! 120 THE FASCINATION OF NUMBERS

and these adjusted values will be found to satisfy the equa-
tion
(13 x37) —(10 x48) =1
Various approximate values for the more important of the
irrational numbers have been suggested at different stages of
mathematical development. The square root of 2 has an
approximate decimal equivalent:

E | V2=141421356 . ..
B L A simpler, though less accurate, approximation is e
= ¥ for (4/2)% =20
- I_7> e
] and (12 —144—2 approx.

The first few convergents derived from the continued
fraction for 4/2 are:
1 3 7 1

i U SRR AR

~

41

9
An approximate value for z is 3-141 59265 . . ., but several
other useful approximations, suitable for the purposes for
which they were suggested, have been used:
(a) 333 (derived from (38)?)
() V10

(c) Between 31 and gl

:

1

The first terms of the continued fraction for x are:

VRN i Fodeia P b it x,m‘yu.u_h.‘,......,nmww,ywwwzfingwmfi Hl
: " 1 it PN N R ) il

 

 

| 3+1
T 7+1
- 1541
: : f 141
g |
i 2024 i,
f and successive convergents are:
} (i) 3
= (ii) 22 =3-142857 approx.
(1ii) $33=3-141509 i
= (iv) $4§=3-141509202 ,,

v
[~

IS

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