By W. W. Rouse Ball
This article is still one of many clearest, such a lot authoritative and such a lot actual works within the box. the traditional historical past treats 1000s of figures and colleges instrumental within the improvement of arithmetic, from the Phoenicians to such 19th-century giants as Grassman, Galois, and Riemann.
Read Online or Download A short account of the history of mathematics PDF
Best mathematics books
A gradual creation to the hugely refined international of discrete arithmetic, Mathematical difficulties and Proofs offers themes starting from straight forward definitions and theorems to complicated subject matters -- similar to cardinal numbers, producing features, homes of Fibonacci numbers, and Euclidean set of rules.
Examines walls and covers of graphs and digraphs, latin squares, pairwise balanced designs with prescribed block sizes, ranks and permanents, extremal graph conception, Hadamard matrices and graph factorizations. This publication is designed to be of curiosity to utilized mathematicians, laptop scientists and communications researchers.
In diesem Lehrbuch finden Sie einen Zugang zur Differenzial- und Integralrechnung, der ausgehend von inhaltlich-anschaulichen Überlegungen die zugehörige Theorie entwickelt. Dabei entsteht die Theorie als Präzisierung und als Überwindung der Grenzen des Anschaulichen. Das Buch richtet sich an Studierende des Lehramts Mathematik für die Sekundarstufe I, die „Elementare research" als „höheren Standpunkt" für die Funktionenlehre benötigen, Studierende für das gymnasiale Lehramt oder in Bachelor-Studiengängen, die einen sinnstiftenden Zugang zur research suchen, und an Mathematiklehrkräfte der Sekundarstufe II, die ihren Analysis-Lehrgang stärker inhaltlich als kalkülorientiert gestalten möchten.
Extra info for A short account of the history of mathematics
Archytas was one of the first to give a solution of the problem to duplicate a cube, that is, to find the side of a cube whose volume is double that of a given cube. 1 The construction given by Archytas is equivalent to the following. On the diameter OA of the base of a right circular cylinder describe a semicircle whose plane is perpendicular to the base of the cylinder. Let the plane containing this semicircle rotate round the generator through O, then the surface traced out by the semicircle will cut the cylinder in a tortuous curve.
I mention the problem and give the construction used by Archytas to illustrate how considerable was the knowledge of the Pythagorean school at the time. Theodorus. Another Pythagorean of about the same date as Archytas was Theodorus of Cyrene, who is√said√to have √ proved √ √geomet√ 3, 5, 6, 7, 8, 10, rically that the numbers represented by √ √ √ √ √ √ 11, 12, 13, 14, 15, and 17 are incommensurable with unity. Theaetetus was one of his pupils. Perhaps Timaeus of Locri and Bryso of Heraclea should be mentioned as other distinguished Pythagoreans of this time.
Eratosthenes gives a somewhat similar account of its origin, but with king Minos as the propounder of the problem. Hippocrates reduced the problem of duplicating the cube to that of finding two means between one straight line (a), and another twice as long (2a). If these means be x and y, we have a : x = x : y = y : 2a, from which it follows that x3 = 2a3 . It is in this form that the problem is usually presented now. Hippocrates did not succeed in finding a construction for these means. CH. III] THE SCHOOLS OF ATHENS AND CYZICUS 35 Plato.