Polygones & Formes Géométriques
High-precision calculators for equilateral and regular polygons. Each solver is equipped with bidirectional solving across all dimensions, live Cartesian SVG blueprints, exact radical algebraic proofs, and machine-readable LLM prompts.
Universal Regular N-Sided Polygon Solver
Universal bidirectional calculating engine for any regular polygon from n = 3 to 1000 sides. Dynamically resolves side length, area, perimeter, inradius, circumradius, flat-to-flat span, and all diagonal classes with Archimedean circle exhaustion convergence and live dynamic blueprints.
Regular Octagon
8-sided regular polytope. Bidirectional solver for side length, area, inradius, circumradius, span, and all 3 diagonal classes with exact radical derivations.
Regular Hexagon
Equiangular polygon with 6 equal sides. Exact formulas for minimal/maximal diameters, apothem r = a√3 / 2, circumradius R = a, and honeycomb tessellations.
Regular Pentagon
5-sided polygon governed by the golden ratio ϕ = (1 + √5) / 2. Diagonals form the classic self-intersecting pentagram star with exact radical proofs.
Regular Decagon
10-sided regular polygon with interior angles of 144°. Circumradius R = a · ϕ, flat-to-flat span, and 4 distinct diagonal classes.
For any regular polygon with n sides of length a:
- Interior Angle (α): α = (n - 2) × 180° / n = π(1 - 2/n) rad
- Apothem / Inradius (ri): ri = a / [2 · tan(π / n)]
- Circumradius (R): R = a / [2 · sin(π / n)]
- Total Area (A): A = (n · a²) / [4 · tan(π / n)] = ½ · n · R² · sin(2π / n)
- Total Diagonals (Nd): Nd = n(n - 3) / 2