The observatory is largely known for housing the 54-year-old 37″ James Gregory Telescope, the largest operational telescope in Scotland. the first full size (0.94m) Schmidt-Cassegrain telescope built. It is used for research projects and mostly run by postgraduate students and postdocs mostly monitoring the brightness variations of stars, active galaxies, and transiting planets
The telescope is named after the inventor of reflecting telescope and Fellow of the Royal Society, James Gregory, a renowned mathematician and astronomer who was the first Regius Professor of Mathematics of the University of St Andrews 1668–74. He discovered infinite series representations for a number of trigonometry functions.
He wrote Vera Circuli et Hyperbolae Quadratura (1667; “The True Squaring of the Circle and of the Hyperbola”) where he used a modification of the method of exhaustion of Archimedes (287–212/211 BCE) to find the areas of the circle and sections of the hyperbola. He also wrote Geometriae Pars Universalis (1668; “The Universal Part of Geometry”) where he collected the main results then known about transforming a very general class of curves into sections of known curves (hence the designation “universal”), finding the areas bounded by such curves, and calculating the volumes of their solids of revolution. In his construction of an infinite sequence of inscribed and circumscribed geometric figures. He was one of the first to distinguish between convergent and divergent infinite series.
In 1670 and 1671, along with English mathematician John Collins, he contributed with important results on infinite series expansions of various trigonometry functions, including what is now known as Gregory’s series for the arctangent function:
arctan (x) = x − x3/3 + x5/5 − x7/7 + …
The arctangent of 1 is known to be equal to π/4. This led to the immediate substitution of 1 for x in this equation to produce the first infinite series expansion for π. Unfortunately, this series converges too slowly to π for the practical generation of digits in its decimal expansion. Nevertheless, it gave rise to more rapidly convergent infinite series for π.