By Joseph S. Madachy

ISBN-10: 0486237621

ISBN-13: 9780486237626

ISBN-10: 0684139642

ISBN-13: 9780684139647

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**Extra info for Mathematics on Vacation (also, Madachy's Mathematical Recreations)**

**Example text**

That such a parabola results by the folding process described can be proven by referring to Fig- 58 A~ MATHEMATICS ON VACATION ____________________________L~______Q~______________~B " ~ " 'N FIGURE 39 ure 39. LN is the fold that brings Q, any point on the straight edge AB, into coincidence with P. A perpendicular from Qintersects LN at M. Right triangles QRM and PRM are congruent, and therefore QM == PM. Then LN is tangent to the parabola at M. In any ellipse, the sum of the distances from any point on the ellipse to both the foci is a constant.

For example, if n is 9, there are 27 different possible Hexagons. Start by drawing a structure diagram with n vertexes. Number the vertexes 1, 2, 3, ... n in any order.

Hence, there is a total of 12 + 80, or 92, solutions to the problem of the queens. The same question could be asked of other chess pieces. A rook (R) can move any number of squares horizontally or vertically, but it cannot move diagonally; a bishop (B) can move any number of squares diagonally; a knight (Kt) can move only from one corner of a 2 X 3 rectangle to the corner diagonally opposite; a king (Kg) can move only one square horizontally, vertically, or diagonally. The maximum number of rooks that can be placed on a chessboard without anyone capturing another can be calculated readily.

### Mathematics on Vacation (also, Madachy's Mathematical Recreations) by Joseph S. Madachy

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