Mathematics Proofs: GCSE & A-Level

Visual mathematics: Another way to sum up consecutive natural numbers. #sigma #visualmath #mathematicsproofs

3D Rotations: Yaw, Pitch and Roll Starter Matrices / Coordinates. #yaw #pitch #roll #aviation #computergraphics

@geometryupdates @GeometricBites Extras:

Visual Mathematics. Pattern related to cubed numbers. #barycentric #cubed

Basic 3D Array formation for Desmos. #desmos #3d #multidimensional

Visual mathematics: Showing that the angles within a triangle must add up to 180 degrees. 🔺👁️💡 #triangles #equilateraltriangle #geometry

Deriving the unit vector in ℝ² by scaling a non-zero vector (x₁, y₁) with λ, where λ = 1 / √(x₁² + y₁²). This turns the vector into length 1 while keeping the same direction.

Cosine Rule & Dot Product Mastery for ℝ². #cosinerule #dotproduct #vectors

GCSE Maths: The difference between the area of a right triangle and the area of a scalene triangle. #gcsemaths #trigonometry

Here are the first three terms of an arithmetic sequence: 8p, 7p − 3, 4p + 2 The sum of the first n terms of the sequence is −1914. Work out the value of n. Show your working clearly.

Context: x.com/mathsproofs/st…

Proof from first principles showing why, if f(x) = xⁿ, then f′(x) = nxⁿ⁻¹. Uses the binomial expansion of (x + h)ⁿ, cancels xⁿ, divides by h, then takes the limit as h → 0.

Context: x.com/mathsproofs/st…

Binomial expansion written out clearly for use with limits, especially expressions like (x + Δx)ⁿ. A useful way to see why the derivative of xⁿ becomes nxⁿ⁻¹. #differentiation #binomialexpansion #pascalstriangle #combinatorics

A compact way to generate the Cartesian product: {0,1,2} × {0,1,2} Use the list [0...8]: x = mod([0...8], 3) y = floor([0...8]/3) So the points are: (mod([0...8], 3), floor([0...8]/3))

I created a simple page on proportional relationships and graphs. It includes formulas, graph descriptions, and Desmos links for examples such as: y = kx² y = kx³ y = k√x y = k/x y = k/x² geometricbites.blogspot.com/p/proportional…

New page added to Geometric Bites: Powers of 10 from 10⁻¹⁰ to 10¹⁰ Powers of 10 from 10^-10 to 10^10 with decimal values, comma formatting, and written number names. geometricbites.blogspot.com/p/powers-of-10…

New page added to Geometric Bites: geometricbites.blogspot.com/p/table-of-fac… The table of factorials from 0! to 15!

Essential trigonometry, GCSE and A-Level maths notes. #trigonometry #gcsemaths #alevelmaths #sohcahtoa #choshacao

Neat LCM hack for ratios, GCSE maths. Use the lowest common multiple. #gcsemaths #lowestcommonmultiple