Pi stories: the Cyclometricus and other tales

Fifth period

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:

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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.

The man who measured Mount Everest

Radhanath Sikdar was an Indian mathematician who, among many other things, calculated the height of Mount Everest in the Himalaya and showed it to be the tallest mountain above sea level.

Sagitarius A*: Van Gogh in the Milky Way

The colour scale in the image shows the amount of infrared (heat) radiation coming from warm dust particles in the filaments and luminous stars within a light year of the Galactic centre. The position of the black hole is indicated by an asterisk. The lines trace the magnetic field directions and reveal the complex interactions between the stars and the dusty filaments, and the impact that they and the gravitational force has on them. The observations were made with the largest telescope in Europe, which allowed details of the fine structure in the magnetic fields to be revealed for the first time.
- E. Lopez-Rodriguez / NASA Ames / University of Texas at San Antonio

A paper published on the Monthly Notices of the Royal Astronomical Society describes tha detailed mapping of the magnetic field around Sagittarius A*, or Sgr A*, the supermassive black hole at the center of the Milky Way. A researchers' team used the infrared camera CanariCam instaled on the Great Canary Telescope to obtain the data needed to reproduce the magnetic lines of gas and dusts that orbit around the center of the galaxy. The colors chosen by the researchers to visualize the structure of the magnetic lines give the result a style that recalls Vincent Van Gogh's paintings.

P F Roche, E Lopez-Rodriguez, CM Telesco, R Schödel, C Packham; The Magnetic Field in the central parsec of the Galaxy, Monthly Notices of the Royal Astronomical Society, sty129, 10.1093/mnras/sty129

Paolo Nespoli reads Emily Dickinson

#1695

There is a solitude of space
A solitude of sea
A solitude of death, but these
Society shall be
Compared with that profounder site
That polar privacy
A soul admitted to itself–
Finite Infinity.

Sputnik-2 or: Laika, Our Hero

Laika was a Soviet space dog who became one of the first animals in space, and the first animal to orbit the Earth. Laika, a stray dog from the streets of Moscow, was selected to be the occupant of the Soviet spacecraft Sputnik 2 that was launched into outer space on November 3, 1957.
Little was known about the impact of spaceflight on living creatures at the time of Laika's mission, and the technology to de-orbit had not yet been developed, so Laika's survival was never expected. Some scientists believed humans would be unable to survive the launch or the conditions of outer space, so engineers viewed flights by animals as a necessary precursor to human missions. The experiment aimed to prove that a living passenger could survive being launched into orbit and endure a Micro-g environment, paving the way for human spaceflight and providing scientists with some of the first data on how living organisms react to spaceflight environments.
Laika died within hours from overheating, possibly caused by a failure of the central R-7 sustainer to separate from the payload. The true cause and time of her death were not made public until 2002; instead, it was widely reported that she died when her oxygen ran out on day six or, as the Soviet government initially claimed, she was euthanised prior to oxygen depletion.
On April 11, 2008, Russian officials unveiled a monument to Laika. A small monument in her honour was built near the military research facility in Moscow that prepared Laika's flight to space. It features a dog standing on top of a rocket. She also appears on the Monument to the Conquerors of Space in Moscow.

video via Popular Science

Abstract: The Universe at Lattice-Fields

Guido, G. and Filippelli, G. (2017) The Universe at Lattice-Fields. Journal of High Energy Physics, Gravitation and Cosmology, 3, 828-860. doi:10.4236/jhepgc.2017.34060.

We formulate the idea of a Universe crossing different evolving phases $U_k^*$ where in each phase one can define a basic field at lattice structure $U_k$ increasing in mass (Universe-lattice). The mass creation in $U_k$ has a double consequence for the equivalence "mass-space": Increasing gravity (with varying metric) and increasing space (expansion). We demonstrate that each phase is at variable metric beginning by open metric and to follow a flat metric and after closed. Then we define the lattice-field of intersection between two lattice fields of base into universe and we analyse the universe in the Nucleo-synthesis phase and in the that of recombination. We show that the phase is built on the intersection of the lattices of the proton and electron. We show $U_H$ [the intersection between proton's anch electron's lattices] to be at variable metric (open in the past, flat in the present and closed in the future). Then, we explain some fundamental aspects of this universe $U_H$: Hubble's law by creating the mass-space in it, its age (13.82 million of Years) as time for reaching the flat metric phase and the value of critic density. In last we talk about dark universe lattice, having hadronic nature, and calculating its spatial step and its density in present phase of [the universe].

For some personal problems, I cannot add the LaTeX figures, so I uploaded them on researchgate.