Geometry Insights

Revealing the Architecture of Mathematics
64 Premium GCSE & A-Level Articles and Counting
By failing to prepare, you are preparing to fail. — Benjamin Franklin

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

How to Generate a Parallelogram in ℝ³

#vectors #matrices #furthermaths

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

New Youtube Video:

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

https://t.co/19DNVsY1V0

#dotproduct #vectors #thalestheorem

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

New Youtube Video:

Proof That (AB)⁻¹ = B⁻¹A⁻¹ for Non-Singular Matrices

https://t.co/ulsATVRR8g

#matrices #matrixalgebra #vectors

[Geometry Insights @geometryupdates]

Proof that (AB)⁻¹ = B⁻¹A⁻¹.

This proof starts from the definition of a matrix inverse and uses only associativity and the identity matrix to show rigorously why the order of the inverses must be reversed.

https://t.co/QaGX7TZq7c

#mathematics #matrices #mathproofs

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

New Youtube Video:

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

https://t.co/KoXuAIlnEH

#vertexform #quadraticgraphs

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

Desmos has released its new Notebook feature.

This is another game changer in modern mathematics.

You can see some examples of the Notebook feature in action right here:

https://t.co/HzhyafXOTc

#graphing #desmos

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

Differentiating vector-valued functions in ℝ³ from first principles.

The derivative of

C(t) = ⟨x(t), y(t), z(t)⟩

is obtained componentwise:

C′(t) = ⟨x′(t), y′(t), z′(t)⟩

giving the instantaneous velocity vector and tangent direction to the curve.

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

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

https://t.co/EXGDE7pgur

#differentiation

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

The surface area of a square based pyramid derived from scratch.

#gcsemaths #mathematicsproofs

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

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

#differentiation

https://t.co/QIgW5JYuZs

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

New Youtube Video:

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

https://t.co/2JhU7pHVMp

#differentiation #calculus

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

New Youtube Video:

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

https://t.co/hEkACZytGL

#vectors #computergraphics

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

New Youtube Video:

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

https://t.co/8iR2DocSZG

#cosinerule #trigonometry

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

New Youtube Video:

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

https://t.co/tVCEEJBT2t

#dotproduct #vectors

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

I showed that a matrix records where the standard basis vectors are sent.

In 2D and 3D, the columns of the matrix are the transformed basis vectors.

A matrix is not just numbers — it is a compact description of how space moves.

#matrices #maths #vectors

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

Now making Youtube videos once again...

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

Quick Memorisation Technique

https://t.co/XeMpJShTHP

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

Vectors: 2D Perpendicular Slopes Mastery

#vectors #gcsemaths #alevelmaths #perpendicular

[Mathematics Proofs: GCSE & A-Level @mathsproofs]

One of the hardest GCSE vector problems solved.

The diagram shows triangle OAB.

OPC and APD are straight lines.

OA = a

OB = b

OD : DB = 1 : 2

AC : CB = 3 : 1

Work out the ratio OP : PC.

#vectors #alevelmaths #geometry

[Geometry Insights @geometryupdates]

Introduction to vectors.

#vectors #alevelmaths #pythagoras

[Geometry Insights @geometryupdates]

Vector to a point on a line between two other vectors.

#vectors #alevelmaths