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Euler’s number. Why is Eule's number "e" the basis of natural logarithm functions
Document from the year 2016 in the subject Mathematics - Miscellaneous, grade: A, , course: IB Math HL, language: English, abstract: When the concept of logarithms was first introduced to me, a plethora of questions revolved around my mind. My inquisitiveness compelled me to think and ask questions as to where are the practical applications of logarithms, why do we take different bases of these functions and what is the need for natural logarithms. Amongst these questions, one particularly intrigued me: why is e particularly the base of the natural logarithm. Why out of all numbers that exist did we choose e as the base of the natural logarithm function? I was fascinated by why taking the base e made the normal logarithm a natural logarithm. Therefore, to quench the curiosity of many others like me, I will show through this paper that why e is the correct choice for the base of exponential and natural logarithm functions. I shall also be exploring the most important property of e, via this paper.
Euler's Pioneering Equation
In just seven symbols, with profound and beautiful simplicity, Euler's Equation connects five of the most important numbers in mathematics. Robin Wilson explores each number in turn, then brings them together to consider the power of the equation as a whole.
e: The Story of a Number
The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.
A Most Elegant Equation
An award-winning science writer introduces us to mathematics using the extraordinary equation that unites five of mathematics' most important numbers Bertrand Russell wrote that mathematics can exalt "as surely as poetry." This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.
Euler's e Essentials
"Euler's e Essentials" is a beginner-friendly guidebook that introduces readers to the fascinating world of mathematics through the lens of Euler's constant, denoted by the symbol e. Written in an accessible and easy-to-understand manner, this book is designed for individuals with little to no mathematical background who are curious about the beauty and significance of mathematical concepts. Through clear explanations, illustrative examples, and real-world applications, readers will embark on a journey to discover the fundamental properties of Euler's constant and its wide-ranging implications in various scientific disciplines, from calculus and physics to finance and biology. Whether you're a high school student exploring mathematics for the first time or an adult learner eager to delve into the mysteries of numbers, "Euler's e Essentials" offers an engaging and enlightening introduction to one of the most important constants in mathematics.
The Value of Number E Euler's Number 240,000 Digits
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.
Dr. Euler's Fabulous Formula
In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.
The First 1000 Euler Numbers
The First 1000 Euler Numbers by Simon Plouffe
Euler
Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.
