Pi — Unleashed

  title={Pi — Unleashed},
  author={J{\"o}rg Arndt and Christophe Haenel},
  booktitle={Springer Berlin Heidelberg},

Origins of Integration

Zur Irrationalit\"at in der Schule

Irrational numbers are introduced usually already introduced in lower secondary level schools. But typically, maybe with the exception of $\sqrt{2}$, no mathematical proof of irrationality is

Integració de funcions racionals i π

El número π denota el quocient entre la longitud d’una circumferència i el seu diàmetre i és indubtablement una de les constants matemàtiques més famosa i fascinant. Als científics els encanten les

Elementary Transcendental Functions

  • S. Chiossi
  • Mathematics
    Essential Mathematics for Undergraduates
  • 2021

Custom Memory Management

This chapter describes memory management methods that are robust and reliable enough to perform dynamic creation polymorphic objects and mapping hardware devices while adhering to the strict constraints of limited microcontroller memory resources.

The General Relativistic Perspective

This paper formulates additional General Relativistic [GR] equations. They do not contradict General Relativity. They examine Dr. Einstein’s equations from a Relativistically distorted Perspective.

Anniversary of Notation for Number π

It was in that year that William Jones made himself noted, without being aware that he was doing anything noteworthy, through his designation of the ratio of the length of the circle to its diameter

The probability of intransitivity in dice and close elections

We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for n-sided dice with pairwise ordering induced by the probability, relative to

The Dynamics of Digits: Calculating Pi with Galperin’s Billiards

In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number π . This classical, one-dimensional three-body system (counting the hard wall)



The quest for PI

This article gives a brief history of the analysis and computation of the mathematical constant $\pi = 3.14159 \ldots$, including a number of the formulas that have been used to compute $\pi$ through

79.36 Pancake functions and approximations to π

to illustrate numerical integration techniques, for example see the recent article [1], the identity (1) gives us the best loved approximation to n, with an error estimate, without the need to do any

Ramanujan—100 years old (fashioned) or 100 years new (fangled)?

Everyone enjoys celebrating birthdays. Admittedly, as we get older, perhaps we enjoy celebrating others' birthdays more than our own. We also rejoice in commemorating the birthdays of many that have

Ramanujan’s Notebooks: Part V

The Best (?) Formula for Computing π to a Thousand Places

In the December 1938 issue of this Monthly, D. H. Lehmer gave a very comprehensive list of formulas for computing π. He rightly chose formulas (23) and (32) as the best self checking pair, with (18)

A simple formula for pi

Mathematical Recreations and Essays

THIS edition differs from the third by containing chapters on the history of the mathematical tripos at Cambridge, Mersenne's numbers, and cryptography and ciphers, besides descriptions of some

Decrypted secrets - methods and maxims of cryptology

This 3rd edition of "Decrypted Secrets" has become a standard book on cryptology and has again been revised and extended in many technical and biographical details.

On the Khintchine constant

It is shown that each of these constants can be cast in terms of an efficient free-parameter series, each series involving values of the Riemann zeta function, rationals, and logarithms of rationals.

Ramanujan--for lowbrows

"No, Inspector," he said. "It is not at all like that, I am assuring you. You see, for a person of my sort-and I admit that we are a rare breed-numbers are so much in our minds there is hardly any