Who invented surface area

Only at the end of middle ages some Arabs and Europeans started thinking of irrationals as some kind of numbers, while giving them telling nicknames, like "deafmute numbers". He was also the first to suggest a possibility that quadrature of the circle was unsolvable with straightedge and compass, although his argument for it was flawed. Archimedes calculated the exact formulas in the way that the ancient Greeks gave formulas in his book On the Sphere and Cylinder. This was not "experimental": He gave a full geometric proof, rigorous for its time period.

He considered this his greatest work. He asked that a diagram representing his proof be inscribed on his tomb. This was apparently done as at least one visitor to later Syracuse reported seeing the diagram. Some people think that Archimedes discovered calculus and found the formulas in that way, but hid his discovery.

Newton did much the same thing later, using Calculus to discover much about gravity but using geometric proofs when he wrote about gravity. Newton finally revealed his own work in Calculus when forced by Leibniz. Newton realized that Calculus would be controversial. Perhaps Archimedes did as well. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. Who calculated for the first time the volume and surface area of the sphere exactly? Ask Question. Asked 6 years, 9 months ago. Active 2 years, 6 months ago. Viewed 9k times. Improve this question. Conifold 62k 5 5 gold badges silver badges bronze badges. I would be surprised if the ancient Greeks and Egyptians didn't use sand to "stumble upon" the formulae and later fill in the proofs to match the prediction by sand.

What do I mean? Make a spherical container. Make a cylindrical container that would very closely circumscribe the spherical one. Some claim there is a lack of rigour in certain of the results of this work but the interesting discussion in [ 43 ] attributes this to a modern day reconstruction. On floating bodies is a work in which Archimedes lays down the basic principles of hydrostatics.

His most famous theorem which gives the weight of a body immersed in a liquid, called Archimedes' principle , is contained in this work.

He also studied the stability of various floating bodies of different shapes and different specific gravities. This he obtained by circumscribing and inscribing a circle with regular polygons having 96 sides. He argues in this work that this number is large enough to count the number of grains of sand which could be fitted into the universe.

There are also important historical remarks in this work, for Archimedes has to give the dimensions of the universe to be able to count the number of grains of sand which it could contain.

He states that Aristarchus has proposed a system with the sun at the centre and the planets, including the Earth, revolving round it. In quoting results on the dimensions he states results due to Eudoxus , Phidias his father , and to Aristarchus. There are other sources which mention Archimedes' work on distances to the heavenly bodies. For example in [ 59 ] Osborne reconstructs and discusses In the Method , Archimedes described the way in which he discovered many of his geometrical results see [ 7 ] But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.

Perhaps the brilliance of Archimedes' geometrical results is best summed up by Plutarch, who writes:- It is not possible to find in all geometry more difficult and intricate questions, or more simple and lucid explanations. Some ascribe this to his natural genius; while others think that incredible effort and toil produced these, to all appearances, easy and unlaboured results. No amount of investigation of yours would succeed in attaining the proof, and yet, once seen, you immediately believe you would have discovered it; by so smooth and so rapid a path he leads you to the conclusion required.

Heath adds his opinion of the quality of Archimedes' work [ 7 ] :- The treatises are, without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader.

There are references to other works of Archimedes which are now lost. Pappus refers to a work by Archimedes on semi-regular polyhedra, Archimedes himself refers to a work on the number system which he proposed in the Sandreckoner , Pappus mentions a treatise On balances and levers , and Theon mentions a treatise by Archimedes about mirrors.

Evidence for further lost works are discussed in [ 67 ] but the evidence is not totally convincing. Archimedes was killed in BC during the capture of Syracuse by the Romans in the Second Punic War after all his efforts to keep the Romans at bay with his machines of war had failed. Plutarch recounts three versions of the story of his killing which had come down to him.

The first version:- Archimedes In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus; which he declining to do before he had worked out his problem to a demonstration, the soldier, enraged, drew his sword and ran him through. The second version Finally, the third version that Plutarch had heard Archimedes considered his most significant accomplishments were those concerning a cylinder circumscribing a sphere, and he asked for a representation of this together with his result on the ratio of the two, to be inscribed on his tomb.

Cicero was in Sicily in 75 BC and he writes how he searched for Archimedes tomb see for example [ 1 ] Accordingly, after taking a good look all around Slaves were sent in with sickles It is perhaps surprising that the mathematical works of Archimedes were relatively little known immediately after his death.

As Clagett writes in [ 1 ] :- Unlike the Elements of Euclid , the works of Archimedes were not widely known in antiquity. It is true that Only after Eutocius brought out editions of some of Archimedes works, with commentaries, in the sixth century AD were the remarkable treatises to become more widely known.

Finally, it is worth remarking that the test used today to determine how close to the original text the various versions of his treatises of Archimedes are, is to determine whether they have retained Archimedes' Dorian dialect.

References show. Biography in Encyclopaedia Britannica. W R Knorr, Archimedes and the pseudo-Euclidean 'Catoptrics' : early stages in the ancient geometric theory of mirrors, Arch.

A Aaboe and J L Berggren, Didactical and other remarks on some theorems of Archimedes and infinitesimals, Centaurus 38 4 , - Book I, Arch. History Exact Sci. Wiskunde 33 , - S E Brodie, Archimedes' axioms for arc-length and area, Math. Storia Sci. G Giorello, Archimede e la metodologia dei programmi di ricerca Italian : With an English translation , Scientia Milano 1 - 4 , - G Goe, Is Archimedes' proof of the principle of the lever fallacious?

Surface Area of a Sphere The Greek mathematician Archimedes discovered that the surface area of a sphere is the same as the lateral surface area of a cylinder having the same radius as the sphere and a height the length of the diameter of the sphere.

Example : Find the surface area of a sphere with radius 5 inches. Subjects Near Me. Download our free learning tools apps and test prep books.