The Mathematical Experience |
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Page 126
... line which has warp and cor- rugation . Alongside this real , concrete instance of a straight line , there exists the mental idea of the mathematical abstrac- tion of an ideal straight line . In the idealized version , all the ...
... line which has warp and cor- rugation . Alongside this real , concrete instance of a straight line , there exists the mental idea of the mathematical abstrac- tion of an ideal straight line . In the idealized version , all the ...
Page 158
... straight line , the shortest path from here to there , the ac- tivity of going directly towards something . In raw nature , untouched by human activity , one sees straight lines in primitive form . The blades of grass or stalks of corn ...
... straight line , the shortest path from here to there , the ac- tivity of going directly towards something . In raw nature , untouched by human activity , one sees straight lines in primitive form . The blades of grass or stalks of corn ...
Page 159
... straight line is intuitively rooted in the kinesthetic and the visual imagi- nations . We feel in our muscles what it is to go straight toward our goal , we can see with our eyes whether some- one else is going straight . The interplay ...
... straight line is intuitively rooted in the kinesthetic and the visual imagi- nations . We feel in our muscles what it is to go straight toward our goal , we can see with our eyes whether some- one else is going straight . The interplay ...
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