Pituuskulmaa

Pituuskulmaa is a geometric concept used to describe the angular width of an object as seen from a particular observation point. It is defined as the angle between the lines from the observer to the object's endpoints, equivalently the angle subtended by the object at the observer's eye. In English this is commonly called angular size or angular width.

The word is Finnish, formed from pituus meaning length and kulma meaning angle. The form pituuskulmaa is the genitive or partitive inflection depending on sentence structure.

Calculating pituuskulmaa can be done in several ways. If the object is a straight segment of length L and lies at a distance D from the observer, perpendicular to the line of sight, the angular size theta is approximately 2 arctan((L/2)/D). For small L/D, theta ≈ L/D radians. In general, if the endpoints of the object are at positions A and B and the observer at O, the angular size is theta = arccos((OA · OB)/(|OA| |OB|)).

Applications include astronomy (angular diameter of planets and the Moon), photography and videography (field of view and framing), and navigation or surveying where the apparent width of objects matters. Limitations arise when the object is extended, curved, or moves relative to the observer, requiring more complex models.

See also angular size, field of view, angular distance. References: introductory geometry texts.