Amazing Traces of a Babylonian Origin in Greek Mathematics by Joran Friberg

By Joran Friberg

A sequel to unforeseen hyperlinks among Egyptian and Babylonian arithmetic (World medical, 2005), this e-book is predicated at the writer s in depth and flooring breaking reports of the lengthy background of Mesopotamian arithmetic, from the overdue 4th to the past due 1st millennium BC. it truly is argued within the booklet that a number of of the main well-known Greek mathematicians seem to have been acquainted with numerous elements of Babylonian metric algebra, a handy identify for an tricky mixture of geometry, metrology, and quadratic equations that's recognized from either Babylonian and pre-Babylonian mathematical clay pills. The publication s use of metric algebra diagrams within the Babylonian type, the place the aspect lengths and components of geometric figures are explicitly indicated, rather than entirely summary lettered diagrams within the Greek type, is vital for a stronger figuring out of many fascinating propositions and buildings in Greek mathematical works. the writer s comparisons with Babylonian arithmetic additionally bring about new solutions to a few very important open questions within the historical past of Greek arithmetic

Show description

Read Online or Download Amazing Traces of a Babylonian Origin in Greek Mathematics PDF

Best history & philosophy books

Elements of Continuum Mechanics and Thermodynamics

This article is meant to supply a latest and built-in therapy of the principles and purposes of continuum mechanics. there's a major raise in curiosity in continuum mechanics as a result of its relevance to microscale phenomena. as well as being adapted for complicated undergraduate scholars and together with quite a few examples and workouts, this article additionally incorporates a bankruptcy on continuum thermodynamics, together with entropy creation in Newtonian viscous fluid movement and thermoelasticity.

Aspects and applications of the random walk

Either the formalism and lots of of the attendant rules concerning the random stroll lie on the middle of an important fraction of latest examine in statistical physics. within the language of physics the random stroll may be defined as a microscopic version for shipping methods that have a few component of randomness.

Trees of life : a visual history of evolution

Brackets and tables, circles and maps, 1554-1872 --
Early botanical networks and timber, 1766-1815 --
The first evolutionary tree, 1786-1820 --
Diverse and strange bushes of the early 19th century, 1817-1834 --
The rule of 5, 1819-1854 --
Pre-Darwinian branching diagrams, 1828-1858 --
Evolution and the bushes of Charles Darwin, 1837-1868 --
The timber of Ernst Haeckel, 1866-1905 --
Post-Darwinian nonconformists, 1868-1896 --
More late-nineteenth-century timber, 1874-1897 --
Trees of the early 20th century, 1901-1930 --
The bushes of Alfred Sherwood Romer, 1933-1966 --
Additional bushes of the mid-twentieth century, 1931-1943 --
The bushes of William King Gregory, 1938-1951 --
Hints of recent methods, 1954-1969 --
Phenograms and cladograms, 1958-1966 --
Early molecular timber, 1962-1987 --
Notable timber of the earlier 4 a long time, 1970-2010 --
Primeval branches and common bushes of lifestyles, 1997-2010

Geophysics, realism, and industry : how commercial interests shaped geophysical conceptions, 1900-1960

Did and trade impact the ideas, values and epistemic foundations of alternative sciences? if this is the case, how and to what volume? This booklet means that the main major impact of on technology within the case reports taken care of the following needed to do with the problem of realism. utilizing wave propagation because the universal thread, this is often the 1st e-book to at the same time examine the emergence of realist attitudes in the direction of the entities of the ionosphere and of the earth's crust.

Extra info for Amazing Traces of a Babylonian Origin in Greek Mathematics

Sample text

C = sq. a + sq. b – 2 b · q B3b : B3a : sq. p – sq. q = D, p – q = b, sq. p – sq. q = D, p + q = b, with D = sq. c – sq. a with D = sq. c – sq. a ‰ 2 b · q = D – sq. b, etc. ‰ 2 b · q = sq. b – D, etc. Fig. 1. Interpretations of the diagrams in El. 12 and El. 13. 8. El. 12-13, Constructive Counterparts to El. 8 23 With the notations introduced in Fig. 1, left, the proof of El. 12 proceeds as follows: sq. p = sq. b + sq. q + 2 b · q sq. p + sq. h = sq. b + sq. q + sq. h + 2 b · q sq. c = sq. b + sq.

The very convenient approximation / = appr. 3 is used in all Babylonian mathematical texts. More precisely, the area A and the diameter d of a circle are expressed as follows in terms of the arc (circumference) a: A = 5 · a, where ‘5’ means ;05 = 5/60 = 1/12 = appr. 1/4/, d = 20 · a, where ‘20’ means ;20 = 20/60 = 1/3 = appr. 1//. In addition to sexagesimal fractions, such as the circle constants ‘5’ and ‘20’, there are also two other kinds of fractions of numbers that appear in Babylonian mathematical texts.

5. El. 8 and the Two Basic Subtractive Quadratic-Linear Systems of Equations El. 8 If a straight line is cut at random, four times the rectangle contained by the whole and one of the segments, together with the square on the remaining segment, is equal to the square described on the whole and the mentioned segment as on one straight line. A C B D G M T K O S E U Q R N P H L F Fig. 1. The diagram in El. 8. 5. El. 8 and the Two Basic Subtractive Quadratic-Linear Systems of Equations 15 In Fig. 2 below, the given straight line AB is called u and the two segments into which it is cut are called s and q.

Download PDF sample

Rated 4.51 of 5 – based on 37 votes