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Interactive Apps

50 interactive tools for exploring mathematical concepts

Functions & Graphs

Function Explorer
Plot and manipulate functions interactively. Adjust parameters and see graphs update in real time.
Free
Graph Transformations
Explore translations, reflections, stretches and combined transformations of functions.
Transformation Walkthrough
Step-by-step guide through function transformations with worked examples.
Rational Functions
Investigate asymptotes, holes and behaviour of rational functions graphically.
Sinusoidal Model
Fit sinusoidal models to real-world data by adjusting amplitude, period and phase.
Trig Unit Circle
Visualise sine, cosine and tangent on the unit circle with dynamic angle control.
Free

Calculus

Derivative Explorer
See the derivative graphically as you drag along a curve. Compare f, f' and f'' side by side.
Area Between Curves
Shade and compute the area between two functions over a chosen interval.
Riemann Sums
Approximate integrals with left, right, midpoint and trapezoidal sums. Adjust the number of rectangles.
Chain Rule Walkthrough
Interactive step-by-step differentiation using the chain rule with colour-coded inner and outer functions.
Volume of Revolution
Rotate regions around axes and visualise the 3D solid with adjustable cross-sections.
Volume of Revolution Walkthrough
Guided walkthrough of setting up and evaluating volume of revolution integrals.
Euler's Method
Step through numerical solutions of differential equations with adjustable step size.
Logistic Explorer
Explore logistic growth models with adjustable carrying capacity, growth rate and initial conditions.
Phase Portrait
Visualise direction fields and solution trajectories for systems of differential equations.
Bouncing Ball Walkthrough
Model a bouncing ball using sequences and series, connecting physics to geometric series.

Sequences & Series

Sequences Visualizer
Plot arithmetic, geometric and recursive sequences. See convergence and divergence visually.
Free
Arithmetic Series Walkthrough
Step-by-step exploration of arithmetic series with visual summation.
Geometric Series Walkthrough
Understand convergence of geometric series through guided interactive examples.
Compound Interest Walkthrough
See how compound interest grows over time with adjustable rates and compounding periods.
Finance TVM
Time value of money calculator for annuities, loans and investments with visual timelines.

Statistics & Probability

Normal Distribution
Explore the bell curve with adjustable mean and standard deviation. Shade probability regions.
Free
Binomial Distribution
Visualise binomial probabilities with adjustable n and p. Compare to normal approximation.
Regression Explorer
Fit linear, quadratic and other regression models to data. See residuals and r-squared.
Population Parameters Walkthrough
Understand the difference between population parameters and sample statistics.
Sampling Variability Walkthrough
See how sample statistics vary from sample to sample through repeated sampling.
Bessel's Correction Walkthrough
Discover why we divide by n-1 for sample variance through interactive simulation.
Central Limit Theorem Walkthrough
Watch the sampling distribution of the mean become normal regardless of population shape.
Confidence Interval Walkthrough
Build intuition for confidence intervals by generating many intervals and checking coverage.
Bayes' Theorem Walkthrough
Step through conditional probability problems using tree diagrams and Bayes' theorem.
Probability Rules Walkthrough
Interactive guide to addition and multiplication rules with visual probability models.
Venn Diagram Walkthrough
Solve probability problems using interactive Venn diagrams with two and three events.
Chi-Squared Walkthrough
Perform chi-squared goodness-of-fit and independence tests step by step.
Type I and Type II Errors
Visualise the relationship between significance level, power, and Type I/II errors.
Binomial Type II Error
Explore Type II error probability in binomial hypothesis tests with adjustable parameters.
Capture-Recapture Simulation
Estimate a hidden population by marking, releasing and recapturing animals. Compare Lincoln-Petersen and Chapman estimators with Monte Carlo trials.
Free
Capture-Recapture Walkthrough
Step-by-step explanation of the capture-recapture method: mark, release, recapture, the proportion equation, and why running many trials converges on the truth.
Free
Box Plot Explorer
Compare age distributions across groups with vertical or horizontal box plots. Toggle groups to see the scale adapt.
Free

Coordinate Geometry

Distance & Midpoint Walkthrough
Calculate distances and midpoints between points with step-by-step visual guidance.
Equation of a Line Walkthrough
Find equations of lines from points and gradients with interactive graph feedback.
Perpendicular Lines Walkthrough
Explore perpendicular gradients and find equations of perpendicular lines step by step.

Vectors

Vector Operations
Add, subtract and scale vectors graphically. See components and resultants in 2D.
Vector Line
Represent lines using vector equations. Adjust direction vectors and position vectors.
Vector Line Walkthrough
Guided practice finding vector equations of lines through points and parallel to directions.

Complex Numbers

Argand Diagram
Plot complex numbers on the Argand plane. Explore modulus, argument and operations.
Matrix Transformations
Apply 2D matrix transformations and see their geometric effect on shapes and points.
Eigenvalue Spirals
Explore phase portraits with complex eigenvalues λ = p ± qi. Adjust p and q to see how stability and rotation direction change.
Free

Graph Theory

Bridges of Königsberg
Solve the classic Königsberg bridge puzzle and discover Eulerian paths.
Free
Graph Navigator
Build and explore graphs interactively. Find paths, cycles and connected components.
Voronoi Builder
Place points and watch Voronoi diagrams form in real time. Explore nearest-neighbour regions.
Adjacency Matrix Walkthrough
Convert between graphs and adjacency matrices with guided step-by-step practice.
Spanning Tree Walkthrough
Find minimum spanning trees using Prim's and Kruskal's algorithms interactively.
Eulerian Path Walkthrough
Determine whether Eulerian paths and circuits exist and trace them step by step.