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Math Timeline Project
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Math Timeline Project
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Euler introduces the notation f(x).Euler introduced and popularized several notational conventions through his numerous and widely circulated textbooks. Most notably, he introduced the concept of a function and was the first to write f(x) to denote the function f applied to the argument x. He also introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm (now also known as Euler's number), the Greek letter Σ for summations and the letter i to denote the imaginary unit.
The first symbols for numbers, simple straight lines, are used in Egypt.Using these number-signs, the Egyptians could add, subtract, multiply and divide; but they had no special symbols for these operations, instead they gave a form of words describing what had to be done. Hieroglyphics were reserved for formal, official inscriptions (because they were too complex for ordinary purposes), and they make the picture writing we see in royal tombs and on temple walls. Numbers were seldom used in hieroglyphic writing. Scribes used a simplified version of hieroglyphic(pictorial), known as hieratic(symbolic), written in ink on papyrus.
Babylonians use multiplication tables.The Babylonians used tablets containing multiples, squares, and reciprocals to perform the operation of multiplication. Let's look at how they would have used a table of multiples.Suppose we want to multiply 23 × 57. A Babylonian student could have used a tablet containing the multiples of 23. Remember, Babylonains used base-60, so the table contains (1,9)60 for 3 × 23 instead of 69.
Napier invents Napier's bones, consisting of numbered sticks, as a mechanical calculator.Napier's bones is a manually-operated calculating device created by John Napier of Merchiston for calculation of products and quotients of numbers. The method was based on Arab mathematics and the lattice multiplication used by Matrakci Nasuh The complete device usually includes a base board with a rim; the user places Napier's rods inside the rim to conduct multiplication or division.
Palaeolithic peoples in central Europe and France record numbers on bones.Paleolithic peoples use tallies on the bones of animals, ivory, and stone to record numbers (central Europe and France). For example, a wolf bone from this period shows 55 cuts arranged in groups of 5.
Read more: http://www.answers.com/topic/year-30-000-bce#ixzz30m4aUDk0
AD(AP+PR+RB) = AD x AP + AD x PR + AD x RB
(+,-,x,/)
http://math.widulski.net/worksheets/BabylonianMultiplication.html
http://en.wikipedia.org/wiki/Leonhard_Euler
http://mathsforeurope.digibel.be/story.htm
http://en.wikipedia.org/wiki/Napier's_bones
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A decimal number system is in use in Egypt. This sort of system is called unary. It is common among ancient civilisations. One advantage of unary systems is that it doesn't matter what order you write the number. You can jumble them up and you can still work out what they mean. But in our system, 123 means something different to 321. The Decimal notation is the writing of numbers in a base-10 numeral system. Examples are Roman numerals, Brahmi numerals, and Chinese numerals, as well as the Hindu-Arabic numerals used by speakers of many European languages. Roman numerals have symbols for the decimal powers (1, 10, 100, 1000) and secondary symbols for half these values (5, 50, 500).
The abacus is developed in the Middle East and in areas around the Mediterranean. It is difficult to imagine counting without numbers, but there was a time when written numbers did not exist. The earliest counting device was the human hand and its fingers, the feet and toes. Then, as even larger quantities (larger than ten human-fingers and toes could represent) were counted, various natural items like pebbles and twigs were used to help keep count.Merchants who traded goods not only needed a way to count goods they bought and sold, but also to calculate the cost of those goods. Until numbers were invented, counting devices were used to make everyday calculations. The abacus is one of many counting devices invented to help count large numbers.
Briggs publishes Arithmetica logarithmica (The Arithmetic of Logarithms) which introduces the terms "mantissa" and "characteristic". It gives the logarithms of the natural numbers from 1 to 20,000 and 90,000 to 100,000 computed to 14 decimal places as well as tables of the sine function to 15 decimal places, and the tangent and secant functions to 10 decimal places. A straightforward way to compute new logarithms from existing ones is to use the square
root. For instance, if log n = a and log m = b are known.The use of square roots had already been alluded to by Napier in his Construction, to which
Briggs added some comments .
Briggs used this method as follows. He first considered the logarithms of 2n p
10.
Cayley gives an abstract definition of a matrix, a term introduced by Sylvester in 1850, and in A Memoir on the Theory of Matrices he studies its properties. The beginnings of matrices and determinants goes back to the second century BC although traces can be seen back to the fourth century BC. However it was not until near the end of the 17th Century that the ideas reappeared and development really got underway.Our late 20th Century methods would have us write the linear equations as the rows of the matrix rather than the columns but of course the method is identical. Most remarkably the author, writing in 200 BC, instructs the reader to multiply the middle column by 3 and subtract the right column as many times as possible, the same is then done subtracting the right column as many times as possible from 3 times the first column.
Hammarström, Harald (17 May 2007). "Rarities in Numeral Systems" (PDF). In Wohlgemuth, Jan; Cysouw, Michael. Rethinking Universals: How rarities affect linguistic theory. Empirical Approaches to Language Typology 45. Berlin: Mouton de Gruyter (published 2010). Archived from the original on 19 August 2007.
A decimal number system, with no zero, is used in China.The Decimal number system is also called HINDU-ARABIC, or ARABIC, or base 10 system. Mathematics commonly uses a positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and a dot (decimal point). This place holding or place notation was much easier than inventing a new character for each number (imagine having to memorize an enormous number of characters just to read the date!). Having a decimal system from the beginning was a big advantage in making mathematical advances.