∞ Demos
Interactive versions of the ideas on the sheets. Nothing to install, nothing to sign up for, and phones work too.
All demos play with it
The grade on each card is the sheet it goes with, not an age limit. Many are fun at any age. Grade 12 demos first, then down to grade 5.
Taylor polynomials
Add terms one at a time and watch a polynomial hug eˣ or sin x.
Newton's method
Tangent after tangent lands on a root. Then a map of which root each start finds.
Gradient descent
Click a start, pick a step size, and follow the slope down a valley.
Eigenvectors
Drag a vector through a matrix. In two directions it only stretches.
Fourier series of a square wave
Add odd harmonics and watch the corners sharpen, overshoot and all.
The central limit theorem
Average any shape of data and the bell appears. Slide n.
Binomial to Poisson
Many trials, tiny chances: the bars settle on one curve.
The secretary game
Pick the best of twenty, no going back. Then let the computer find the 37% rule.
Kelly betting
A favourable coin. Bet too much and go broke; bet the right fraction and grow.
Foxes and rabbits
Two populations chase each other round a loop.
Inversion in a circle
Drag lines and circles and watch the plane turn inside out.
The binomial option tree
Price an option by copying it, and see that the real probability drops out.
Sine wave explorer
Four sliders, four jobs: height, speed, slide and lift.
Solve any triangle
Give three parts and watch the sine or cosine rule find the rest.
Log axes
Switch an axis to a log scale and a curve turns into a line.
Row reduction, step by step
Clear one unknown at a time until the answer falls out.
Buffon's needle
Drop ten thousand needles on a lined floor and π appears.
Counting necklaces
See every necklace, and the average that counts them.
Max flow, min cut
Push traffic through a network until a bottleneck stops you.
Rotate a cube
Turn a wireframe cube and watch the matrix that does it.
Shift, stretch, flip
Drag four sliders and watch a graph slide, stretch and flip.
Quadratic explorer
Slide a, b, c or drag the vertex. Watch the two roots meet and vanish.
The unit circle
Drag a point round a circle. Sine is its height.
Secant to tangent
Slide two points together and the slope settles on the derivative.
Area by slices
Rectangles under a curve. More of them, less error.
The logistic map
One simple rule: steady, then cycles, then chaos. Then find the calm island at r = 3.83.
Build a sound from sines
Mix eight sine waves and hear the sound change.
The test that cries wolf
A 99% test, a rare disease, and most positives are wrong. Count the dots.
The Galton board
Balls bounce through pegs and pile up in a bell.
Fit a line
Click to place points. The best line appears, and one outlier wrecks it.
RSA by hand
Two small primes, a public lock, a private key. Every step shown.
The random surfer
Draw links between six pages. Watch where a random surfer ends up.
Slicing a cone
Tilt a plane through a cone: circle, ellipse, parabola, hyperbola.
An epidemic in a box
A town of 1,000. Slide R₀ and vaccinate. Watch the curve collapse.
Lights Out
Clear the board, get a hint, or let the solver prove it can't be done.
Factoring with tiles
Arrange the tiles into a rectangle and read off the factors.
Three ratios
Change the angle, stretch the triangle. The ratios only care about the angle.
Build a box plot
Drag the data and watch five numbers redraw the box.
Logic gates
Flip the switches and wire an adder out of AND, OR and NOT.
Shortest path, step by step
Settle the nearest place, again and again, until the route appears.
The Game of Life
Four rules, a grid, and a glider that walks.
Unbeatable noughts and crosses
It never loses. See why every square is a win, a draw or a loss.
Stable matching
Run the proposals one round at a time and find a matching with no regrets.
Slope and intercept
Slide m and b, drag two points, and see the rise-over-run triangle.
Two lines
Move two lines until they cross, run parallel, or lie on top of each other.
Slide, flip, turn, scale
Move a triangle on a grid and read the coordinate rule for each move.
Parallel lines and a transversal
Swing the crossing line and watch which angles stay equal.
Euclid's algorithm
Cut squares off a rectangle until none is left. The last square is the gcd.
The birthday paradox
Fill rooms with people. By 23 a shared birthday is more likely than not.
The Koch snowflake
Add bumps forever. Watch the perimeter run away while the area settles.
Area by shoelace
Click out a polygon and watch the criss-cross sum give its area.
Taxicab circles
Measure distance along the grid, and a circle becomes a diamond.
Play Chomp
Eat the chocolate, avoid the poisoned square, and try to beat a perfect player.
Trapping π
Polygons inside and outside a circle squeeze π from both sides.
Beat the forecaster
Give rain probabilities for ten days and get scored on honesty.
Is it proportional?
Type a table, see the points, and test them against one straight line.
Undo it backwards
Solve an equation on a balance. A wrong move tips it.
Roll a wheel once
Any wheel rolls a little more than three of its own widths.
Three sticks
Slide the lengths and see when a triangle will not close.
Slicing a cube
Tilt a knife through a cube and count the sides of the cut.
The long run
Roll a die ten thousand times and watch one in six appear.
Ask a sample
Ask fifty of five thousand. How close do you get?
Pentominoes
Twelve pieces, sixty squares, one rectangle to fill.
The Sieve
Watch the primes get left behind.
Bit flipper
Eight switches, 256 numbers.
Pascal's triangle, coloured
Colour the multiples and a fractal appears.
Ten thousand dice rolls
The histogram finds its shape.
Sunflower seeds
Turn the angle and watch the spirals break.
Times tables on a circle
Multiplication mod n draws a heart.
Complex plane
Drag a number. See it rotate when you multiply by i.
Hear the ratios
Octaves, fifths, and the Pythagorean comma, out loud.
Darts for π
Random points, a quarter circle, and a famous number.
Hailstone numbers
Halve it or triple-plus-one. Nobody knows if it always lands.
Matrix machine
Four numbers warp a picture.
The Mandelbrot set
Square, add, repeat. Zoom forever.
Play Nim
Beat the computer, or learn why you can't. Now with a last-counter-loses mode.
Code breaker
Shift letters, count them, crack the message.
Guess my number
Seven questions are always enough for 1 to 100.
Monty Hall
Play it, then simulate ten thousand games.
Towers of Hanoi
Move the disks, or watch the recursion do it.
First digits
Powers of two, Fibonacci, factorials. All obey the law.
Growth race
Slide the rates and watch the exponential win.
Prime spiral
Primes on a spiral line up in ways nobody fully understands.
Weekday trainer
Learn to name the day of any date in your head.
Trace the graph
One stroke, every edge once. Euler tells you when it's possible.
Colour the map
Four crayons, no matching neighbours.
Make the computer use six
Four colours are enough. Can you trick the greedy algorithm?
Mind reader
Lie once. It still finds your number, and the lie.
Dice in a circle
A beats B beats C beats D beats A.
Pick's theorem
Draw any shape on the dots. Count, don't measure.
Sequence detective
Type a sequence, get the formula, and meet a trap.
Vigenère
A keyword cipher, and the trick that cracked it.
Slide the digits
Times ten slides every digit one place left. Watch it happen.
Fraction bars
Cut two bars into the same size pieces and adding is easy.
The multiplication rectangle
See the four pieces inside a long multiplication.
Shapes that tile
Fit shapes round a point. Some close up, some leave a gap.
Will it fold?
Six squares. Cube or not a cube? Then meet all eleven nets.
Ways home
Count the routes across a grid of streets and spot the pattern.
Race to 21
Add 1, 2 or 3. Beat the computer, or learn its secret.
Find the fake coin
One light coin, a balance, and as few weighings as you can.