Deriving the Plane Through A Perpendicular to Vector A: A · (P − A) = 0, A · P = ‖A‖² #dotproduct

Cross Product Derived from First Principles: N = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁)

How to Prove the Identity (|A||B|sinθ)²=|A|²|B|²-(A.B)² #dotproduct #crossproduct #vectors

The 3²+4²=5² GIF, Pythagoras' Theorem, Projection from 3D to 2D on Desmos, By Tiago Hands #desmos

How to Generate a Parallelogram in ℝ³: P = A + u(B − A) + v(C − A), 0 ≤ u ≤ 1, 0 ≤ v ≤ 1 #vectors

Deriving an Alternative Equation of a Circle Using Thales's Theorem & the Dot Product #dotproduct

Proof That (AB)⁻¹ = B⁻¹A⁻¹ for Non-Singular Matrices #matrices #matrixalgebra #vectors

How to Put a Quadratic into Vertex Form | f(x) = ax² + bx + c → a(x + b/(2a))² + c − b²/(4a)

How to Derive the Tangent to a Curve in ℝ³: C′(t) = ⟨x′(t), y′(t), z′(t)⟩ #differentiation

How To Find the Normal to a Curve at x = a | Formula Proof: h(x) = (−1/f′(a))(x − a) + f(a)

How to Derive the Tangent Line for a Curve in ℝ²: y = f′(a)(x − a) + f(a) #differentiation #calculus

How to Derive Vector Projection: proj_A B = ((A · B)/|A|²)A #vectors #computergraphics

How to Quickly Derive the Cosine Rule, a²=b²+c²-2bccosθ, Pure Mathematics #cosinerule #trigonometry

Vectors (Dot Product): How to Derive A.B=|A||B|cosθ in ℝ² From First Principles #dotproduct #vectors

How to Find the Inverse of a 2x2 Matrix, Further Pure Mathematics 3 #matrices #furthermaths

Rhombus (Kite) within a Square | Area = (1/3)·x² | Visual Proof Tutorial | Response to Mathinity

Drawing the Impossible Cuboid | ⏩ Speed x10.2 | 🎶 Music Only | 🚫 No Commentary

Drawing the Double Penrose Tribar Hexagram Lock | ⏩ Speed x9 | 🎶 Music Only | 🚫 No Commentary

Drawing the Penrose Tribar Made of Cubes with Central Hexagram | Speed x12 | Music Only

Drawing the Penrose Tribar with Central Hexagram | ⏩ Speed x4.07 | 🎶 Music Only | 🚫 No Commentary

Drawing the Penrose Hexagon on Isometric Paper | ⏩ Speed x4.07 | 🎶 Music Only | 🚫 No Commentary

Vectors: How to Quickly Generate a Line Between Two Points on Desmos 3D

Deriving and Understanding |(x - a) + i(y - b)| = d, Complex Numbers & Circles

Finding the Midpoint Between Two Points Using Vectors ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Deriving (x - x₁) / (x₂ - x₁) = (y - y₁) / (y₂ - y₁) = (z - z₁) / (z₂ - z₁) | 3D Equation of a Line

Completing The Square: A clever visual way to show that (x + a/2)² - (a/2)² = x(x + a) = x² + ax

Math Animations: Cardioid, Cycloid and Deltoid in Sync #mathanimations #trigonometry

Pythagoras' Theorem and Egyptian Tangram: The 345 and 12345 Design, Mathemagic, 3²+4²=5²

The Very Special 1, 2, 3, 4, 5 Egyptian Tangram and its Connection to the 3-4-5 Right Triangle #math

The 3-4-5 Right Triangle Constructed on Squared Paper in 27 Mins #PythagorasTheorem #Pythagoras

How to Derive the General Equation of a Straight Line ax+by+c=0 through y=mx+c #linearalgebra

How to Derive Equation of Line (x/a)+(y/b)=1 in Terms of x and y Intercept, a≠0, b≠0.

Complex Analysis: How to Graph the Julia Set Fractal on Desmos #desmos #mathart #fractalart

Complex Analysis: How to Graph the Mandelbrot Set Fractal on Desmos #desmos #mathart #fractalart

Microsoft Excel: How to Quickly Organise and Sum Up Expense Data Using the Pivot Table Feature

Complex Analysis: |z/|z||=|z|/|z|=1 when z=x+iy and x²+y²≠0 proof #complexnumbers

Reverse Triangle Inequality: ||x|-|y||≤|x-y| is true because -|x-y|≤|x|-|y|≤|x-y| #realanalysis

Real Analysis: How to show that for |x-a|≤r, a-r≤x≤a+r. #inequalities #math #alevelmaths

Desmos Tips: How to Create a 3D Array on Desmos and what L.x, L.y and L.z Stand For #Desmos #Arrays

Desmos Tips: How to Create a 2D Array on Desmos #desmos #graphing #math

Desmos Tricks: How to Create the Sequence of Triangular Numbers on Desmos #desmos #triangularnumbers

Desmos Tricks: How to Separate the Even Numbers from the Odd Numbers in a List #desmos #math

Desmos Tricks: How to Create the Fibonacci Sequence on Desmos #fibonaccisequence #math

How to Sum Up All Integers 1 to n using The Reverse Summation Method S=[n(n+1)]/2 #gauss

The Alternate Segment Theorem - Full Geometric Proof #algebra #geometry #alternatesegmenttheorem

Expanding (x+y)^3 using the CASIO fx-CG500 Calculator #Casio #scientificcalculator #calculator

A Line Passing through (a, b) Perpendicular to y=mx+c is y=(1/m)*(a-x)+b #linearalgebra #visualmath

Visual Mathematics: Why the Product of Two Perpendicular Gradients m and -1/m is Equal to -1

How to Reverse Engineer a Quadratic Sequence of the Form f(n)=an^2+bn+c and Find Its Solutions

How to show that a+ar+ar^2+ar^3+... converges to a/(1-r) using a clever visual proof #convergence

How to Find the Turning Point of a Curve y=x^2+bx+c by Completing The Square #GCSEMaths #ALevelMaths

How to Derive the Cosine Rule using The Chord Theorem and Thales's Theorem #VisualMath #Trigonometry

Geometry: How to Prove The Chord Theorem, ab=cd, Full Explanation #circletheorem #visualmath

Circle Theorems: Angles Subtended by the same Arc at the Circumference are Equal, Geometric Proof

How to find the Derivative of the Area of a Circle with respect to its Radius, dA/dr=2πr

Signed Distance Fields: How to get the Distance from a Point to a Line, d=(ma+c-b)/√(1+m^2)

Pythagoras' Theorem: How to Prove a^2+b^2=c^2 using Thales's Theorem

|a-b|²=(a-b)²=|a|²+|b|²-2ab - Vector Proof - A-Level Mathematics

If a≡b(modm), then ka≡kb(modm): Modular Congruence - Further Pure Mathematics 2, Proof

If a|b and a|c, this implies that a|bn+cm for all a, b, c, m, n ∈ Z where a≠0 #FP2 #mathsproof