...indefinitely increased, the apothem of the polygon approaches the radius of the circle as its limit. Given a regular polygon of n sides inscribed in the circle of radius OA, s being one side and a the apothem. To prove that a approaches r as a limit, if n is increased...

...equal. If the circumference of a circle be divided into n equal arcs. (1) The po1nts of division are the vertices of a regular polygon of n sides inscribed in the circle; (2) If tangents be drawn to the circle at these points, these tangents are the sides of a regular polygon...

...indefinitely increased, the apothem of the polygon approaches the radius of the circle as its limit. Given a regular polygon of n sides inscribed in the circle of radius OA, s being one side and a the apothem. To prove that a approaches r as a limit, if n is increased...

...indefinitely increased, the apothem of the polygon approaches the radius of the circle as its limit. Given a regular polygon of n sides inscribed in the circle of radius OA, s being one side and a the apothem. To prove that a approaches r as a limit, if n is increased...

...indefinitely increased, the apothem of the polygon approaches the radius of the circle as its limit. Given a regular polygon of n sides inscribed in the circle of radius OA, s being one side and a the apothem. To prove that a approaches r as a limit, if n is increased...

...+ 2(nl)w; that these are all different is easily seen from their representative points, which form a regular polygon of n sides inscribed in the circle of radius = ?•". m (jf + it/)' ~i is defined as = = r n cos - 0 - t sin — 0 I; 1 . ™ / m . . . m \ •...

...(12) . r, r2, r3, . . . ,'r"-i, r" = 1. ThieYг complex numbers (10), and therefore the numbers (12), are represented -geometrically by the vertices of...unity and center at the origin with one vertex on the x-axis (Fig. 14). Fig. 14 For n = 3, the numbers (12) are со, <o2, 1, shown in Fig. 13. For n = 4,...

...r, r 2 , r 3 , . . . , r"- i , r" = 1. The n complex numbers (10), and therefore the numbers (12), are represented geometrically by the vertices of a...unity and center at the origin with one vertex on the x-axis (Fig. 14). Fig. 14 Fig. 15 For n = 3, the numbers (12) are ш, <о 2 , 1, shown in Fig. 13....

...= l. We note that the nth roots of unity are represented in the Argand diagram by points which are vertices of a regular polygon of n sides inscribed in the circle | z | = 1, one of the vertices being 2=1. If we write z"= 1 =cos 2kir + i sin Zk-n, where k is zero...

...by taking k = 0, 1, . . . , n — 1 successively. As we have seen, for n > 2 the n images of z are the vertices of a regular polygon of n sides inscribed in the circle \w\ - p. If we consider in the z-plane, the n angular regions Gjt = {z: 0 < \z\ < oo, Ikir < arg z...