Geometry API

Prove geometric theorems using advanced algebraic methods. Access our A5 (Wu's Method) and A6 (Gröbner Basis) models via simple API calls.

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Get Your API Key

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Available Models

A5 Wu's Method

Fast algebraic solver using characteristic sets. Best for standard geometry proofs.

  • Average: 1-30 seconds
  • Angle relationships
  • Parallel & perpendicular lines
  • Triangle congruence

A6 Gröbner Basis

Comprehensive solver using Buchberger's algorithm. Handles complex cases.

  • Average: 5-120 seconds
  • Circle theorems
  • Complex constructions
  • Advanced proofs
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How to Use the API

How it works: You send geometry problems to our API, and our servers run the A5/A6 theorem provers. You don't need to install anything locally — just make HTTP requests with your API key.

Get Your API Key

Enter your email above and verify it. You'll receive an API key like: gai_live_abc123...

Submit a Problem

Send a POST request to our API with your geometry problem. The API queues your problem and returns a job ID.

cURL (Terminal / Command Prompt) 
curl -X POST https://idef-mathematics.com/api/v1/problems \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{"problem": "In triangle ABC, AB=AC. Prove angle ABC = angle ACB", "options": {"model": "A5"}}'

Response:

JSON Response 
{
  "job_id": "abc123def456",
  "status": "queued",
  "model": "A5"
}

Get the Result

Use the job_id to check if your proof is complete. Poll this endpoint until status is "completed".

cURL 
curl https://idef-mathematics.com/api/v1/jobs/YOUR_JOB_ID \
  -H "Authorization: Bearer YOUR_API_KEY"

Response (when completed):

JSON Response 
{
  "job_id": "abc123def456",
  "status": "completed",
  "result": {
    "proved": true,
    "proof_trace": "Step 1: Given AB = AC...",
    "computation_time": 1.24
  }
}

💡 Tip: For easier usage, download our Python SDK or Bash client from the Download page. They handle polling automatically.

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Problem Format

You can submit problems in natural language or structured GIVEN/GOAL format.

Natural Language

"In triangle ABC, if AB = AC, prove that angle ABC = angle ACB"

Structured Format (More Precise)

"GIVEN:\nPOINTS A,B,C\nEQLEN A B A C\nGOAL:\nEQANG A B C A C B"

Available Predicates

EQLEN A B C D — AB = CD
EQANG A B C D E F — ∠ABC = ∠DEF
COLL A B C — A, B, C collinear
PARA A B C D — AB ∥ CD
PERP A B C D — AB ⊥ CD
MIDP M A B — M is midpoint of AB
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API Endpoints

Method Endpoint Description
POST /api/v1/problems Submit a problem for proving
GET /api/v1/jobs/{job_id} Get result of a submitted problem
GET /api/v1/models List available models
GET /api/v1/status Check API status