By Eric W. Weisstein

Upon book, the 1st version of the **CRC** **Concise Encyclopedia of arithmetic **received overwhelming accolades for its extraordinary scope, clarity, and software. It quickly took its position one of the best promoting books within the historical past of Chapman & Hall/CRC, and its recognition keeps unabated.

Yet additionally unabated has been the commitment of writer Eric Weisstein to amassing, cataloging, and referencing mathematical proof, formulation, and definitions. He has now up-to-date lots of the unique entries and elevated the *Encyclopedia* to incorporate one thousand extra pages of illustrated entries.

The accessibility of the *Encyclopedia* in addition to its vast insurance and cost effective cost make it beautiful to the widest attainable diversity of readers and definitely a needs to for libraries, from the secondary to the pro and examine degrees. For mathematical definitions, formulation, figures, tabulations, and references, this is often easily the main notable compendium available.

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6) References Alladi, K. and Grinstead, C. “On the Decomposition of n! ” J. Number Th. 9, 452-458, 1977. Finch, S. ” http : //wua. html. Guy, R. K. ” §B22 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 79, 1994. Allegory A technical resemblance FUNCTIONS mathematical object which bears the same to binary relations as CATEGORIES do to and SETS. see also CATEGORY References Model ENTROPY so METHOD F’reyd, P. J. and Scedrov, A. Categories, Allegories. dam, Netherlands: North-Holland, 1990.

IMath. 7,167-184, 1881, Updown Numbers AssociArnold, V. I. “Bernoulli-Euler ated with Function Singularities, Their Combinatorics and Duke Math. J. 63, 537-555, 1991. ” Calculus and Combinatorics of BerArnold, V. I. “Snake noulli, Euler, and Springer Numbers for Coxeter Groups+” Russian Math. Surveys 47, 3-45, 1992, Bauslaugh, B. ” BIT 30, 17-26, 1990. Conway, J. H. and Guy, R. K. In The Book of Numbers. New York: Springer-Verlag, pp. 110-111, 1996. Dijrrie, H. ” §lS in 100 Great Problems of Elementary Mathematics: Th eir History and Solutions.

The triangle HlHzH3 has the minimum PERIMETER of any TRIANGLE inscribed in a given ACUTE TRIANGLE (Johnson 1929, pp. 161-165). The PERIMETER of ~lHlHzH3 is 2A/R (Johnson 1929, p. 191). Additional properties involving the FEET of the altitudes are given by Johnson (1929, pp. 261-262). see also CEVIAN, FOOT, ORTHOCENTER, LAR, PERPENDICULAR FOOT Amenable Number A number n which a2, . ) Uk by either that can be built up from INTEGERS al, ADDITION or MULTIPLICATION such f)i i=l = fiai = 72. i=l The numbers {al, .