Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For K-12 Students · Direction Field

Direction Field for the birthday paradox

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate the birthday paradox live below — adjust the inputs and watch it respond, right in your browser.

Direction Field / Slope FieldLive

dy/dx = f(x, y) · drag the start point

Controls

dy/dx = f(x, y)

▶ Run in Python

Data Inspector

Equationdy/dx = f(x,y)

Curves1

IntegratorRK2

Governing equation

\frac{d y}{d x} = f (x, y) = y - x

Reading this result: Every tick shows the slope dy/dx = f(x,y) at that point; drag the start point and RK2 rethreads the solution curve live, always staying tangent to the arrows. That start point alone picks which one curve you get — click elsewhere to pin extra curves for comparison.

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More with Direction Field

Direction Field for compound interest Direction Field for a population curve Direction Field for a loan payoff Direction Field for a logistic map Direction Field for a Fibonacci sequence Direction Field for a fractal tree Direction Field for a Fourier series Direction Field for a Taylor approximation

Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Direction Field for the birthday paradox" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.