Inscription of a circle into a four-cornered


Figure 1 shows part of a circle inscribed in a 4x4 square with the length a. V and W are crossing-points of the mid-lines of the square with RS and ST resp.. b is the distance from V to Z equal W to Z. Alpha corresponds to the angle in-between WZ and YZ

Figure 2 shows the “perspective” view of a 8x8 square including center-lines (red) corresponding to inclinations of 30, 60 and 90 degree, and a frame-work of tangents (blue) suitable for the circle to be inscribed.

Figure 3 shows the grid with the circle inscribed.

Figure 4 and 5 present photographic equivalents

Conclusions :

The distance b - estimated as shown in the graph - is b = 1.008 a, thus b less than 1 % longer than a.  The angle alpha - estimated as shown the graph - is 29 degree and 45 “, thus less than 1 % different from 30 degree.

V and W are therefore suitable points of repair for drawing the segment of a circle in such a square, RS and SW present suitable tangents to this circle segment in V and W, and the angle in-between WZ YZ is suitable to present an angle of 30 degree, he concept thus suitable for situations requesting high accuracy.