Oldalhosszak

Oldalhosszak, in Hungarian, translates to side lengths in English. In geometry, an oldalhossz is the length of a side of a polygon or of a line segment. These are scalar quantities that measure the distance between the endpoints of the side, typically expressed in units of length such as meters or centimeters.

In triangles, the three side lengths are commonly denoted by a, b, and c, with the angles opposite them labeled A, B, and C. The side lengths determine the triangle up to congruence, and they must satisfy the triangle inequalities: a + b > c, a + c > b, and b + c > a. Equality would indicate a degenerate triangle, where the points are collinear.

For polygons in general, the perimeter is the sum of the successive side lengths. Side lengths are preserved under rigid motions (translations, rotations, reflections) and, in dimensions two and higher, do not uniquely determine a polygon; different shapes can share the same multiset of side lengths.

Computing side lengths from coordinates uses the distance formula: the distance between two points equals the square root of the sum of squared differences in coordinates. Conversely, knowing the coordinates allows calculation of all side lengths. In non-Euclidean geometries, the concept of side length depends on the chosen metric.

Applications include solving problems in trigonometry, surveying, computer graphics, and architecture. The study of oldalhosszak intersects with properties such as regularity (equal side lengths) and symmetry, as seen in regular polygons where all side lengths are equal.