Manual Reference Pages - citer (3)
NAME
citer(3f) - [M_math:geometry] determine various geometric properties of a circle segment given radius and area of the segment.
CONTENTS
Synopsis
Description
SYNOPSIS
Usage:
SUBROUTINE CITER(A,R,H,S,C,DADH) DOUBLEPRECISION,INTENT(IN) :: A,R DOUBLEPRECISION,INTENT(OUT) :: H,S,C,DADH
DESCRIPTION
This subroutine determines various geometric properties of a segment of a circle given the radius of the circle and area of the segment.The figure below defines the geometry under consideration. This figure was taken directly from page 12 of the CRC Standard Mathematical Tables, 21st Edition, Published by the Chemical Rubber Company, Cleveland, OH. This page of the CRC Standard Mathematical Tables covers Mensuration Formulae for Circles.
In the figure below, the arc labeled "S" is the portion of the circle defined by angle "THETA". "C" is a secant, "H" is the height of the segment between "S" and "C", and "D" is the shortest distance from the center of the circle to the secant "C".
Specifically, this subroutine determines H, S, C, and the derivative of the segment area with respect to H given the radius of the circle, "R", and the area of the segment between "S" and "C".
Diagram:
> _________________ S > /|\ __---*****---__ > | _-- --_ > H * * > ___\|/___ *_______________________* > /|\ \ C / > | \ / > | \ / > | \ / > | \ / > | \ / > D \ / R > | \ THETA / > | \ / > | \ / > | \ / > ___\|/_______________ * >
| citer (3) | October 17, 2020 |
