On the Shoulders of GiantsInstitute of Physics Pub., 1994 - 288 Seiten Malcolm Lines 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. 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 strucutre of solids, an illustration of how, time and time again, a mathematical theorem perhaps developed by a Greek philosopher is shown to be relevant to today's newly developed physics proof. Well illustrated, quoting from mathematicians such as Poincar^D'e and Euclid, 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. This book will be of interest to all readers with an interest in physics, mathematics and those with a general intereset in their influence on how scientific research has proceeded. Some prior knowledge of physics and mathematics is required. |
Inhalt
Introduction | 1 |
From Aristotle to the structure of glass | 10 |
From Euclid to general relativity | 34 |
Urheberrecht | |
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algebra angles atoms Brillouin zone called cell century chaos chapter classical completely complex numbers context convex polygons crystal curve defined differential equations diffraction dimensional electron Emilio Segrè energy equal equation of motion Euclidean exactly example exist experimental fact fashion finite force Fourier fractal fractal dimension fraction geometry glass group theory infinite number integers interactions involved knots known Koch snowflake large number lattice magnetic manner mathematical mathematician measure molecules nature Newton Newtonian orbitals oscillations packing parallel postulate particle particular pattern Peano curve Penrose Penrose tiles phonons physicist physics plane polygons polyominoes position possible postulate problem properties quantum quasicrystal quasicrystalline random ratio result rotation sequence shown in figure simple simplest solid solution spacetime spheres square straight line string structure symmetry symmetry group tails temperature tensor tetrahedra three dimensions three-dimensional tiles topological tosses triangle values vector velocity vibrational Voronoi wave function zero