### Pi stories: the Cyclometricus and other tales

It was 1621 when the Cyclometricus by Willebrord Snellius, a pupil of Ludolph van Ceulen, was published. Snellius proved that the perimeter of the inscribed polygon converges to the circumference twice than the circumscribed polygon. As a good pupil of van Ceulen, Snellius managed to get 7 decimal places for the $\pi$ by using a 96-sided polygon. His best result, however, was 35 decimal places, which improved his master's result, 32.
The next improvement is dated 1630 by Christoph Grienberger, the last mathematician to evaluate $\pi$ using the polygon method, while the first successful method change came out thanks to the british mathematician and astronomer Abraham Sharp who determined 72 decimal places of $\pi$, of which 71 correct, using a series of arctangents. A few years later, John Machin improved Sharp's result with the following formula and that allowed him to achieve the remarkable result of 100 decimal places! $\frac{\pi}{4} = 4 \arctan \frac{1}{5} - \arctan \frac{1}{239}$ Machin's approach proved successful, so much so that the slovenian baron Jurij Vega improved on two occasions the above formula obtaining a greater number of decimal digits of $\pi$, the first time in 1789 with a formula similar to Euler's one $\frac{\pi}{4} = 5 \arctan \frac{1}{7} + 2 \arctan \frac{3}{79}$ then in 1794 with a Hutton-like formula $\frac{\pi}{4} = 2 \arctan \frac{1}{3} + \arctan \frac{1}{7}$ The arctangent era continued with William Rutherford $\frac{\pi}{4} = 4 \arctan \frac{1}{5} - \arctan \frac{1}{70} + \arctan \frac{1}{99}$ and with Zacharias Dase $\frac{\pi}{4} = \arctan \frac{1}{2} + \arctan \frac{1}{5} + \arctan \frac{1}{8}$ Finally comes the british William Shanks that pushing the full potential of the Machin's formula managed to get 707 decimal places, of which only 527 were correct after Ferguson's controls in 1946. Here, however, we are going in the era of mechanical calculation, prologue to computer era.

### Women in physics

I would share some free ebooks from IOP about the contribution of women in physics:
Women and Physics by Laura McCullough (pdf)
This book begins with an examination of the numbers of women in physics in English-speaking countries, moving on to examine factors that affect girls and their decision to continue in science, right through to education and on into the problems that women in physics careers face. Looking at all of these topics with one eye on the progress that the field has made in the past few years, and another on those things that we have yet to address, the book surveys the most current research as it tries to identify strategies and topics that have significant impact on issues that women have in the field.
Beyond Curie: Four women in physics and their remarkable discoveries, 1903 to 1963 by Scott Calvin (pdf)
In the 116 year history of the Nobel Prize in Physics, only two women have won the award; Marie Curie (1903) and Maria Mayer (1963). During the 60 years between those awards, several women did work of similar calibre. This book focuses on those women, providing biographies for each that discuss both how they made their discoveries and the gender-specific reception of those discoveries. It also discusses the Nobel process and how society and the scientific community's treatment of them were influenced by their gender.
After the War: Women in physics in the United States by Ruth H Howes, Caroline L Herzenberg (pdf)
This book examines the lives and contributions of American women physicists who were active in the years following World War II, during the middle decades of the 20th century. It covers the strategies they used to survive and thrive in a time where their gender was against them. The percentage of woman taking PhDs in physics has risen from 6% in 1983 to 20% in 2012 (an all-time high for women). By understanding the history of women in physics, these gains can continue.
It discusses two major classes of women physicists; those who worked on military projects, and those who worked in industrial laboratories and at universities largely in the late 1940s and 1950s. While it includes minimal discussion of physics and physicists in the 1960s and later, this book focuses on the challenges and successes of women physicists in the years immediately following World War II and before the eras of affirmative actions and the use of the personal computer.