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Invidious > Channel > MathTheBeautiful

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YT 5 minutes 28 seconds MathTheBeautiful The MOST Fundamental Concepts in Differential Geometry, & SURPRISE: Math always start in the middle! YT 8 minutes 17 seconds MathTheBeautiful Areas and the trouble with √2. Lesson 2 of a complete course on Differential Geometry YT 6 minutes 7 seconds MathTheBeautiful How the Greeks Approached the Concept of Area. Archimedes' Method of Exhaustions

YT 11 minutes 43 seconds MathTheBeautiful Why Does Area Change Quadratically w/ Size? A Simple Question That Requires the Concept of Infinity YT 7 minutes 19 seconds MathTheBeautiful The Challenge of π or How Archimedes Squared the Circle. Introduction to Differential Geometry YT 9 minutes 29 seconds MathTheBeautiful How Archimedes "Squared" the Sphere or One of the Greatest Unifying Moments in Science History

YT 17 minutes MathTheBeautiful A Lesson in Daring, Flair, and Beauty: Archimedes' Incredible Breakthrough in Squaring the Parabola YT 19 minutes 22 seconds MathTheBeautiful Squaring the Parabola by Means of Ordinary Calculus: A lesson in containing analytical calculations YT 4 minutes 21 seconds MathTheBeautiful Mr. Tibbs, the Queen's butler in BFG made a math mistake. Did the Movie Get It Right? We Investigate

YT 19 minutes 17 seconds MathTheBeautiful What Is a Vector? It depends! Geometric perspective vs Linear Algebra vs ℝⁿ YT 33 minutes 11 seconds MathTheBeautiful The Dot Product and the Inner Product: Comparing These Key Concepts in Linear Algebra, Geometry, ℝⁿ YT 58 seconds MathTheBeautiful The SIMPLEST proof ot the Pythagorean Theorem - a visual approach even a kindergartener would get!

YT 10 minutes 15 seconds MathTheBeautiful The Dot Product Proof of the Pythagorean Theorem - The power of Vectors Is on Full Display! YT 2 minutes 48 seconds MathTheBeautiful The Diagonals of a Rhombus Intersect at a Right Angle - A Dot Product Proof YT 16 minutes 27 seconds MathTheBeautiful The Vector Equation of a Straight Line. This will help us solve a number of difficult problems soon!

YT 12 minutes 49 seconds MathTheBeautiful A Simple Solution to an Otherwise Challenging Problem - Algebra and Geometry Working Together! YT 14 minutes 6 seconds MathTheBeautiful The Bisector Theorem: A Vector-Based Proof - No Ingenuity Required! YT 5 minutes 58 seconds MathTheBeautiful Introduction to Affine Spaces: What you can do in Linear Algebra w/o inner products. Less Is More!

YT 10 minutes 38 seconds MathTheBeautiful The Medians of a Triangle Are Concurrent, A Vector-Based Proof - As Straightforward as It Gets! YT 11 minutes 49 seconds MathTheBeautiful Ceva's Theorem, A Vector Based Proof - No Ingenuity Required! Concurrent Lines in a Triangle YT 11 minutes 49 seconds MathTheBeautiful The Orthogonal Projection Expressed in Terms of The Dot Product

YT 16 minutes 4 seconds MathTheBeautiful The Heights of a Triangle Are Concurrent, a Vector-Based Proof That Does Not Require Any Ingenuity! YT 14 minutes 16 seconds MathTheBeautiful My Proof of Pythagoras' Theorem is NOT circular! YT 10 minutes 50 seconds MathTheBeautiful Differentiation of Vectors: What It Actually Means to DIfferentiate a Vector-Valued Function!

YT 8 minutes 11 seconds MathTheBeautiful The Geometric Interpretation of a Vector-Valued Function: It's a curve - end of story. YT 11 minutes 5 seconds MathTheBeautiful The Geometric Interpretation of the DERIVATIVE of a Vector-Valued Function YT 8 minutes 47 seconds MathTheBeautiful The Main Intuitive Idea of Calculus (applied to curves in Differential Geometry)

YT 14 minutes 20 seconds MathTheBeautiful The Properties of Vector Differentiation YT 9 minutes 50 seconds MathTheBeautiful Constant Speed Motion - Analysis via differentiation of vector-valued functions YT 3 minutes 14 seconds MathTheBeautiful Classical Euclidean Geometry Is Limited to Three Dimensions

YT 11 minutes 57 seconds MathTheBeautiful Kinematic Analysis of a Rigid Bar YT 15 minutes 14 seconds MathTheBeautiful The Closest Point on a Curve to a Given Point: Combing Calculus And Geometry YT 14 minutes 17 seconds MathTheBeautiful The Arc Length Parameterization

YT 19 minutes 33 seconds MathTheBeautiful Linear Decomposition by the Dot Product YT 18 minutes 18 seconds MathTheBeautiful The Curvature of a Curve, Its Principal Normal, And Its Osculating Plane YT 16 minutes 50 seconds MathTheBeautiful The Torsion of a Curve

YT 22 minutes 44 seconds MathTheBeautiful Geometric Integrals - a Fundamental Concept to Be Accepted on an Intuitive Basis YT 5 minutes 31 seconds MathTheBeautiful Arithmetic Integrals And the Fundamental Theorem of Calculus YT 6 minutes 7 seconds MathTheBeautiful The Need for Arbitrary Parameterizations of Curves

YT 9 minutes 21 seconds MathTheBeautiful The Derivative of the Inverse Function - Why It Is Confusing (and how to eventually fix it) YT 14 minutes 9 seconds MathTheBeautiful The Derivative of the Inverse Function, or How to Reparameterize a Curve YT 4 minutes 10 seconds MathTheBeautiful Why Change of Variables Is Often an Inherently Ambiguous Task

YT 16 minutes 31 seconds MathTheBeautiful From Physical to Arithmetic Integrals - How to Achieve Invariance YT 9 minutes 28 seconds MathTheBeautiful Converting a Physical Integral into an Arithmetic One: Identifying the Challenge YT 15 minutes 32 seconds MathTheBeautiful From Physical to Arithmetic Integrals - Achieving Complete Agreement with Intuition

YT 22 minutes 41 seconds MathTheBeautiful The Geometric Expression for the Arc Length of a Curve YT 7 minutes 17 seconds MathTheBeautiful The Expression for the Arc Length of a Curve in Cartesian Coordinates YT 29 minutes 19 seconds MathTheBeautiful A brief review of curves and integration over curves.

YT 8 minutes 23 seconds MathTheBeautiful The FIRST of the seven beauties! The integral of the unit tangent over a curve. YT 4 minutes 33 seconds MathTheBeautiful The THIRD of the seven beauties. The integral of unit normal over a curve. YT 9 minutes 14 seconds MathTheBeautiful The FOURTH of the seven beauties. The integral of the position vector dotted the curvature normal.

YT 2 minutes 15 seconds MathTheBeautiful The FIFTH of the seven beauties. The integral of the position vector dotted with the unit tangent. YT 5 minutes 49 seconds MathTheBeautiful The SIXTH of the seven beauties. The integral of the position vector dotted with the unit normal.