Math Tools

Factor a symmetric positive-definite matrix A into L·Lᵀ, showing the lower triangular matrix L.

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Find a circle chord's length from the radius and central angle, or radius and perpendicular distance.

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Calculate a circle's radius, diameter, circumference, and area from any one known value.

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Calculate the area and arc length of a circle sector, and the area of the corresponding segment.

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Find a triangle's circumradius (and circumcenter, if vertices are given) — the circle passing through all three vertices.

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Classify a triangle by its sides (scalene/isosceles/equilateral) and angles (acute/right/obtuse), with the reasoning shown.

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Find the angle between the hour and minute hands of a clock at any given time.

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Calculate the cofactor matrix of a 2×2 up to 6×6 matrix, a key building block for finding a matrix inverse.

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Find the cofunction value of a trig function and angle using the complementary-angle identities.

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Flip one or more virtual coins with a genuinely random, fair 50/50 outcome each time.

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Simulate the Collatz (3n+1) sequence for any starting number, showing every step until it reaches 1.

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Find a basis for a matrix's column space and its rank, using the original matrix's pivot columns.

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Calculate the number of ways to choose items from a set when repetition is allowed.

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Solve for pressure, volume, or temperature using the Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂).

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Compare two fractions to find which is larger, smaller, or if they are equal, using cross-multiplication.

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Find the complement of an angle (90° minus the angle).

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Convert ax²+bx+c to vertex form a(x-h)²+k, showing every completing-the-square algebra step.

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Add, subtract, multiply, or divide two complex numbers, with modulus shown.

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Find all n-th roots of a complex number using De Moivre's theorem, shown in both rectangular and polar form.

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Combine a sum or difference of logarithms into a single logarithm using the product and quotient rules.

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Compute a matrix's condition number (the ratio of its largest to smallest singular value) for a 2x2 to 6x6 matrix.

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Calculate a confidence interval for a population mean from a sample mean, standard deviation, and size.

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Classify a general second-degree equation as a circle, ellipse, parabola, or hyperbola.

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Solve for the starting integer given a sum and count of consecutive integers, or list a sequence and its sum given a start.

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