Arc (geometry)

An arc is a curve segment bounded by two points on a larger curve, most commonly a portion of a circle or other smooth path. Arcs are fundamental to geometry, appearing everywhere from architectural design to celestial mechanics.

The simplest arc is a circular arc: a section of a circle's circumference defined by a center point and two endpoints. Its properties—angle, radius, arc length, and chord—form the basis of trigonometric relationships and appear in Navigation, Engineering, and mathematical modeling.

Arcs extend beyond circles. An elliptical arc follows an ellipse, crucial in planetary orbits and architectural curves. Parabolic arcs model projectile paths and reflector shapes. Arbitrary curves can be locally approximated by arcs through differential geometry.

In practical contexts, arcs appear in tessellations, decorative patterns, and the rotation of objects. Engineers use arcs to distribute forces smoothly; artists employ them for visual rhythm.

The concept bridges pure mathematics and physical reality, making arcs indispensable across disciplines.

Related

Circle, Radius, Circumference, Calculus, Trigonometry, Ellipse, Parabola