The Reuleaux triangle is derived from an equilateral triangle. It is produced by replacing each side of the equilateral triangle with the arc of a circle. These two-dimensional triangles can be used to create somatocharts. Three-numeral somatotype data can additionally be plotted within a standard rectangular coordinate axis system.
Geometric figures may be analyzed according to their component parts. Perhaps the most basic components of the Reuleaux triangle consist of those points which comprise it. The position of a point in a plane can be given by means of two numbers. For example, x, y can be the distances of a point, P, from two given perpendicular lines. Given this information, the position of P can be determined when the values of both x and y are known. These numbers then become the cartesian coordinates of P.
Points may also exist in three-dimensional space. For these, distances, x, y, z may be given. Furthermore, a straight line in three-dimensional Euclidean space is determined by any two distinct points that lie on it. For example, points A(x1, y1, z1) and B(x2, y2, z2) might be two points on line AB. Additionally, line AB could be further defined as consisting of the points P(x, y, z) for which a value of the ratio (/( can be found such that
x = (x1 + (x2, y = (y1 + (y2, z = (z1 + (z2.
Every value of (/( determines a single point on the line AB. In addition, ( = 0 determines point B and ( = 0 determines point A. Furthermore, the two values (, ( cannot equal zero simultaneously.
The coordinates of point, P, satisfy the relation which is found by eliminating the ratios -1:(:(. These coordinates are as follows:
ªx x1 x2ª = 0.
ªy y1 y2ª
ªz z1 z2ª
(y1z2 - y2z1)x + (z1x2 - z2x1)y + (x1y2 - x2y1)z = 0
This equation, being of the form lx + my + nz = 0, is called a linear equation....