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Real Analysis
book

Real Analysis

by V. Karunakaran
May 2024
Intermediate to advanced content levelIntermediate to advanced
585 pages
15h 38m
English
Pearson India
Content preview from Real Analysis
“real: chapter_03” 2011/5/22 22:50 page 19 #19
Sequences and Series 3-19
This representation of π as a limit serves actually as a basis for numer-
ical computations which can be explained as follows. Using Figure
3.1 for reference, we construct lines touching the circle and parallel
to the sides of the inscribed n-gon. These lines form a circumscribed
polygon similar to the inscribed n-gon and having larger dimensions.
Indeed if b and B are, respectively, the sides opposite to the angle
2π/n in the above triangles and h, H are their respective heights
then we have (from elementary geometry), H = 1, h = cos π/n,
h/H = b/B, f
n
= (n/2) bh, F
n
= (
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Publisher Resources

ISBN: 9781299447561Publisher Website