Area of a circle "ds" over the whole circle formula_33 is just the arc length, which is its circumference, so this shows that the area "A" enclosed by the circle is equal to formula_34 times the circumference of the circle. Note that the area of a semicircle of radius r can be computed by the integral formula_35. By trigonometric substitution, we substitute formula_36, hence formula_37 The last step follows since the trigonometric identity formula_42 implies that formula_43 and formula_44 have equal integrals over the interval formula_45, using integration by substitution. But on the other hand, since formula_46, the sum of the two integrals is
Mohr's circle points formula_117 on the Mohr circle and the centre of the circle. This double angle relation comes from the fact that the parametric equations for the Mohr circle are a function of formula_35. It can also be seen that the planes formula_80 and formula_81 in the material element around formula_7 of Figure 5 are separated by an angle formula_135, which in the Mohr circle is represented by a formula_136 angle (double the angle). The second approach involves the determination of a point on the Mohr circle called the "pole" or the "origin of planes". Any straight line drawn from the