Dividing a circle into areas lines (there are two points on one side and one on the other). So the recurrence can be expressed as which can be easily reduced to using the sums of the first formula_3 natural numbers and the first formula_3 squares, this combines to Finally which yields The lemma asserts that the number of regions is maximal if all "inner" intersections of chords are simple (exactly two chords pass through each point of intersection in the interior). This will be the case if the points on the circle are chosen "in general position". Under this assumption of "generic intersection", the number
Mohr's circle stress formula_95 is the abscissa of the centre formula_85, given by and the length of the radius formula_98 of the circle (based on the equation of a circle passing through two points), is given by The maximum and minimum shear stresses correspond to the ordinates of the highest and lowest points on the circle, respectively. These points are located at the intersection of the circle with the vertical line passing through the center of the circle, formula_85. Thus, the magnitude of the maximum and minimum shear stresses are equal to the value of the circle's radius formula_98 As mentioned before,