Kolmnurga

Kolmnurk is the Estonian term for triangle, a polygon with three sides and three interior angles. The form kolmnurga is the genitive singular used in phrases such as “kolmnurga külgede pikkused,” meaning the lengths of the triangle’s sides. In geometry, a triangle is the basic polygon and the simplest closed figure formed by three straight-line segments.

Properties of a kolmnurk include that the sum of its interior angles is always 180 degrees, and the triangle inequality states that the sum of any two side lengths exceeds the third. Triangles are classified by sides—equilateral (all sides equal), isosceles (two sides equal), scalene (all sides different—and by angles—acute (all angles less than 90°), right (one angle exactly 90°), and obtuse (one angle greater than 90°).

Key formulas for calculating the area and other measures include: Area = base × height ÷ 2; Area = sqrt(s(s−a)(s−b)(s−c)) via Heron’s formula, where s is the semiperimeter (a+b+c)/2. For two sides a and b with included angle C, Area = 1/2 ab sin C. In right triangles, Pythagoras’ theorem a² + b² = c² applies.

Important geometric concepts associated with kolmnurgad are centers such as the centroid (intersection of medians), circumcenter (perpendicular bisectors), incenter (angle bisectors), and orthocenter (altitudes). Triangles also underpin similarity and congruence, providing foundational results in Euclid’s Elements and modern geometry.

Applications of triangles appear across trigonometry, surveying, architecture, engineering, and computer graphics, including polygonal modeling and mesh generation. The study of kolmnurk connects algebra, geometry, and measurement, serving as a cornerstone of mathematical education.