This paper takes a known point from Brocard geometry, a known result from the geometry of the equilateral triangle, and bring in Euler's [empty set] function. It then demonstrates how to obtain new Brocard Geometric number theory results from them. Furthermore, this paper aims to determine a [triangle]ABC whose Crelle-Brocard Point [omega]…

The author has always been fascinated by the title identity. It's charming and simple, as well as easy to believe after pressing a few calculator keys. Several fine proofs have appeared in the literature, including several proofs without words. His own earlier proof is trigonometric, and he has often been dissatisfied with not being able to…

An integral, either definite or improper, cannot always be computed by elementary methods, such as reversed usage of differentiation formulae. Graphical properties, in particular symmetries, can be useful to compute the integral, via an auxiliary computation. We present graded examples, then prove a general result. (Contains 4 figures.)

An old way to determine asymptotes for curves described in polar coordinates is presented. Practice in solving trigonometric equations, in differentiation, and in calculating limits is involved. (MNS)

How to determine when there is a unique solution when two sides and an angle of a triangle are known, using simple algebra and the law of cosines, is described. (MNS)

Presents an approach to Vieta's formula involving pi and infinite product expansions of the sine and cosine functions. Indicates how the formula could be used in computing approximations of pi. (MVL)