Second week is over and I am so excited for the feedback and your excitement. For those of you that do not know what is happening: every day in December I am writing a fact about the history of mathematics. The posts go live on Facebook (event and page) and on Tumblr. Also, for those of you that want to read what happened in the first week, you can check First Week of History Fatcs. Here are some points:
The symbol “x” for multiplication was introduced by the English mathematician William Oughtred in 1631 in his “Key to mathematics”. As a symbol, it was not exactly new having been employed in so-called “cross multiplication” when dividing fractions.
It was not really accepted by arithmeticians, however, and did not come into general use in textbooks in elementary arithmetic until the latter half of the 19th century. Nor was it well received by algebraists because of its resemblance to the variable x, and so the dot – suggested by the English mathematician and astronomer Thomas Harriot in his “Artis analyticae praxis”, published posthumously in 1631 – came to be employed. Adriaan Vlacq, the Dutch publisher and computer of tables of logarithms, had suggested a dot in his “Aritmetica logarithmica” in 1628, though not as an active symbol.
The first mathematician of undisputed prominence to use the dot in a general fashion for algebraic multiplication was Leibniz in 1686; later algebraists used the dot in cases where the absence of a symbol would not have sufficed.
The concept of powers was known to the old Babylonians and Egyptians; in the Rhind Papyrus, Ahmes the Scribe used a word meaning mass or quantity to denote the unknown quantity the we call x.
In the days of rhetorical mathematics, powers of unknown had to have names before they could be described by symbols. The ancient Greeks, to whom mathematics meant geometry, called the square of the unknown a tetragon number, that is, a four-corner number.
Diophantos of Alexandria used the word “power” for the square of the unknown; the third power was a “cube”; the fourth, a “power-power”; the fifth, a “power-cube”; and the sixth, a “cube-cube”.
The first algebraic power symbols corresponding to our x^2, x^3, x^4, etc., to appear in print were found in the “Arithmetica integra” by the German mathematician Michael Stifel.
The term “function” first appeared in 1692 in a mathematical article in the “Acta Eruditorem” to denote various tasks that a straight line may accomplish with respect to a curve, such as forming a chord, tangent, or normal. The article was signed O.V.E. but is attributed to Gottfried von Leibniz. In another article from 1964, Leibniz gave the term “function” a more specific meaning by letting it denote the slope of a curve, a definition that has very little in common with the present day mathematical definition of function.
The Swiss mathematician Leonhard Euler in 1749 defined a function as a variable quantity that is dependent upon another quantity, thereby approaching today’s definition.
Euler’s definition was challenged when the French physicist and mathematician Joseph Fourier in 1822 presented his work on heat flow. For his investigations, Fourier introduced series with sines and cosines as terms, which led to the concept that a given representation of a function may be valid for only a certain range of values.
Based on Fourier’s investigations, Lejeune Dirichlet in 1837 proposed that, from the mathematical point of view, a function is a correspondence that “assigns a unique value of the dependent variable to every permitted value of an independent value”.
Some facts about the history of calculating devices:
c.2600 BC – the world’s oldest datable mathematical table comes from the Sumerian city of Shuruppag to the north of Uruk. It is ruled into 3 columns on each side: the first 2 columns list length measures followed by the Sumerian word for “equal”, and the final column gives the products of these lengths in area measure.
c.300 BC – the Samalis tablet, which is the earliest known surviving example of a counting board, was found on the Greek island of Salamis in 1846. It is made of white marble, has 3 sets of Greek numbers arranged around its edges, and measures approximately 150cm x 75cm x 4.5cm.
Yesterday, I have posted about earlier calculation tablets, so I thought that some of the earlier development of calculation tablets will be interesting! You can see the development up to the pocket calculator from 1971.
Hope you found this helpful. Thank you for your help and support. You can find me on Facebook, Tumblr, Google+, Twitter,Instagram and Lettrs, I will try to post there as often as possible. Don’t forget that maths is everywhere! Enjoy!