# Pi - The most important but weird number

Number Theory Level 3

The famous Indian astronomer, Aryabhata, approximated the value of $$\pi$$ as $$3.1416$$ and then expressed it as a continued fraction of the form

$\large a+\frac{1}{b+\frac{1}{c+\frac{1}{d}}},$

where $$a,b,c,d$$ are positive integers. Find $$a+b+c+d$$.

Details and assumptions

• Use the approximation $$\pi = 3.1416$$.
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