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The science of Physics is based on observations that lead to the formulation of mathematical relationships between measured quantities. Some would consider Physics an exact science. Its discoveries and laws are basic to understanding in all areas of science and technology. Four Physics foibles 1) Kurt Godel proved that there are unknowables in our mathematics. 2) Werner Heisenberg showed that there are uncertainties in our measurements. 3) Entropy says that we can only predict the probabilities of events. 4)Chaos Theory deals with things that are effectively impossible to predict like turbulence and long term weather forecasting. The word foible as defined by Webster: An odd feature or mild failing in a person's character a weakness. In fencing, the weaker part of a sword blade. It is the acceptance of these foibles in Physics that has led to broader understanding. In the process of examining these 'weaknesses' in science, many creative and practical solutions have been discovered. There are a number of original computer programs throughout the book. No other person, living or dead - other than the author - has edited or examined the programs. No effort has been made to optimize any of these programs. The author has relied on the computer's results to serve as his default editor. Computer programs are included that take you through puzzles and paradoxes, distribute molecules, follow ameba populations, prove and disprove Murphy's Law, flip coins, and play lottery and casino games. Many have asked about the book. Some with a technical background - and some not - have questioned: What do dice, poker, lotto, and heads-or-tails have to do with Physics? The mathematical study of games of chance is as old as mathematics itself. The connection between games of chance and Nature's laws can be rigorously refined in the field of Statistical Mathematics. If you can analyze multiple coin flips, you can view molecular distribution. If you can understand the results of a game of Roulette, you can understand Radioactive decay. Also included are polls, number systems, wave packets, the search for Pi and the elusive Random, Internet quotes, and more. And in the the process of reading, stop and listen to the words of the science gurus displayed in cartoons throughout.
This book contains 1 million digits of pi on 371 pages (Decimal Places from 1 to 1,000,000) and is the perfect gift for everyone who loves math, especially on Pi day and for birthdays!ESTIMATED NUMBERS PER PAGE: 2714NUMBER OF PAGES: 371 pagesPAPER / TRIM SIZE: 6" x 9" (15,24cm x 22,86 cm)PAPER COLOR: White paperCOVER: Softcover paperback - glossy finishBOOK BINDING: Perfect bound
Renowned mathematician Ian Stewart uses remarkable (and some unremarkable) numbers to introduce readers to the beauty of mathematics. At its heart, mathematics is about numbers, our fundamental tools for understanding the world. In Professor Stewart's Incredible Numbers, Ian Stewart offers a delightful introduction to the numbers that surround us, from the common (Pi and 2) to the uncommon but no less consequential (1.059463 and 43,252,003,274,489,856,000). Along the way, Stewart takes us through prime numbers, cubic equations, the concept of zero, the possible positions on the Rubik's Cube, the role of numbers in human history, and beyond! An unfailingly genial guide, Stewart brings his characteristic wit and erudition to bear on these incredible numbers, offering an engaging primer on the principles and power of math.
"It makes alive the contents of the elements of mathematics."—Albert Einstein Taking only the most elementary knowledge for granted, Lancelot Hogben leads readers of this famous book through the whole course from simple arithmetic to calculus. His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order—a language Hogben shows one can both master and enjoy.
Communication and, indeed, our comprehension of the world in general are largely ordered by the number and measurement systems that have arisen over time. This book delves into the history of mathematical reasoning and the progression of numerical thought around the world. With detailed biographies of seminal thinkers and theorists, readers develop a sophisticated understanding of some of the most fundamental arithmetical concepts as well as the individuals who established them.
SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.
Explains mathematics from counting to calculus in the light of man's changing social achievements.
Fundamental Causation addresses issues in the metaphysics of deterministic singular causation, the metaphysics of events, property instances, facts, preventions, and omissions, as well as the debate between causal reductionists and causal anti-reductionists. The book also pays special attention to causation and causal structure in physics. Weaver argues that causation is a multigrade obtaining relation that is transitive, irreflexive, and asymmetric. When causation is singular, deterministic and such that it relates purely contingent events, the relation is also universal, intrinsic, and well-founded. He shows that proper causal relata are events understood as states of substances at ontological indices. He then proves that causation cannot be reduced to some non-causal base, and that the best account of that relation should be unashamedly primitivist about the dependence relation that underwrites its very nature. The book demonstrates a distinctive realist and anti-reductionist account of causation by detailing precisely how the account outperforms reductionist and competing anti-reductionist accounts in that it handles all of the difficult cases while overcoming all of the general objections to anti-reductionism upon which other anti-reductionist accounts falter. This book offers an original and interesting view of causation and will appeal to scholars and advanced students in the areas of metaphysics, philosophy of science, and philosophy of physics.
Number theory proves to be a virtually inexhaustible source of intriguing puzzle problems. Includes divisors, perfect numbers, the congruences of Gauss, scales of notation, the Pell equation, more. Solutions to all problems.
An elegantly dramatized and illustrated dialog on the square root of two and the whole concept of irrational numbers.