Revealing the Architecture of Mathematics
64 Premium GCSE & A-Level Articles and Counting
By failing to prepare, you are preparing to fail. — Benjamin Franklin
New Youtube Video:
Deriving an Alternative Equation of a Circle Using Thales's Theorem & the Dot Product
https://t.co/19DNVsY1V0
#dotproduct#vectors#thalestheorem
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
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
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
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.
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
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
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