Math
Tower of Hanoi
Solve the Tower of Hanoi with a visible recursive move sequence or legal manual moves. Compare your move count with the exact minimum 2^n − 1.
Available for Windows
Makarov Math Suite
160 interactive modules bring geometry, topology, fractals, calculus, algebra, probability and algorithms into view. Rotate a surface, change a construction or follow an algorithm one step at a time.
160 modules · Page 7 / 8
Math
Rubik's cube as a group
Treat a Rubik cube as exact facelet permutations. Animate products, inverses, conjugation and a commutator, then inspect cycle counts and the order of the resulting group element.
Math
The del operator: grad, div, curl, Laplacian
Connect gradient, divergence, curl and Laplacian with visible fields, a movable probe and independently calculated boundary and area integrals.
Math
Klein bottle and the projective plane
Explore a Klein-bottle immersion and a Roman-surface image of the projective plane. Follow a local normal and inspect the identifications behind non-orientability.
Math
Kuramoto synchronisation
Watch forty coupled phase oscillators synchronize. Adjust coupling and natural-frequency spread while following individual phases and the complex order parameter.
Math
Epidemic: SIR on a network
Compare an SIR compartment model with stochastic infection and recovery on a contact network. Explore transmission, recovery, initial immunity and variability between runs.
Math
Queues: why 90 % busy means waiting
Run an event-based FIFO M/M/1 queue. Inspect congestion, measured residence times, stable and overloaded regimes, and the finite-run approach to Little’s law.
Math
Stable matching
Watch Gale–Shapley matching progress through proposals, tentative engagements and rejections. Reverse the proposing side and verify the absence of blocking pairs at completion.
Math
Prisoner's dilemma tournament
Compare five strategies in a noisy repeated prisoner’s dilemma, inspect cooperation histories and watch population shares evolve from a tournament payoff matrix.
Math
Kalman filter
Track a moving target with a two-dimensional Kalman filter. Tune process and measurement noise, compare raw observations with the estimate, and inspect the covariance ellipse.
Math
Bézier curves and splines
Edit control points and inspect the geometric construction of cubic Bézier curves and clamped cubic B-splines.
Math
Convex hull
Construct convex hulls with Jarvis wrapping, Graham scan and QuickHull, add points and compare orientation-test counts.
Math
Elliptic curves
Visualize the elliptic-curve group law with real chords and tangents, and calculate exact point sums in small prime fields.
Math
Enigma
Operate a historically wired three-rotor Enigma with visible signal paths, plugboard pairs, reversible encryption and correct double stepping.
Math
Genetic algorithm
Experiment with selection, crossover, mutation and elitism in a working genetic algorithm on multimodal fitness landscapes.
Math
The leaning tower of blocks
Build the classical harmonic block stack and inspect the centre of mass and support margin at every layer.
Math
Wallpaper groups
Draw a seed motif and generate all 17 wallpaper groups using lattice translations, rotations, reflections and glide reflections.
Math
Interpolation and Runge's phenomenon
Compare polynomial and cubic-spline interpolation, expose Runge’s phenomenon and measure the effect of Chebyshev nodes.
Math
Continued fractions
Build continued fractions term by term and inspect convergents, denominators and approximation errors for famous constants and custom decimals.
Math
Möbius transformations
Transform complex grids and circles by translations, rotations, reciprocals and fractional linear maps, with a Riemann-sphere view.
Some modules belong to more than one Suite. Shared experiments have one description here.