S. C. Johnson
Abstract
The function F(x) = (1/2-x) (1-x2)1/2+x(1+(1-(1/2+x)2)1/2) has a maximum at about x = .343771, where it attains the value of approximately .674981. This value is the root of an irreducible polynomial of tenth degree over the integers; the problem is to find this polynomial. The obvious way of proceeding is as follows:(1) Differentiate F(x), set it equal to zero, and clear radicals. The result is a tenth degree polynomial P(x) over the integers which has a root at about x = .343771.
- ALTRAN User's Manual (Vol. I), W. S. Brown, available from Bell Telephone Laboratories, Inc., Murray Hill, New Jersey 07974.Google Scholar
- R. L. Graham, The Largest Small Hexagon (to appear).Google Scholar
Index Terms
- Problem #7
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