Math & Science

Plot 3D surfaces from z = f(x, y), polar z = f(r, theta), or fully parametric equations. Exact evaluation via mathjs, real holes where a function is undefined, and OBJ or STL export for 3D printing.

Aspect ratios reduced exactly by the greatest common divisor, with the reduction multiplied back as a check, resizes that say whether they are exact, and named ratios that carry a note where the name is not the ratio.

Body mass index against all eight rows of the WHO adult table, each naming its source, with the pound and inch at their exact defined values and a note when the adult table does not apply.

Molar mass, equation balancing, pH and the gas laws on all 118 elements of the IUPAC 2021 table, with every interval mass and every approximation named.

Exact ages and date differences worked out on the calendar itself, with no arithmetic on milliseconds, so the answer is the same in every time zone. Shows which days are not 86,400 seconds long.

Linear, quadratic, cubic and higher equations and systems, with exact rational coefficients, numerically stable roots and each root substituted back to show its residual.

Loans, compound growth, savings goals and rates of return on integers, with an amortisation schedule whose payments add up to the total and a balance that closes at exactly zero.

Add, subtract, multiply, divide, compare and simplify fractions of any size, exactly. Reads mixed numbers and repeating decimals, and gives the decimal expansion with its repeating cycle.

The greatest common divisor and lowest common multiple of any whole numbers at any size, with the Euclidean algorithm written out, Bezout coefficients, and the two answers checked against each other.

Area, perimeter, volume and surface area for twenty-four shapes, drawn to scale, with every assumption stated and every approximation named.

Plot functions with a real expression parser, poles drawn as gaps, and roots, turning points and integrals found by bracketing with the check printed.

Determinants, inverses, eigenvalues and row reduction over exact fractions, with A times its inverse shown to be exactly the identity and the condition number reported.

Ten kinds of percentage question, answered in exact arithmetic rather than floating point, with the working shown. Includes percentage points, finding the whole, and tax both ways.

Twelve kinds of physics problem with every constant named as defined, measured or conventional, results printed to the figures those constants justify, and an independent check on each answer.

Whether a number is prime, at any size, decided by deterministic Miller-Rabin rather than trial division. Prime factorisation, every divisor, the primes either side and Goldbach pairs.

Exact arithmetic on rationals, with both evaluation conventions named and the precedence table the parser runs on printed on the page.

Mean, median, both variances, all nine quantile definitions and the moment coefficients of shape, each with the definition it is under and where to reproduce it.

Add and subtract durations with the sign kept, so one hour minus two hours is minus one hour. Also moves a time of day forward or back and says how many midnights it crossed.

The tip, the tax and everybody's share worked out in whole pennies, so the amounts printed add up to the total printed. Says who pays the odd penny, and what rounding does to the tip rate.

Truth tables with the reading printed, so A implies B implies C shows its brackets. Refuses a chain of NAND or NOR rather than guessing, and reads a name like nota as one variable.