The Mathematical Experience |
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Page 230
... geometry was consistent if Euclidean geometry was consistent ; now Euclidean geometry is consistent if ele- mentary algebra is consistent . The Euclidean sphere was a model for the non - Euclidean plane ; the set of pairs of co ...
... geometry was consistent if Euclidean geometry was consistent ; now Euclidean geometry is consistent if ele- mentary algebra is consistent . The Euclidean sphere was a model for the non - Euclidean plane ; the set of pairs of co ...
Page 313
... geometry of Euclid has a priori truth for the universe , that it is the model for physical space . ( 4 ) The incompleteness of the logical structure of classi- cal Euclidean geometry as discovered in the nineteenth century and as ...
... geometry of Euclid has a priori truth for the universe , that it is the model for physical space . ( 4 ) The incompleteness of the logical structure of classi- cal Euclidean geometry as discovered in the nineteenth century and as ...
Page 341
... Euclidean geometry in Chapter 5 , we saw how the attempt to prove Euclid's fifth postulate ( the postulate of parallels , which was not as " self - evident " as the other four postulates ) led to the discovery of non- Euclidean geometry ...
... Euclidean geometry in Chapter 5 , we saw how the attempt to prove Euclid's fifth postulate ( the postulate of parallels , which was not as " self - evident " as the other four postulates ) led to the discovery of non- Euclidean geometry ...
Other editions - View all
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience: Study Edition Philip J. Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 1995 |
Common terms and phrases
abstract aesthetic algebra algorithmic analysis analytic answer applications argument arithmetic asserts axiom of choice Bibliography calculus called century circle complex conjecture construct continuum hypothesis course definition differential equations elements ematics Euclid Euclidean geometry Euler example existence experience fact figure finite formal language formalist formula Fourier Fourier series function Further Readings G. H. Hardy Hilbert human hypercube hypersquares idea ideal infinite set infinitesimal infinity integers intuition knowledge Lakatos logic mathe mathematical objects mathematical proof mathematicians matics means ment method natural numbers non-Euclidean geometry non-Riemannian nonstandard notion number theory parallel postulate philosophy of mathematics physical Platonism Platonist possible postulate prime number prime number theorem problem proof proved question real numbers reason restricted set theory result rigorous sense solution square statement straight line symbols theorem thing tion triangle true truth universe words zero