Mathematics in the period of disunity Chinese mathematics

liu hui s survey of sea island



sunzi algorithm division 400 ad



al khwarizmi division in 9th century



statue of zu chongzhi.

in third century liu hui wrote commentary on 9 chapters , wrote haidao suanjing dealt using pythagorean theorem (already known 9 chapters), , triple, quadruple triangulation surveying; accomplishment in mathematical surveying exceeded accomplished in west millennium. first chinese mathematician calculate π=3.1416 π algorithm. discovered usage of cavalieri s principle find accurate formula volume of cylinder, , developed elements of integral , differential calculus during 3rd century ce.

fraction interpolation pi

in fourth century, influential mathematician named zu chongzhi, introduced da ming li. calendar calculated predict many cosmological cycles occur in period of time. little known life. today, sources found in book of sui, know zu chongzhi 1 of generations of mathematicians. used liu hui s pi-algorithm applied 12288-gon , obtained value of pi 7 accurate decimal places (between 3.1415926 , 3.1415927), remain accurate approximation of π available next 900 years. used chengtian s interpolation method approximating irrational number fraction in astronomy , mathematical works, obtained






355
113





{\displaystyle {\tfrac {355}{113}}}

fraction approximate pi; yoshio mikami commented neither greeks, nor hindus nor arabs knew fraction approximation pi, not until dutch mathematician adrian anthoniszoom rediscovered in 1585, chinese had therefore been possessed of extraordinary of fractional values on whole millennium earlier europe

along son, zu geng, zu chongzhi used cavalieri method find accurate solution calculating volume of sphere. besides containing formulas volume of sphere, book included formulas of cubic equations , accurate value of pi. work, zhui shu discarded out of syllabus of mathematics during song dynasty , lost. many believed zhui shu contains formulas , methods linear, matrix algebra, algorithm calculating value of π, formula volume of sphere. text should associate astronomical methods of interpolation, contain knowledge, similar our modern mathematics.

a mathematical manual called sunzi mathematical classic dated between 200—400 ce contained detailed step step description of multiplication , division algorithm counting rods. earliest record of multiplication , division algorithm using hindu arabic numerals in writing al khwarizmi in 9th century. khwarizmi s step step division algorithm identical sunzi division algorithm described in sunzi mathematical classic 4 centuries earlier. khwarizmi s work translated latin in 13th century , spread west, division algorithm later evolved galley division. route of transmission of chinese place value decimal arithmetic know how west unclear, how sunzi s division , multiplication algorithm rod calculus ended in hindu arabic numeral form in khwarizmi s work unclear, al khwarizmi never given sankrit source nor quoted sanskrit stanza. however, influence of rod calculus on hindu division evident, example in division example, 324 should 32400, rod calculus used blanks zeros.

in fifth century manual called zhang qiujian suanjing discussed linear , quadratic equations. point chinese had concept of negative numbers.