Abstract: This is the unifying principle proposed by the author to calculate mathematically correct value of solid angle subtended by any polygonal plane at any point in the space. According to this theory, if the location of foot of perpendicular drawn from the given point in the space to the plane of polygon is specified then the polygonal plane can be internally or externally or both divided into certain number of triangles by joining all the vertices of polygon to the foot of perpendicular. Further each of the triangles can be internally or externally sub-divided in two right triangles having common vertex at the foot of perpendicular. Thus, the solid angle subtended by the polygonal plane at any point is the algebraic sum of solid angles subtended by the triangles at the same point such that the algebraic sum of areas of all these triangles is equal to the area of polygon. This theory requires only one standard formula for the solid angle subtended by a right triangular plane for finding out the solid angle subtended by any polygonal plane. The applications of solid angle subtended by the planes & plates are wider in the field of Radiometry for analysis of radiation energy emitted by point-sources. This field requires precise values of radiation energy emitted by uniform point-sources like radioactive elements. Also, this theory is extremely useful in case studies & practical computations.
Keywords: Theory of Polygon, HCR’s Standard Formula-1, Solid angle, Polygonal plane, F.O.P., Element Method, Algebraic sum.
Title: HCR’S THEORY OF POLYGON “Solid Angle Subtended By Any Polygonal Plane at Any Point in the Space”
Author: Mr Harish Chandra Rajpoot
International Journal of Mathematics and Physical Sciences Research
ISSN 2348-5736 (Online)
Research Publish Journals
