Quadrature

Drive the error under tolerance by choosing a numerical integration method and subdivision count — all on a limited compute budget.

How to play

Each round sets an integral, a target error tolerance, and a compute budget. Pick a method, set the number of subdivisions, and run an estimate. Each run spends budget based on its cost; drive the absolute error below tolerance before the budget runs out. Smarter methods reach the target on far less budget than brute-force rectangles.

• Choose a method: left, right or midpoint rectangles, trapezoid, or parabolic panels
• Set the subdivision count and run an estimate
• Each run costs budget — get under the error tolerance before it's gone
• Solve with budget to spare and few runs for the highest score

Game modes

• Daily: a fixed integral shared each day (scored on the leaderboard)
• Practice: fresh randomized problems

Controls

• Desktop: click a method, drag the subdivisions slider, and click Run estimate
• Phone & tablet: tap a method, drag the slider, and tap Run (mouse or touch only)

Tips & strategy

• Higher-order methods converge much faster, so a few subdivisions of a parabolic rule often beats hundreds of rectangles
• Don't over-subdivide — every run costs budget, so estimate the smallest count that clears the tolerance

What you'll learn

Quadrature is about numerical integration, teaching why the choice of method matters.

• Skills: integration, numerical methods, calculus
• Best for: advanced high school / college
• For parents & teachers: numerical integration and why method matters.

About Quadrature

Quadrature is an original free browser calculus game about numerical integration, teaching why method choice matters as much as raw effort when approximating the area under a curve.

A free, original browser game on PlayPendium — no download, no install. Browse all games →