Breakthrough in Squaring the Parabola
How the Greeks Approached the Concept of Area. Archimedes' Method of Exhaustions
The MOST Fundamental Concepts in Differential Geometry, & SURPRISE: Math always start in the middle!
Gilbert Strang's Final MIT Lecture
The Strang Decomposition A = CR
An elementary surface integral formula you've never heard of
Vector Calculus 25: The Frenet Identities for a Planar Curve
Vector Calculus 24: The Principal Normal and Curvature of a Planar Curve
Vector Calculus 23: The Laws of Vector Differentiation
Vector Calculus 22: The Distance Between a Point and a Curve
Vector Calculus 20: Heron's Problem, a Vector-Analytic Solution
Vector Calculus 0: Why Vector Calculus?
Nothingburger integrals involving the natural logarithm - Integration by Substitution, Calculus 2