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1981
In Chapter 3 we saw that the group G which we have been discussing is formed from the transformation $$ y = \frac{{xT + xx'{v_1} + {v_2}}}{{xu{'_2} + xx'b + d}} $$ (1) (And at the same time we have $$ yy'\left( {\frac{{xu{'_1} + xx'a + c}}{{xu{'_2} + xx'b + d}}} \right).) $$ (2) Observe that the matrix $$ M = \left( {\begin ...
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In Chapter 3 we saw that the group G which we have been discussing is formed from the transformation $$ y = \frac{{xT + xx'{v_1} + {v_2}}}{{xu{'_2} + xx'b + d}} $$ (1) (And at the same time we have $$ yy'\left( {\frac{{xu{'_1} + xx'a + c}}{{xu{'_2} + xx'b + d}}} \right).) $$ (2) Observe that the matrix $$ M = \left( {\begin ...
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2000
Certainly one of the greatest mathematical discoveries of the nineteenth century was that of non-Euclidean geometry: seen but not revealed by Gauss, and developed in all its glory by Bolyai and Lobachevsky. The purpose of this chapter is to give an account of this theory, but we do not always follow the historical development. Rather, with hindsight we
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Certainly one of the greatest mathematical discoveries of the nineteenth century was that of non-Euclidean geometry: seen but not revealed by Gauss, and developed in all its glory by Bolyai and Lobachevsky. The purpose of this chapter is to give an account of this theory, but we do not always follow the historical development. Rather, with hindsight we
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2014
The fruitless attempts to prove Euclid’s parallel postulate, in particular the theory of limit parallels, lead eventually the mathematicians of the nineteenth century to consider that the negation of this postulate could possibly be taken as an axiom.
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The fruitless attempts to prove Euclid’s parallel postulate, in particular the theory of limit parallels, lead eventually the mathematicians of the nineteenth century to consider that the negation of this postulate could possibly be taken as an axiom.
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Report on Progress in Non-Euclidean Geometry
Science, 1899(1899). Report on Progress in Non-Euclidean Geometry. The American Mathematical Monthly: Vol. 6, No. 10, pp. 219-233.
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The American Mathematical Monthly, 1900 Practical Non-Euclidean Geometry
The Mathematical Gazette, 19251. In order to understand the meaning to be attached to Non-Euclidean Geometry and the use of the model measuring tape described below, it is advisable to say a few words upon Euclidean Geometry.
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Introduction to non-Euclidean Geometry
The Mathematics Teacher, 1964A teacher of high school geometry describes a successful unit that convinces pupils that what we prove depends on what we assume.
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Programmable interactions and emergent geometry in an array of atom clouds
Nature, 2021Avikar Periwal +2 more
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