Have fun with mathematics and discover the value of e in this book featuring about 240,000 digits of the number e. Great gift for kids of all ages as well as adults, anyone with an appreciation for mathematics, logical equations, problem solving, aspiring scientists, physicists and more.

The number e, called sometimes Euler's number, is a mathematical constant that is the base of natural logarithm. The number e can be calculated as is the limit of (1 + 1/n)n as n approaches infinity Here we present that number printed, in his first two million digits, in a single volume.

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 23. Chapters: E, Transcendental number, Chaitin's constant, Liouville number, Lindemann-Weierstrass theorem, Baker's theorem, Schanuel's conjecture, Schneider-Lang theorem, List of representations of e, Gelfond-Schneider theorem, Four exponentials conjecture, Gelfond-Schneider constant, Gelfond's constant, Universal parabolic constant, Cahen's constant, Six exponentials theorem, Gauss's constant, Prouhet-Thue-Morse constant, Hilbert number, Hypertranscendental number. Excerpt: The mathematical constant is the unique real number such that the value of the derivative (slope of the tangent line) of the function () = at the point = 0 is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base . The number is also commonly defined as the base of the natural logarithm (using an integral to define the latter), as the limit of a certain sequence, or as the sum of a certain series (see the alternative characterizations, below). The number is sometimes called Euler's number after the Swiss mathematician Leonhard Euler. ( is not to be confused with -the Euler-Mascheroni constant, sometimes called simply Euler's constant.) It is also sometimes known as Napier's constant, although the symbol is in honor of Euler. The number is of eminent importance in mathematics, alongside 0, 1, and . All five of these numbers play important and recurring roles across mathematics, and are the five constants appearing in one formulation of Euler's identity. The number is irrational; it is not a ratio of integers. Furthermore, it is transcendental; it is not a root of any non-zero polynomial with rational coefficients. The numerical value of truncated to 50 decimal places is (sequence A001113 in OEIS). The first references to the constant were published in 1618 in the...

Have fun with mathematics and discover the value of the square root of φ, the Golden Ratio in this book featuring about approximately 240,000 digits. Great gift for kids of all ages as well as adults, anyone with an appreciation for mathematics, logical equations, problem solving, aspiring scientists, math and science school teachers, physicists and more.

A great gift for anyone interested in maths, this book contains: 1.000.000 digits of the Euler's number (e), A total of 446 pages, Each page contains 42 rows, each divided into 5 columns of 10 digits, High quality printing, Standard format (6 x 9 in)

Book intended for university students (undergraduates) and all those who wish to know more about the astonishing numbers that are e, π and i. The book is structured around solved exercises or problems. It details the study of the e, π and i numbers, so familiar to science students. Familiar ? ... not so sure ... How did we come to create the exponential and logarithm functions ? How do we calculate the values of e and π ? Thanks to which formulas ? And where do these formulas come from ? When and how were they discovered ? And by whom ? In the midst of the Italian renaissance, some mathematicians, seeking to solve equations of the type x3 + px + q = 0 bring to light, dumbfounded, an imaginary number that came out of nowhere but essential to their calculations. They do not yet realize that they have just discovered complex numbers ! How did they do it ? Can π and e be written in fractional form ? These questions and their answers are dealt with throughout the book in the form of corrected exercises calling on the basic mathematical knowledge acquired in classroom. Euler's method for the calculation of e; Archimedes' method, of Snellius, of Machin, of Brent-Salamin, BBP are reviewed for the calculation of π. Elementary algorithms for computer programming complete the study. The last exercise of the book concerns the demonstration of the relation: eix = cosx + i sinx to highlight Euler's formula: eiπ + 1 = 0 we have to face the facts: π, e and i are linked together ! Plan of the book : 1 - Reminders about sets of numbers sets of numbers classification other type of classification - transcendence 2 - Power and exponential functions power functions (solved problem) exponential and logarithm functions (solved problem) 3 - e, the Euler number search for e by two different sequences (solved problem) e is irrational (solved problem) 4 - π , the number of Archimedes knowledge of the circle - definition of π and interest calculation of π by Archimedes' method (solved problem) calculation of π by Snellius method (solved problem) calculation of π by Machin's method (solved problem) calculation of π by the Brent-Salamin method (solved problem) calculation of π by the method of Bailey-Borwein-Plouffe (solved problem) π is irrational (solved problem) 5 - i and complex numbers discovery of i when solving x3 + px + q = 0 (solved problem) history of complex numbers : algebraic form trigonometric form (solved exercise) exponential form (solved exercise) e , π , i are related to each other by Euler's formula : eiπ + 1 = 0

The number e, the base of the natural logarithm, has been know to exist for many years. The constant e was discovered by the Swiss mathematician Jacob Bernoulli while studying compound interest. It is named e to honor Leonard Euler. The first references to the constant were published in 1618 in the table of an appendix of a work on logarithms by John Napier. John Napier did not actually define the constant, but he used it. The discovery of the constant itself is credited to Jacob Bernoulli in 1683, who attempted to find the value of the following expression (which is equal to e): limit as n approaches infinity of (1+1/n)^n.