Millar, J. A 76, , Ruskey, F. Johnson , p. Ambiguous An expression is said to be ambiguous or poorly defined if its definition does not assign it a unique interpretation or value. The first few amenable numbers are. References S. Geometry Revisited. Assoc, Amer. Boston, MA: Houghton Mifflin, Symbolically, amicable pairs satisfy s m. In , Fermat found the pair , and in , Descartes found , By , Euler had found 30 pairs, a number which he later extended to There were known as of Scott There are a total of amicable pairs below lo8 Cohen , below lOlo te Ri-?
The first few amicable pairs are 2. AFT exhaustive tabulation is maintained by D. Let an amicable pair be denoted is called a regular amicable. Pairs which are not are called irregular or exotic te Riele However, Moews found a triple in , and te Riele found a quadruple in In November , a quintuple and sextuple were discovered. The sextuple is , , , , , , , , , , , , all having PAIR SUM Amazingly, the sextuple is smaller than any known quadruple or quintuple, and is likely smaller than any quintuple.
References Alanen, J. Battiato, S. Item 62 in Beeler, M. Borho, W. Bratley, P. Ore, 0. Number Theory and Its History.
Pedersen, J. Pomerance, C. Scott, E. Amsterdam: Stichting Math.
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Centrum, Weisstein, E. IO, , Costello, P. Debrecen 4, , Lee, E. Moews, D. Dickson , found eight sets of amicable triples with two equal numbers, and two sets with distinct numbers. New York: Chelsea, p. Mason, T. Monthly 28, , Burde, G. The term is also used to refer to the maximum offset from its baseline level.
Jones In the hands of a skilled mathematician, analogy can be a very powerful tool for suggesting new and extending old results. However, subtleties can render results obtained by analogy incorrect, so rigorous PROOF is still needed. M, and Feshbach, H. New McGraw-Hill, pp. The study of the GEOMETRY of figures by algebraic represent ation and manipulation of equations describing their positions, configurations, and separations.
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Keierences Bottazzini, U. Bressoud, D. A Radical Approach to Real Analysis. Ehrlich, P. Norwell, MA: Kluwer, Hairer, E. Analysis by Its History. Royden, H. Real Analysis, 3rd ed. Wheeden, R. New York: Dekker, Whittaker, E. Morse, P. Methods of Theoretical Physics, Part I.
A Treatise on the Difierential Geometry of Surfaces. Stacey, F.
Physics of the Earth, 2nd ed. New York: Wiley, Curves.
Cambridge, England: Cambridge University Press, p. Comtet, L. Advanced Combinatorics. Hilton, P. However, it has not yet been proven. References Andrews, G. Paule, P.
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Combinatorics 1, RlO, , Monthly 83, , Square Roots. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p, 21, Rivera, C. Cambridge, England: Cambridge University Press,. Introductory Non-Euclidean York: Dover, pp. References J. Monthly , , Klee, V. Old and New. The term annihilator is used in several different ways in various aspects of mathematics. It is most commonly used to mean the SET of all functions satisfying a given set of conditions which is zero on every member of a given SET.
Anosov bicollared knots in IF1 or open region between them.
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Kirby, R. Wilmington, Perish Press, p. The concept of anomalous cancellation can be extended to arbitrary bases. Very few classes of Anosov diffeomorphisms are known. Points and Central Lines in the Kimberling, C. Four interesting theorems from Johnson follow. The antilaplacian is never unique. Antimagic ble, and squares timagic ders There are 18 families of ansquares of order four.
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Antimagic squares of orare illustrated above Madachy Antimorph A number which can be represented both in the form X02 - Dyo2 and in the form Dxr2 - y Antipodal Points Two points are antipodal i. Dover, p. Cromwell, P. Furthermore, the group of the outer complement is not even finitely generated.