Han mathematics Chinese mathematics

the 9 chapters on mathematical art.

in han dynasty, numbers developed place value decimal system , used on counting board set of counting rods called chousuan, consisting of 9 symbols blank space on counting board representing zero. mathematicians liu xin (d. 23) , zhang heng (78–139) gave more accurate approximations pi chinese of previous centuries had used. zhang applied mathematics in work in astronomy. hundreds of examples of practical use of mathematics qin , han administrators have been excavated, proving many of topics discussed in theoretical treatises in use.

suan shu shu

the suàn shù shū (writings on reckoning) ancient chinese text on mathematics approximately 7 thousand characters in length, written on 190 bamboo strips. discovered other writings in 1984 when archaeologists opened tomb @ zhangjiashan in hubei province. documentary evidence tomb known have been closed in 186 bc, in western han dynasty. while relationship 9 chapters still under discussion scholars, of contents paralleled there. text of suan shu shu less systematic 9 chapters, , appears consist of number of more or less independent short sections of text drawn number of sources. linguistic hints point qin dynasty.

in example of elementary mathematics in suàn shù shū, square root approximated using excess , deficiency method says combine excess , deficiency divisor; (taking) deficiency numerator multiplied excess denominator , excess numerator times deficiency denominator, combine them dividend.

the 9 chapters on mathematical art

the 9 chapters on mathematical art chinese mathematics book, oldest archeological date being 179 ad (traditionally dated 1000 bc), perhaps 300–200 bc. although author(s) unknown, made huge contribution in eastern world. methods made everyday life , gradually taught advanced methods. contains evidence of gaussian elimination , cramer s rule system of linear equations.

the 9 chapters on mathematical art 1 of influential of chinese mathematical books , composed of 246 problems. chapter 8 deals solving determinate , indeterminate simultaneous linear equations using positive , negative numbers, 1 problem dealing solving 4 equations in 5 unknowns. estimates concerning chou pei suan ching, considered oldest of mathematical classics, differ thousand years. date of 300 bc appear reasonable, placing in close competition treatise, jiu zhang suanshu, composed 250 bc, is, shortly before han dynasty (202 bc). old @ chou pei, , perhaps influential of chinese mathematical books, jiuzhang suanshu, or 9 chapters on mathematical art. book includes 246 problems on surveying, agriculture, partnerships, engineering, taxation, calculation, solution of equations, , properties of right triangles. chapter 8 of 9 chapters significant solution of problems of simultaneous linear equations, using both positive , negative numbers. earliest known magic squares appeared in china. chinese fond of patterns, natural outcome of arranging counting rods in rows on counting board carry out computation; hence,it not surprising first record (of ancient unknown origin) of magic square appeared there. concern such patterns led author of 9 chapters solve system of simultaneous linear equations placing coefficients , constant terms of linear equations matrix , performing column reducing operations on matrix reduce triangular form represented equations



36
z
=
99


{\displaystyle 36z=99}

,



5
y
+
z
=
24


{\displaystyle 5y+z=24}

, ,



3
x
+
2
y
+
z
=
39


{\displaystyle 3x+2y+z=39}

values of



z


{\displaystyle z}

,



y


{\displaystyle y}

, ,



x


{\displaystyle x}

successively found ease. last problem in chapter involves 4 equations in 5 unknowns, , topic of indeterminate equations remain favorite among oriental peoples.