kartiotyppi

Kartiotyppi, in Finnish geometry, refers to a classification of cones. A cone is a solid consisting of all line segments joining a fixed apex to points on a base figure lying in a plane. The base is typically a circle, ellipse, or another planar curve. Kartiotyypit thus denote the family of cones defined by their base shape and the position of the apex relative to the base.

Common types by base shape are circular cones, elliptical cones, and more general cones where the base is any planar curve. By apex alignment, cones are described as right cones when the apex projects orthogonally to the center of the base, and oblique cones when it does not.

Key properties: the volume of a cone equals one third of the base area times the height. For a circular cone with base radius r and height h, V = (1/3) π r^2 h. The lateral surface area for a circular cone is A_lateral = π r l, where l is the slant height, l = sqrt(r^2 + h^2). Elliptical and other-base cones require more general formulas, typically involving the base ellipse parameters and the slant height measured along generators.

Applications of karityyppit appear in geometry, architecture, and computer graphics, where cones are used in modeling, rendering, or calculating volumes and surface areas. The term is used in Finnish-language geometry literature to refer to this classification, while international terminology often uses “cone type” or simply “cone” to describe these classifications.