Abstract
AbstractThe idea of using a mirror that provides optical rays all converging to a single point originated in the Hellenistic period of Greece more than two millennia ago. Because of the straightforward geometrical properties of conics as meridional sections of stigmatic mirrors, catoptrics was constituted long before dioptrics. Nevertheless, and surprisingly, the first telescopes built were not reflectors but refractors.In Greece it was long known that some problems of a geometric nature were not soluble by straightedge and compass. A legend of the Classic period of Greece states that the gods were unhappy because geometry was not sufficiently studied. The oracle of Delos, which was consulted before major decisions, said ~430 BC that recovery of the gods’ clemency would require solving three problems: the angle trisection, the cube duplication, and the circle squaring. The first two problems were rapidly solved, but the third has baffled mathematicians for 2,300 years until F. Lindemann (1882) demonstrated that p is transcendental, and thus showing that the construction of the circle length by purely geometrical means is insoluble.KeywordsSpherical AberrationLarge TelescopeAperture AngleAspherical SurfaceConcave Mirror
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