EllipsenflächenrechnerFormel

## Ellipse Calculations

### Area

**Area = pi × a × b**

Where a is the semi-major axis and b is the semi-minor axis.

### Circumference (Ramanujan Approximation)

**C ≈ pi × (3(a+b) - sqrt((3a+b)(a+3b)))**

There is no exact closed-form formula for the circumference of an ellipse. Ramanujan's approximation is remarkably accurate.

### Eccentricity

**e = sqrt(1 - b²/a²)** (when a ≥ b)

Eccentricity ranges from 0 (circle) to 1 (degenerate line).

Lösungsbeispiel

Ellipse with semi-major axis 6 and semi-minor axis 4.

  1. Area = pi × 6 × 4 ≈ 75.3982
  2. Circumference ≈ pi × (30 - √(22 × 16)) ≈ 31.7302
  3. Eccentricity = √(1 - 16/36) ≈ 0.7454