# Algebra and Geometry Solvers

Quadratic and cubic roots, triangle solver, shape areas and volumes, linear systems, matrices, vectors, trig, complex numbers, series, coordinate geometry.

## How to pay

Machine-payable over x402. USDC on: Base (eip155:8453), Solana (solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp), Polygon (eip155:137), Arbitrum One (eip155:42161).
No accounts. No API keys. No signup. The paying wallet is the account.

## Machine-readable

- OpenAPI: https://math-geometry.x402tookit.com/openapi.json
- x402 manifest: https://math-geometry.x402tookit.com/.well-known/x402
- Catalog (free): https://math-geometry.x402tookit.com/catalog
- Health (free): https://math-geometry.x402tookit.com/health
- Uptime (free): https://math-geometry.x402tookit.com/uptime

## Endpoints (11)

### GET /complex-ops — $0.02
Complex number arithmetic, modulus and argument, integer powers, square root and n-th roots, in rectangular and polar form.
Params: op: string, z: string, w?: string, n?: integer
Example: https://math-geometry.x402tookit.com/complex-ops?op=multiply&z=3%2B4i&w=1-2i

### GET /coordinate-geometry — $0.02
Plane geometry from coordinates: line through two points, distance, circle through three points, polygon area, intersections.
Params: mode: string, p1?: string, p2?: string, p3?: string, p4?: string, points?: string
Example: https://math-geometry.x402tookit.com/coordinate-geometry?mode=line&p1=1%2C2&p2=3%2C6

### GET /cubic-solve — $0.02
Solve ax^3 + bx^2 + cx + d = 0: all three roots (real and complex) by Cardano and the trigonometric method.
Params: a: number, b: number, c: number, d: number
Example: https://math-geometry.x402tookit.com/cubic-solve?a=1&b=-6&c=11&d=-6

### GET /linear-system — $0.02
Solve linear equations Ax = b (up to 6 unknowns): unique, none or infinite solutions, with rank and determinant.
Params: matrix: string, constants: string
Example: https://math-geometry.x402tookit.com/linear-system?matrix=2%2C1%2C-1%3B-3%2C-1%2C2%3B-2%2C1%2C2&constants=8%2C-11%2C-3

### GET /matrix-ops — $0.02
Matrix determinant, inverse, transpose, rank, trace, product with a second matrix, and eigenvalues of 2x2 and 3x3 matrices.
Params: op: string, matrix: string, other?: string
Example: https://math-geometry.x402tookit.com/matrix-ops?op=inverse&matrix=4%2C7%3B2%2C6

### GET /quadratic-solve — $0.02
Solve ax^2 + bx + c = 0: real or complex roots, discriminant, vertex, axis of symmetry and factored form.
Params: a: number, b: number, c: number
Example: https://math-geometry.x402tookit.com/quadratic-solve?a=1&b=-5&c=6

### GET /sequence-sum — $0.02
Arithmetic and geometric sequences: n-th term and sum (and infinite sum when it converges), plus Fibonacci and Lucas numbers.
Params: type: string, first?: number, step?: number, n: integer
Example: https://math-geometry.x402tookit.com/sequence-sum?type=arithmetic&first=1&step=2&n=10

### GET /shape-measure — $0.02
Area, perimeter, surface area and volume of circles, polygons, sectors, spheres, cylinders, cones, boxes, tori and more.
Params: shape: string, r?: number, h?: number, w?: number, l?: number, a?: number, b?: number, c?: number, base?: number, height?: number, sides?: integer, side?: number, angleDeg?: number, baseArea?: number, R?: number
Example: https://math-geometry.x402tookit.com/shape-measure?shape=cylinder&r=2&h=5

### GET /triangle-solve — $0.02
Solve a triangle from any three of sides a, b, c and angles A, B, C (degrees), incl. ambiguous SSA, with area and radii.
Params: a?: number, b?: number, c?: number, A?: number, B?: number, C?: number
Example: https://math-geometry.x402tookit.com/triangle-solve?a=3&b=4&c=5

### GET /trig-values — $0.02
Sine, cosine, tangent of an angle in degrees or radians, exact values at special angles, and inverse trig functions.
Params: angle?: number, unit?: string, inverse?: string, value?: number
Example: https://math-geometry.x402tookit.com/trig-values?angle=30&unit=deg

### GET /vector-ops — $0.02
Vector operations: dot and cross product, magnitudes, angle between vectors, projection, unit vectors and distance.
Params: u: string, v: string
Example: https://math-geometry.x402tookit.com/vector-ops?u=1%2C2%2C3&v=4%2C5%2C6

## Terms

All results are computed locally with standard algorithms in double-precision arithmetic (about 15 significant digits), provided as is. Ill-conditioned problems (nearly singular matrices, nearly equal roots) lose accuracy and are flagged where detected. Inputs travel in the query string, so keep them small.