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H. C. Chan, $\pi$ in terms of $\phi$: Some Recent Developments, Proceedings of the Twelfth International Conference in Fibonacci Numbers, (2010): 17-25. Read Pi in terms of Phi (Fib Conf 2006).

H. C. Chan, $\pi$ in terms of $\phi$, Fibonacci Quart. 44 (2006): 141–144. Read Pi in terms of phi.

H. C. Chan, More Formulas for $\pi$, Amer. Math. Monthly 113: 452-455. Read More formulas for Pi.

H. C. Chan, Machin-type formulas expressing $\pi$ in terms of $\phi$, Fibonacci Quart. 46/47 (2008/2009): 32–37 Read Pi via Machin.

In college, we often learn of many infinite series that give the value of pi including one called the Leibniz series, named after Gottfried Leibniz. It is also called the Gregory–Leibniz series, recognizing the work of James Gregory. This unnecessarily attributes the discovery to the west, however, the formula was first discovered in India by Madhava of Sangamagrama and so is also called the Madhava–Leibniz series. Indian mathematicians made vast and fundamental contributions to our modern mathematics.

$\pi=4\sum_{k=0}^{\infty}\frac{(-1)^{k}}{2k+1}$