By Ivor Grattan-Guinness

Arithmetic is without doubt one of the most elementary -- and so much historic -- different types of wisdom. but the main points of its historic improvement stay vague to all yet a number of experts. The two-volume significant other Encyclopedia of the historical past and Philosophy of the Mathematical Sciences recovers this mathematical historical past, bringing jointly some of the world's best historians of arithmetic to ascertain the historical past and philosophy of the mathematical sciences in a cultural context, tracing their evolution from precedent days to the 20th century.In 176 concise articles divided into twelve elements, participants describe and research the range of difficulties, theories, proofs, and methods in all parts of natural and utilized arithmetic, together with chance and facts. This crucial reference paintings demonstrates the continued significance of arithmetic and its use in physics, astronomy, engineering, machine technology, philosophy, and the social sciences. additionally addressed is the background of upper schooling in arithmetic. rigorously illustrated, with annotated bibliographies of assets for every article, The spouse Encyclopedia is a helpful examine instrument for college students and academics in all branches of mathematics.Contents of quantity 1: -Ancient and Non-Western Traditions -The Western center a while and the Renaissance -Calculus and Mathematical research -Functions, sequence, and strategies in research -Logic, Set Theories, and the rules of arithmetic -Algebras and quantity TheoryContents of quantity 2: -Geometries and Topology -Mechanics and Mechanical Engineering -Physics, Mathematical Physics, and electric Engineering -Probability, information, and the Social Sciences -Higher schooling andInstitutions -Mathematics and tradition -Select Bibliography, Chronology, Biographical Notes, and Index

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**Extra info for Companion encyclopedia of the history and philosophy of the mathematical sciences, Volume 2 **

**Sample text**

It is usually to one’s advantage to find coordinate axes with respect to which a given curve has a particularly simple equation. Figure 2 A straight line and parabola plotted in Cartesian coordinates Coordinate methods can be used to find where two curves meet. To find where the line with equation meets the circle with equation Page 849 , one proceeds algebraically. Eliminating y between the two equations, one obtains, , whose solutions are x=0 and . The corresponding y-values are y=−1 and , respectively.

A polygon is regular if its edges are equal and its angles are equal. ) He goes on to say (correctly) that if h is an integer relatively Page 871 Figure 4 The illustration of Poinsot’s definition of regular polygons (from his 1809) Page 872 prime to m, and if m points, equidistributed on a circle, are connected by segments each of which spans h of the arcs determined by the points, then a regular polygon is obtained. In modern notation, such a polygon would be designated {m/h}; convex polygons correspond to h=1, and the pentagram {5/2} to m=5 and h=2 (see Figure 4, taken from Poinsot’s paper).

In that way his algebraic geometry was more cumbersome than ours, but in another way it was more flexible. Our coordinate axes are usually at right angles to one another; his were not so restricted. This helps to simplify the equations that arise, but complicates their interpretation. The modern perpendicular system became standard with, and because of, Euler. Was Descartes really the first to do this? Coordinate systems have been claimed for the Greeks (by Coolidge 1940), and even for the Egyptians.