In geometry his greatest achievement was an accurate value of ?. His rule is stated as: dn^2+(2ad)n=2s, which implies the approximation 3.1416 which is correct to the last decimal place.

Each such answer to the great question, invariably asserted by the followers of its propounder, if not by himself, to be complete and final, remains in high authority and esteem, it may be for one century, or it may be for twenty: but, as invariably, Time proves each reply to have been a mere approximation to the truth tolerable chiefly on account of the ignorance of those by whom it was accepted, and wholly intolerable when tested by the larger knowledge of their successors.
thomas henry huxleyMr. Darwin's hypothesis is not, so far as I am aware, inconsistent with any known biological fact; on the contrary, if admitted, the facts of Development, of Comparative Anatomy, of Geographical Distribution, and of Palaeontology, become connected together, and exhibit a meaning such as they never possessed before; and I, for one, am fully convinced that if not precisely true, that hypothesis is as near an approximation to the truth as, for example, the Copernican hypothesis was to the true theory of the planetary motions.
thomas henry huxleyThe capacity of the human mind for formulating and solving complex problems is very small compared with the size of the problems whose solution is required for objectively rational behavior in the real world or even for a reasonable approximation to such objective rationality.
Herbert Simon (1957) Models of Man. p.198The principle of bounded rationality [is] the capacity of the human mind for formulating and solving complex problems is very small compared with the size of the problems whose solution is required for objectively rational behavior in the real world or even for a reasonable approximation to such objective rationality.
Herbert A. Simon, (1947). Administrative Behavior: A Study of DecisionMaking Processes in Administrative Organization. p. 198To a good approximation, all species are insects.
Robert May, quoted in Richard Dawkins, The Selfish Gene (1989), p. 251.The societal division of labor obtains the dignity of an ontological condition. If truth presupposes freedom from toil, and if this freedom is, in the social reality, the prerogative of a minority, then the reality allows such a truth only in approximation and for a privileged group.
Herbert Marcuse (1964), One Dimensional Man, pp. 128130Let us suppose that we have set the problem of finding a solution to the equation This is a problem for which the Babylonians around 1700 BC found the excellent approximation ...This is the identical problem which Pythagoras asserted had no fractional solution and in whose honor he was supposed to have sacrificed a hecatomb of oxen the problem which caused the existentialist crisis in ancient Greek mathematics. The exists (as the diagonal of the unit square); yet it does not exist (as a fraction)!
Philip J. Davis and Reuben Hersh, The Mathematical Experience (1980) p.180