The Mathematical Experience |
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Page 134
... triangle , then the angle at A equals the angle at B. " Suppose that some time later , mathematician Beta said to himself that while what Alpha said is perfectly true , it is not necessary that ABC be equilateral for the conclusions to ...
... triangle , then the angle at A equals the angle at B. " Suppose that some time later , mathematician Beta said to himself that while what Alpha said is perfectly true , it is not necessary that ABC be equilateral for the conclusions to ...
Page 148
... triangle ABD is equal to the triangle FBC . [ 1.4 ] Now the parallelogram BL is double of the triangle ABD , for they have the same base BD and are in the same parallels BD , AL . [ 1.41 ] And the square GB is double of the triangle FBC ...
... triangle ABD is equal to the triangle FBC . [ 1.4 ] Now the parallelogram BL is double of the triangle ABD , for they have the same base BD and are in the same parallels BD , AL . [ 1.41 ] And the square GB is double of the triangle FBC ...
Page 238
... triangles , all of which have altitude 1. For a triangle the area is half the base times the altitude . Therefore the sum of the areas of the triangles is half the sum of the bases . But the sum of the areas of the triangles is the area ...
... triangles , all of which have altitude 1. For a triangle the area is half the base times the altitude . Therefore the sum of the areas of the triangles is half the sum of the bases . But the sum of the areas of the triangles is the area ...
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