On the Shoulders of Giants
CRC Press, 1 Ιαν 1994 - 296 σελίδες
Mathematics is the only science with a methodology based upon deductive logic, whereas physics is a quantitative science based upon experiment and observation in which trial and error are inherent. Physics uses the most relevant mathematics, for example using group theory to explain the theoretical basis for the crystalline structure of solids, an illustration of how, time and time again, a mathematical theorem perhaps developed by a Greek philosopher is relevant to today's newly developed physics proof.
On the Shoulders of Giants investigates the relationship between the disciplines of physics and mathematics and shows how many of the most significant advances of 20th-century physics rely on mathematics developed, sometimes much earlier, with no particular physics application in mind. Quoting from mathematicians such as Poincaré and Euclid and physicists such as Newton and Feynman, the links between the two disciplines are explored in the author's entertaining style, providing a fascinating account of the twists and turns in scientific progress through the ages.
Challenging, stimulating, and questioning, the book explains how the uncanny ability of formal and abstract mathematics can interpret the properties of the physical world. Using a wide ranging set of examples, it illustrates the manner in which mathematics has been applied to physics and even points to directions for future research. The book discusses how to fill space without leaving gaps; Euclidean geometry, its limitations, and the bending of space; the laws of musical harmony, sound vibrations, and the confinement of electrons in solids; how to tile a floor efficiently; Newton's Laws of Motion, chaos, and the weather; group theory and garlic; the laws of chance; route-planning in Konigsberg with Euler; the rules that turn bath bubbles into suds; the shape of soot; and the Schrödinger equation and why a pendulum can never stop.
Requiring some prior knowledge of physics and mathematics, this well-illustrated book will be of interest to all readers with an interest in physics and mathematics, in learning more about the role of mathematics as the formal language of physics, and in how physics and mathematics have influenced scientific research.
Τι λένε οι χρήστες - Σύνταξη κριτικής
Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
From Aristotle to the structure of glass
From Euclid to general relativity
From plucking strings to electrons in solids
From tiling floors to quasicrystals
from Newton to quantum chaos
from Galois to superstrings
From coin tossing to entropy
from the bridges of Königsberg
From parabolas to fractons
from Zeno to Schrödinger
Άλλες εκδόσεις - Προβολή όλων
actually algebra angles appear associated atoms become called cell century chapter close completely concept concerning constant contain context continuous crystal curve defined difficult dimensions direction distance electron elements energy equal equation exactly example exist experimental expressed extremely faces fact fashion field figure finally follows force four fractal function geometry given glass heads important infinite involved kind known least length less light limit manner mathematical mathematician matter mean measure method motion nature necessary objects observed operations original oscillations packing particle particular pattern perhaps periodic physicist physics plane position possible probability problem properties quantum quantum mechanics question referred regular remains result rotation rules sense shown sides simple solid solution space square structure symmetry tails temperature theory tiles triangle true unit universe values vibrational wave zero