Because of the π that goes to a few accurately, can the quantity does not come out.
The before time in Zu Chong, the numerical value of π returns energy to come out. But autonomy round art only then, do not have again " quantity " view. (attention, the art that cut a circle also does not need " measure " , just calculate) have the aid of cuts round method, value computation went to a π with Zu Chong's successful father and son 7 fraction, namely 3.1415926. But such doing that what still do not have a future apparently, zu Chong's father and son was calculated 24000 edges form, make 7 fraction namely. Although this number side polygonal turns over times again, turn over times again, also cannot go to 10.
The art that cut a circle is no good, that what method is OK?
Look cast only " round circumference " , the maths with more profound have the aid of is academic. One is called Wei Da's mathematician, made first time attempt:
So a posture, add all the time, be close to indefinitely at 2/ π . However the problem still is in: This number calculates very hard, have simple formula?
Still have really.
Have the aid of of Lai cloth Ni Ci he (with Newton at the same time) the calculus of the invention, spread out according to Taylor, made a progression:
Laibunici is progressional: π / 4=1-1/3+1/5-1/7+1/9...
Although good calculate, but convergence is too slow. So he himself also did not continue to calculate.
Appeared later a few in a way rely on chart, for instance:
Ma Qing is formulary: π / 4=4 (1/5- (1/5) 3/3+ (1/5) ^5/5-(1/5)^7/7+ ... ) + (1/239- (1/239) 3/3+(1/239)^5/5-(1/239)^7/7+ ... )
This once calculated 137
Contemporary computer, law of commonly used gauss:
Convergent and super fast, calculate ten can arrive accurately on ten million.
Say so, inside contemporary π value computation, do not have at all " measure " so process. So, metrical error, nonexistent also ~
