The Mathematical Experience |
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Page 240
... circle as an infi- nite - sided polygon . We wish to get a logically acceptable proof of the formula " The area of a circle with a radius of one unit equals half the circumference , " which we discov- ered by a logically unacceptable ...
... circle as an infi- nite - sided polygon . We wish to get a logically acceptable proof of the formula " The area of a circle with a radius of one unit equals half the circumference , " which we discov- ered by a logically unacceptable ...
Page 279
... circle must be a di- ameter . The first is clear , but the second may be slightly less clear . If AB is not a ... circle problem ( i.e. , simultaneously bisect the area of two circles ) has one and only one solution if the centers of the ...
... circle must be a di- ameter . The first is clear , but the second may be slightly less clear . If AB is not a ... circle problem ( i.e. , simultaneously bisect the area of two circles ) has one and only one solution if the centers of the ...
Page 288
... circles having the same radius pass through a point , the circle through their other three points of intersection also has the same radius . This is the theorem that we have to prove . The statement is short and clear , but does not ...
... circles having the same radius pass through a point , the circle through their other three points of intersection also has the same radius . This is the theorem that we have to prove . The statement is short and clear , but does not ...
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 |
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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