Page 165 - Excel for Scientists and Engineers: Numerical Methods

142 EXCEL: NUMERICAL METHODS

Figure 7-16. Approximating the circumference of a circle of radius 1.
Note that the rows between 9 and 5 1 are hidden.
(folder 'Chapter 07 Examples', workbook 'Curve Distance', sheet 'Curve Distance (Circle)')
The procedure is illustrated by estimating the length of one quarter of a circle
of radius r = 1. The equation of the circle is x2 + y2 = 1 , or y =m . As shown
in Figure 7-16, the value of y and the distance d between successive points was
calculated from x = 0 to x = 1 , using an x increment of 0.025. Near the end of the
range of x values, where y changes more rapidly, the x increment was decreased.
The formula in cell C6 is

=SQRT((A8-A5)"2+( B8-B5)"2)
The sum of the distances x 2, in cell C59 is a reasonable estimate of x.