Euler's Formula and Special Relativity

Euler's Formula and Special Relativity
Author: Dr. Thomas Stark
Publisher: Magus Books
Total Pages: 175
Release:
Genre: Philosophy
ISBN:

What are space and time? Where do they come from? How are they possible? The answer lies in the most important and powerful equation ever discovered: Euler's Formula. This extraordinary formula is the basis of eternal existence. It furnishes the building blocks of reality. It not only explains the pre-time, pre-space domain that produces the Big Bang universe, it also solves the intractable problem of Cartesian dualism by showing exactly how mind produces matter. As we demonstrate mathematically, Euler's Formula is the true basis of Einstein's special theory of relativity, and the all-important Lorentz transformations. Euler's Formula reveals the exact difference between Einstein's relativity and Lorentz's relativity, and shows how they can be reconciled via a higher level of theory. Reality is nothing like what it seems. Do you want to know how deep the rabbit hole goes? Are you ready for the ride of your life? Are you ready to discover the true secrets of reality?

Relativistic Hydrodynamics

Relativistic Hydrodynamics
Author: Luciano Rezzolla
Publisher: OUP Oxford
Total Pages: 752
Release: 2013-09-26
Genre: Science
ISBN: 0191509914

Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solution of the equations, and over to the applications in modern physics and astrophysics. Numerous figures, diagrams, and a variety of exercises aid the material in the book. The most obvious applications of this work range from astrophysics (black holes, neutron stars, gamma-ray bursts, and active galaxies) to cosmology (early-universe hydrodynamics and phase transitions) and particle physics (heavy-ion collisions). It is often said that fluids are either seen as solutions of partial differential equations or as "wet". Fluids in this book are definitely wet, but the mathematical beauty of differential equations is not washed out.

Dr. Euler's Fabulous Formula

Dr. Euler's Fabulous Formula
Author: Paul J. Nahin
Publisher: Princeton University Press
Total Pages: 416
Release: 2017-04-04
Genre: Mathematics
ISBN: 0691175918

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.

STEAM Education

STEAM Education
Author: Myint Swe Khine
Publisher: Springer
Total Pages: 192
Release: 2019-01-30
Genre: Education
ISBN: 3030040038

This book looks at the value of integrating the arts and sciences in the school curriculum. It argues that this will help students further their understanding of analytical concepts through the use of creativity. The authors illustrate how schools can work towards presenting common practices, concepts, and content. Coverage features case studies and lessons learned from classrooms across the United States. The notion of STEAM (Science, Technology, Engineering, Arts, and Mathematics) is an emerging discipline unique in its desire to provide a well-rounded approach to education. The chapters of this volume examine STEAM in a variety of settings, from kindergarten to higher education. Readers will learn about the practical considerations involved when introducing the arts and creativity into traditionally left brain processes. This includes best practices for creating and sustaining successful STEAM initiatives in any school, college, or university. For instance, one chapter discusses novel approaches to teach writing with the scientific method in order to help students better present their ideas. The authors also detail how the arts can engage more diverse learners, including students who are not traditionally interested in STEM subjects. They provide three concrete examples of classroom-tested inquiries: designing a prosthetic arm for a child, making a paleontology investigation, and taking a closer look at the arts within roller coaster engineering. This book is an invaluable resource for teachers and teacher trainers, university faculty, researchers, and school administrators. It will also be of interest to science, mathematics, engineering, computer science, information technology, arts and design and technology teachers.

Euler's Pioneering Equation

Euler's Pioneering Equation
Author: Robin Wilson
Publisher: Oxford University Press
Total Pages: 200
Release: 2018-02-22
Genre: Mathematics
ISBN: 0192514067

In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence". What is it that makes Euler's identity, eiπ + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.

Neutron and X-ray Optics

Neutron and X-ray Optics
Author: Jay Theodore Cremer Jr.
Publisher: Newnes
Total Pages: 1124
Release: 2013-02-18
Genre: Science
ISBN: 0124071597

Covering a wide range of topics related to neutron and x-ray optics, this book explores the aspects of neutron and x-ray optics and their associated background and applications in a manner accessible to both lower-level students while retaining the detail necessary to advanced students and researchers. It is a self-contained book with detailed mathematical derivations, background, and physical concepts presented in a linear fashion. A wide variety of sources were consulted and condensed to provide detailed derivations and coverage of the topics of neutron and x-ray optics as well as the background material needed to understand the physical and mathematical reasoning directly related or indirectly related to the theory and practice of neutron and x-ray optics. The book is written in a clear and detailed manner, making it easy to follow for a range of readers from undergraduate and graduate science, engineering, and medicine. It will prove beneficial as a standalone reference or as a complement to textbooks. - Supplies a historical context of covered topics. - Detailed presentation makes information easy to understand for researchers within or outside the field. - Incorporates reviews of all relevant literature in one convenient resource.

The Mathematical Universe

The Mathematical Universe
Author: Mike Hockney
Publisher: Magus Books
Total Pages: 428
Release:
Genre: Mathematics
ISBN:

The universe is a mathematical hologram. It's made of ontological mathematics. It's a living, thinking, self-optimising holographic organism composed of immortal, indestructible, ontological mathematical units called monads, defined by the most powerful and beautiful equation in the whole of mathematics: Euler's Formula. Monads have a much more resonant name: souls. We all inhabit Soul World, a wondrous immaterial Singularity outside space and time. Our souls are individual mathematical singularities: autonomous, uncaused, uncreated, dimensionless frequency domains. Via Fourier mathematics, these imperishable, immaterial monadic souls can collectively create the spacetime domain of the material world. Where each soul is a single frequency domain, the material world of space and time is their collective Fourier output. What is "matter"? It's simply dimensional energy: energy existing in the Fourier spacetime domain rather than in the Fourier dimensionless frequency domain. Welcome to Soul World.

Special Relativity, Tensors, And Energy Tensor: With Worked Problems

Special Relativity, Tensors, And Energy Tensor: With Worked Problems
Author: Somnath Datta
Publisher: World Scientific
Total Pages: 384
Release: 2021-03-02
Genre: Science
ISBN: 9811228132

This book takes the reader from the preliminary ideas of the Special Theory of Relativity (STR) to the doorsteps of the General Theory of Relativity (GTR).The first part explains the main concepts in a layman's language, including STR, the Lorentz transformation, relativistic mechanics. Thereafter the concept of tensors is built up in detail, especially Maxwell's stress tensor with illustrative examples, culminating in the energy-momentum conservation in electromagnetic fields. Mathematical structure of Minkowski's space-time is constructed and explained graphically. The equation of motion is formulated and then illustrated by the example of relativistic rocket. The principle of covariance is explained with the covariant equations of classical electrodynamics. Finally, the book constructs the energy tensor which constitutes the source term in Einstein's field equation, which clears the passage to the GTR.In the book, the concepts of tensors are developed carefully and a large number of numerical examples taken from atomic and nuclear physics. The graphs of important equations are included. This is suitable for studies in classical electrodynamics, modern physics, and relativity.

AN ESSAY ON THE MATHEMATICAL METHODS OF THEORY OF GENERAL RELATIVITY

AN ESSAY ON THE MATHEMATICAL METHODS OF THEORY OF GENERAL RELATIVITY
Author: Edoardo Confalonieri
Publisher: Edoardo Confalonieri
Total Pages: 2233
Release: 2019-01-21
Genre:
ISBN:

The basic concepts of a method for a general integral of the Field Equations of the Theory of General Relativity are outlined. An extended and revised version is currently in preparation, and it will be uploaded as soon as ready for publication.