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The illustrated formula library

Mathlab

A formula collection that explains itself. Every formula here, from the area of a circle to the escape velocity of a rocket and the slowing of time near a black hole, comes with a picture you can move, the reason it is true, and worked examples that guide you to the answer instead of just handing it over.

Browse the library The formula sheet Build a worksheet
Fig. 0Times tables on a circle
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Put 200 dots around a circle and number them. Join every dot to the dot at twice its number, so 1 joins 2, 2 joins 4, 3 joins 6, counting round again after the last dot. A heart appears, the curve mathematicians call a cardioid. Try multiplying by 3, then press play.

The library

Shelves of formulas for mathematics, physics and chemistry, numbered like a reference book. Each entry shows what the formula means, lets you move it, proves where it comes from and walks you through using it.

Inside every entry

Every formula is explained the same way, so you always know where to look. It is built for understanding, not for copying answers.

  1. 1 · The formula cardEvery symbol named

    Each letter has its own colour, meaning and unit, and the colours follow it through the whole page.

  2. 2 · The live figureMove it and watch

    Drag and slide. The drawing changes, and the numbers flow straight into the formula.

  3. 3 · Where it comes fromStep by step

    A short proof or derivation, one step at a time, with a picture that follows along.

  4. 4 · Worked exampleUnderstand, plan, solve, check

    A real problem solved in four steps, revealed one at a time so you can think ahead.

  5. 5 · Your turnHints, not answers

    Try a problem yourself. Stuck? Climb a ladder of hints that ends with the method, never just the number.

Classic problems

The stories behind the formulas: famous puzzles from history, each with a live figure, three challenges to solve and the trick that cracked it.

The toolbox

Formulas are tools, but so are ways of thinking. Mathematicians carry a set of tricks for attacking problems they have never seen before. Collect them here.