Tag: approximation

trigonometry – A 1,400 years old approximation to the sine function by Mahabhaskariya of Bhaskara I

The Question : 210 people think this question is useful The approximation $$\sin(x) \simeq \frac{16 (\pi -x) x}{5 \pi ^2-4 (\pi -x) x}\qquad (0\leq x\leq\pi)$$ was proposed by Mahabhaskariya of Bhaskara I, a seventh-century Indian mathematician. I wondered how much this could be improved using our computers and so I tried (very immodestly) to see

alculus – Motivation for Ramanujan’s mysterious $\pi$ formula

The Question : 102 people think this question is useful The following formula for $\pi$ was discovered by Ramanujan: $$\frac1{\pi} = \frac{2\sqrt{2}}{9801} \sum_{k=0}^\infty \frac{(4k)!(1103+26390k)}{(k!)^4 396^{4k}}\!$$ Does anyone know how it works, or what the motivation for it is? The Question Comments : This article by W. Zudilin may give you some references where you may