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Page 25
... figures of pure mathemat- ics , at least on a par with Banach . But after he bade farewell to his friends at the Scottish Café , something died for- ever within him , and his career as a pure mathematician went permanently adrift . Like ...
... figures of pure mathemat- ics , at least on a par with Banach . But after he bade farewell to his friends at the Scottish Café , something died for- ever within him , and his career as a pure mathematician went permanently adrift . Like ...
Page 30
... figure out a way to obliterate all memory of its source . In a last - ditch effort to salvage our pride , we will also manage to find fault with the person to whom we are indebted . Stan Ulam's weaknesses were all too appar- ent and ...
... figure out a way to obliterate all memory of its source . In a last - ditch effort to salvage our pride , we will also manage to find fault with the person to whom we are indebted . Stan Ulam's weaknesses were all too appar- ent and ...
Page 55
... Figure 19.1 . Two possible solutions . The line segment rotates within the curve , and in each position cuts off half the area and half the perimeter . 153 MAZUR PRIZE : A live goose November 6 , 1936 43 MAZUR PRIZE : One bottle of wine ...
... Figure 19.1 . Two possible solutions . The line segment rotates within the curve , and in each position cuts off half the area and half the perimeter . 153 MAZUR PRIZE : A live goose November 6 , 1936 43 MAZUR PRIZE : One bottle of wine ...
Page 87
... Figure 12 shows a few samples from our computer studies in which the values of h ( i / 2 " ) are computed for n = 10 . S. Graf , S. C. Williams , and I studied this method in detail ( Graf , Mauldin , and Williams 1986 ) . For example ...
... Figure 12 shows a few samples from our computer studies in which the values of h ( i / 2 " ) are computed for n = 10 . S. Graf , S. C. Williams , and I studied this method in detail ( Graf , Mauldin , and Williams 1986 ) . For example ...
Page 97
... ( Figure 3 gives a glimpse of some interesting cases . ) Unless someone writes a fast program to evaluate automatically the amusement value of limit sets , that is as far as such studies will ever go : the case that comes next ( when ...
... ( Figure 3 gives a glimpse of some interesting cases . ) Unless someone writes a fast program to evaluate automatically the amusement value of limit sets , that is as far as such studies will ever go : the case that comes next ( when ...
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Popular passages
Page 299 - Talibus orabat dictis, arasque tenebat, cum sic orsa loqui vates : ' Sate sanguine divom, 125 Tros Anchisiade, facilis descensus Averno ; noctes atque dies patet atri janua Ditis ; sed revocare gradum superasque evadere ad auras, hoc opus, hie labor est.
Page 231 - But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.
Page 210 - The low-velocity equation of state for a lattice gas can be written as p - ^p (l - |v2), where p is the pressure, p is the density, and v is the flow speed.
Page 316 - Southeastern Conference on Combinatorics. Graph Theory, and Computing (Florida Atlantic University, Boca Raton, Florida, April 2-6, 1979), 3-18.
Page 121 - He is a member of the National Academy of Sciences and a Fellow of the American Academy of Arts and Sciences, the American Physical Society and the American Association for the Advancement of Science.
Page 231 - A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws...
Page 224 - Instead, we conclude by remarking that really efficient high-speed computing devices may, in the field of non-linear partial differential equations as well as in many other fields, which are now difficult or entirely denied of access, provide us with those heuristic hints which are needed in all parts of mathematics for genuine progress.
Page 272 - Let us say here that the results of our computations show features which were, from the beginning, surprising to us. Instead of a gradual, continuous flow of energy from the first mode to the higher modes, all of the problems show an entirely different behavior.
Page 58 - That was dramatized by Bertrand, who considered the problem of finding the probability that a chord of a circle chosen "at random" be longer than the side of an equilateral triangle inscribed in the circle.