Birthday Paradox

Type any function and see its shape straight away. Plot up to three at once in three colours to compare them, drag the trace point to read a value off a curve, and see where each one crosses zero.

Spin a spinner, flip a coin or roll a die and watch two sets of bars: the chances the shapes predict, and the results you actually got. Ten spins prove nothing; a few hundred and the two are hard to tell apart.

Move m and watch the line tilt; move b and watch it slide. Or drag the two points on the line and read the equation it writes back. A rise-over-run staircase climbs the line so slope becomes something you can count.

Two bodies under gravity trace an ellipse forever and you can write the formula down. Add a third and no such formula exists. Run the figure-eight orbit, nudge one mass, and watch a stable pattern become unpredictable while the total energy stays put.

Approximate the area under a curve with strips and choose how each takes its height: left edge, right edge, middle, or a sloping top. Push the strip count up and watch the error fall, with the running total plotted as its own curve.