# Alhazen'S Billiard Problem Extended Essay

This work has provided a mechanism for organizing what has turned out to be a fairly large collection of mathematics. Ackermann Number A number of the form n t • • • T™ where Arrow Nota- n TION has been used.

This work has provided a mechanism for organizing what has turned out to be a fairly large collection of mathematics. Ackermann Number A number of the form n t • • • T™ where Arrow Nota- n TION has been used.

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First, the entire text and all the equations and figures are available in searchable electronic form on CD-ROM. see also Crunode, Spinode, Tacnode Acoptic Polyhedron A term invented by B. see also Addition, Augend, Plus, Radicand Addition i i - 15 8- J- 249 * 407- Y carries (-addend 1 Y addend 2 hsum The combining of two or more quantities using the PLUS operator.

Second, the entries are extensively cross-linked and cross-referenced, not only to related entries but also to many external sites on the Internet. It also provides a highly efficient way to "navigate" from one related concept to another, a feature that is especially powerful in the electronic version. Griinbaum in an attempt to pro- mote concrete and precise POLYHEDRON terminology. The individual numbers being combined are called ADDENDS, and the total is called the Sum. Addition Chain An addition chain for a number n is a SEQUENCE 1 = ao 2 15 contain a in base 3, which would imply that the maximum persistence in base 3 is 3 (Guy, 1994).

These formulas are comprehensible to readers with only minimal mathematical background, and are interesting to both those with and without formal mathematics training. n l X n (i) (2) be the step interval, and consider the Maclaurin Se- ries of y about x n , y n i = y n ( -T-) ( x ~ x n) (x - x n ) 2 .

However, they have not previously been collected in a single convenient location. V dx J n 1 \dxj n \ dx 2 J (3) (4) Here, the Derivatives of y are given by the Backward Differences \dx/ n Xn i ~ X 3/n i - y n h (5) (6) (7) etc.

While undertaking the Word to T^}K conversion, I also began cross-referencing entries, anticipating that eventually I would be able to convert the entire document to hypertext. The selection of topics included in this compendium is not based on any fixed set of criteria, but rather reflects my own random walk through mathematics.

## Comments Alhazen'S Billiard Problem Extended Essay

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