Pi - The most important but weird number
The famous Indian astronomer, Aryabhata, approximated the value of
π
as
3
.
1
4
1
6
and then expressed it as a continued fraction of the form
a + b + c + d 1 1 1 ,
where a , b , c , d are positive integers. Find a + b + c + d .
Details and Assumptions:
- Use the approximation π = 3 . 1 4 1 6 .
The answer is 37.
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1 solution
Discussions for this problem are now closed
You can write it as: 3 + 7 + 1 6 + 1 1 1 1 1
I have written that only in my solution mentioned above.
He means that instead of using the \frac{} function, you can use the \cfrac{} function in your L A T E X
How did Aryabhata get this even he don't know value of pi
Solution:
3 . 1 4 1 6 = 3 + 1 0 0 0 0 1 4 1 6
= 3 + 1 4 1 6 1 0 0 0 0 1
= 3 + 1 4 1 6 9 9 1 2 + 8 8 1
= 3 + 7 + 1 4 1 6 8 8 1
= 3 + 7 + 8 8 1 4 1 6 1 1
= 3 + 7 + 8 8 1 4 0 8 + 8 1 1
= 3 + 7 + 1 6 + 1 1 1 1 1
Therefore, a = 3 , b = 7 , c = 1 6 , d = 1 1
Sum = a + b + c + d = 3 + 7 + 1 6 + 1 1 = 3 7
Thus, the answer is: a + b + c + d = 3 + 7 + 1 6 + 1 1 = 3 7