HISTORY OF MATHEMATICSANCIENT MATHEMATICSI. BABYLONIAN NUMERALS The Babylonian Tablet Plimpton 332- The tablet presents a list of Pythagorean triples written in Babylonian numerals Babylonian Numeral System- The Babylonians developed a number system that was sexagesimal in nature, which means that instead of having a base of ten decimal!, it had a base of "#$ Sexagesimal System- Based "# numeral system The S%uare &oot of 2 - There is evidence that the Babylonians may have had an understanding of irrational numbers particularly that of '2 after the discovery of the (ale tablet (B)* +2*,$II. CHINESE MATHEMATICS -iu.hang Suanshu/ or 0Nine )hapters on the 1athematical 2rt/- 3t is an important tool in the education of such a civil service, covering hundreds of problems in practical areas such as trade, taxation, engineering and the payment of wages 1agic s%uares- These are s%uares of numbers where each row, column and diagonal added up to the same total )hinese &emainder Theorem- This uses the remainders after dividing an un4nown number by a succession of smaller numbers, such as 3, 5 and +, in order to calculate the smallest value of the un4nown number$ )alculating 6evices- Babylonian 1arble )ounting Board- &oman Bron.e 0Poc4et0 2bacus- )hinese 7ooden 2bacusIII. ANCIENT INDIAN MATHEMATICS Brahmi numerals- 3t is an ancient system for writing numerals$ 3t was developed thousands of years ago in 3ndia$ Brahmi numerals do not include a symbol for #$0Sulba Sutras/ or 8Sulva Sutras8! - 3t listed several simple Pythagorean triples, as well as a statement of the simplified Pythagorean theorem for the sides of a s%uare andfor a rectangle Brahmagupta- 2n 3ndian 1athematician who established the basic mathematical rules for dealing with .ero9 : ; # < := : > # < := and : x # < # - ?e also established rules for dealing with negative numbers, and pointed out that %uadratic e%uations could in theory have two possible solutions, one of which could be negative$ 0Surya Siddhanta/- 2 text from an un4nown author which contains the roots of modern trigonometry, including the first real use of sines, cosines, inverse sines, tangents and secants$ 2ryabhata - 2 great 3ndian mathematician and astronomer who produced categorical definitions of sine, cosine, versine and inverse sine, andspecified complete sine and versine tables, in 3$+5@ intervals from #@ to ,#@, to an accuracy of A decimal places$ Bhas4ara 33- Bne of the most accomplished of all 3ndiaCs great mathematicians who is credited with explaining the previously misunderstood operation of division by .ero$ They were the first to develop9- Set theory- Dogarithms- )ubic e%uations- Euadratic e%uations- Se%uencesIV. ANCIENT EGYPT ?ieroglyphics- 3t is a system that employs characters in the form of pictures ?ieratic- 3t is an ancient system for writing numerals$ 3t was developed thousands of years ago in 3ndia$ Brahmi numerals do not include a symbol for #$ &osetta stone- 3t is a bloc4 of basalt with engravings made on its polished surface$ 3t was named after the village where it was found in :+,,, &ashid 4nown as &osetta to Furopeans! &hind Papyrus- 3t was brought by &hind in Duxor in :*5* and willed to the British museum- ?ieratic script from :"5# B) by scribe 2hmesV. GREEK AND HELLENISTIC MATHEMATICS 2ttic or ?erodianic numerals- 3t was a base :# system similar to the earlier Fgyptian one, with symbols for :, 5, :#, 5#, :##, 5## and :,### repeated as many times needed to represent the desired number Thales - ?e established what has become 4nown as Thales' Theore, whereby if a triangle is drawn within a circle with the long side as a diameter of the circle, then the opposite angle will always be a right angle - ?e is also credited with another theorem, also 4nown as Thales' Theore or !he I"!er#e$! Theore, about the ratios of the line segments that are created if two intersecting lines are intercepted by a pair of parallels Pythagoras- ?e was the first to reali.e that a complete system of mathematics could be constructed, where geometric elements corresponded withnumbers$ - PythagorasC Theorem or the Pythagorean Theorem! is one of the best 4nown of all mathematical theorems$ ?ippocrates of )hios - ?is influential boo4 0The Elee"!s% was the first compilation of theelements of geometry, and his wor4 was an important source for FuclidGs later wor4$ Fudoxus of )nidus - They are credited with the first implementation of the 0method of exhaustion/, an early method of integration by successive approximations which he used for the calculation of the volume of the pyramid and cone 3dea of proof, and the deductive method of using logical steps to prove or disprove theorems from initial assumed axioms- 3t is this concept of proof that give mathematics its power and ensures that proven theories are as true today as they were two thousand years ago, and which laid the foundations for the systematic approach to mathematics of Fuclid and those who cameafter him$BABYLONIAN MATHEMATICSBa&'lo"(a" N)eral S's!e The Babylonians developed a number system that was sexagesimal in nature, which means that instead of having a base of ten decimal!, it had a base of "#$ Se*a+es(al S's!e Based "# numeral system )ount up to 5, before moving on to the next position Symbol for "# is the same as :The S,)are Roo! o- . There is evidence that the Babylonians may have had an understanding of irrational numbers particularly that of '2 after the discovery of the (ale tablet (B)* +2*,$P'!ha+oras' Theore 3t states that the length of the diagonal is the length of the side multiplied by the s%uare root of 2$ 2n accurate approximation of this %uantity in sexagesimal notation is written along one diagonal$ Bne side is labelled with its length, and the product of this number by the s%uare root of 2 is also written along the diagonal$Pl($!o" /.. #la' !a&le! The tablet appears to list :5 perfect Pythagorean triangles with whole number sides$ Suggests that the Babylonians may well have 4nown the secret of right>angled triangles many centuries before the Pythagoras$EGYPTIAN MATHEMATICSE+'$!(a" S)r0e'("+ The PharaohCs surveyors used eas)ree"!s &ase1 o" &o1' $ar!s to measure land and buildings very early in Fgyptian history, and a 1e#(al ")er(# s's!e was developed based on our ten fingers$ E+'$!(a" N)&ers a"1 Tr(al a"1 Error The Fgyptians used!r(al a"1 error !e#h"(,)esto arrive at solutions toproblems, and had little interest in loo4ing for formulae or complexinterrelationships between sets of numbers$ Theformulasthat theFgyptiansdevelopedgavethemwaystoestimatetheareas and volumesof shapesand solids,which,whilst notperfectly accurate,were a close enough approximation for their purposes$ The Fgyptian mathematicians could solve simple %uadratic e%uations by using aseries of guesses to find the closest answer, 4nown as &r)!e -or#e e!ho1$Co$le* E+'$!(a" Ma!hea!(#s2 Vol)es a"1 Fra#!(o"s The Rh("1 $a$'r)s discovered by ?enry &hind, in the :,th century, dates from:"5# B)F and is filled with problems and solutions, also including a section onfractions$ The Fgyptians preferred to reduce all fractions to unit fractions, such as:HA, :H2 and :H*, rather than 2H5 or +H:"$ The Mos#o3 $a$'r)s contained further problems showing how to calculate thevolume of a truncated pyramid and wor4 out the surface area of half a sphere$This showed that the Fgyptians used a value of 25"H*: for Pi which, at a figure of3$:", is close to our modern number, and was arrived at through brute force andcalculatingtheareaof polygons$ )ertainly, it wasaccurateenoughfor mostpractical uses Their standard of measurement was the #)&(!, around 52$3 cm long, and they used rulers and 4notted ropes to ma4e measurements$S)$er#o$)!ers The FgyptiansC )se o- &r)!e -or#e a"1 !r(al a"1 error e!ho1s to solve problems are used today when a supercomputer is used to discover prime numbers to calculate a few more decimal places for Pi, it uses force to perform huge numbers of calculations every second$E+'$!(a" N)erals 2ncient Fgyptian texts could be written in either hieroglyphics or in hieratic$ 3n either representation the number system was always given in &ase 45$ E+'$!(a" Fra#!(o"s The ancient Fgyptians used )"(! -ra#!(o"s fractions with a numerator of :! with the sole exception of 2H3$PAMPANGA STATE AGRICULTURAL UNIVERSITYMAGALANG6 PAMPANGAHISTORY OFMATHEMATICSSUBMITTED BY2N2I2&&B, )213DDF S$SUBMITTED TO26&$ FP3J2N32 KBS3B)BREFERENCES2The Story of 1athematics$ 2#:#!$ Kree4 1athematics$ &etrieved fromhttp9HHwww$storyofmathematics$comHgree4$htmlThe Story of 1athematics$ 2#:#!$ )hinese 1athematics$ &etrieved fromhttp9HHwww$storyofmathematics$comHchinese$htmlThe Story of 1athematics$ 2#:#!$ Fgyptian 1athematics$ &etrieved fromhttp9HHwww$storyofmathematics$comHegyptian$htmlFxplorable$ 2#:5!$ Babylonian 1athematics$ &etrieved fromhttps9HHexplorable$comHbabylonian>mathematics?istory of 1ath 1ac Tutorials$ 2#:5!$ 3ndian 1athematics$ &etrieved fromhttp9HHwww>history$mcs$st>and$ac$u4H3ndexesH3ndians$html