(12-09-2019 01:44 PM)SlideRule Wrote: Reference:

Using A Minicalculator to Find An Approximate Value for Π, E. J. Bolduc (University of Florida)

"One of the many ways to use a minicalculator in a classroom is in the calculation of an approximate value for n using a variation of the method of Archimedes … if a circle of radius 1 is chosen, then the area of any inscribed polygon is less than Π and the area of any circumscribed polygon is greater than n. He finally arrived at the fact that 3(10/17) < Π < 3(1/7). We can use the idea that, as the numbers of sides of an inscribed polygon increases, the perimeter of the polygon approaches the circumference of the circle and the ratio of the perimeter to the diameter of the circle is an approximation for Π …

We now have our iterative formula, S’ = √2r² - r√4r² - S²"

I leave the recursion and subsequent calculation to the reader, but after nine iterations, the equation yields 3.141592…

BEST!

SlideRule

Here's a simple BASIC version from Problems for Computer Solution by Stephen J. Rogowski:

Code:

`50 PRINT "ARCHIMEDEAN DETERMINATION OF PI!"`

60 PRINT

70 PRINT "NO. OF SIDES","INSCR PER","CIRCUM PER"

80 PRINT

100 FOR X=2 TO 15

105 LET N=2^X

110 LET D=360/N

120 LET T=3.1415927*(D/180)

130 LET A=2*N*SIN(T/2)

140 LET B=2*N*TAN(T/2)

150 PRINT N,A/2,B/2

155 IF A=B THEN GOTO 170

160 NEXT X

170 END