In The Sand Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing else is known. Proof of archimedean property. Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia.The date of birth is based on a statement by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years. Biography. Ask Question Asked 6 years ago. This is the proof I presented in class. It is also sometimes called the axiom of Archimedes, although this name is doubly deceptive: it is neither an axiom (it is rather a consequence of the least upper bound property) nor attributed to Archimedes (in fact, Archimedes credits it … Active 1 year, 4 months ago. Hot-air balloons and ships are the applications of Archimedes principle. This theorem is known as the Archimedean property of real numbers. 3 $\begingroup$ I am trying to self-study Baby Rudin (and it's proving quite challenging to me) ... kinda like a pidgeonhole principle. It can be proved mathematically using Newtons's Laws and Divergence Theorem. Archimedes principle is the buoyant force of an immersed body which is the product of density of liquid immersed in, acceleration due to gravity, and its volume. The Archimedean Property Definition An ordered field F has the Archimedean Property if, given any positive x and y in F there is an integer n > 0 so that nx > y. Theorem The set of real numbers (an ordered field with the Least Upper Bound property) has the Archimedean Property. Viewed 8k times 5.