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Function Transformation Playground
Explore vertical and horizontal graph transformations across familiar functions.
Beauty in maths topic
Calculus and Change
Calculus is the mathematics of change: how quantities move, accumulate, stabilise and respond to different inputs.
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live pages
6
prototype tools
7
planned ideas
What this area includes
Functions and graph transformations
Rates of change, gradients and slope fields
Area, accumulation and numerical approximation
Optimisation and models that evolve over time
Questions to explore
What does the graph tell us before we calculate?
When does a numerical method become trustworthy?
How can a local rule shape a whole curve?
Working pages and tools
These are the pages currently available to open from this topic.
ToolPrototype
Area Approximation Explorer
Compare rectangles, midpoint approximations, trapezia and exact integrals.
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Differential Equation Slope Field
Explore slope fields, initial conditions and numerical solution curves.
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Gradient Descent Visualiser
Watch optimisation move across a loss landscape.
ToolPrototype
GCSE Algebra Fluency Builder
Practise expanding, factorising, rearranging and solving with carefully staged difficulty.
ToolPrototype
A Level Calculus Revision Lab
Revise tangent gradients, derivatives, definite integrals and trapezium-rule estimates interactively.
Planned directions
These ideas are not built yet, but they show where this topic could grow next.
ideaPlanned
GCSE Quadratics Lab
Planned revision lab connecting factorising, completing the square, graphs, roots and the quadratic formula.
ideaPlanned
Further Maths Differential Equations Lab
Planned lab for first-order differential equations, slope fields, particular solutions and stability.
ideaPlanned
Sound Waves and Fourier
Planned bridge from musical timbre to waves, harmonics and decomposing sound into simpler frequencies.
ideaPlanned
Secret Sharing
Planned tool showing how a secret can be split using polynomials and reconstructed only with enough pieces.
ideaPlanned
Vector Fields and Motion
Planned bridge between mechanics and differential equations using arrows, paths and changing velocity.
ideaPlanned
Fourier Patterns
Planned bridge from waves and rotations to complex numbers, calculus and signal patterns.
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Diffusion on Graphs
Planned exploration of heat, pollution or information flowing across connected networks.
Connected topics
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Beauty in Maths
A portal for connected mathematical explorations: pattern, surprise, structure, nature and emergence.
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Fractals and Infinite Detail
Self-similarity, recursion, iteration, dimension and patterns that repeat at different scales.
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Financial Maths and Risk
Growth, uncertainty, modelling, risk, portfolios and the mathematics behind financial decisions.
How to use this section
Use these tools to move between visual intuition, symbolic methods and modelling decisions.