Answers 297If readers require a closer approximation or further information as to the
manner of solving this puzzle, I cannot do better than refer them to a paper,
on "Solutions of Numerical Functional Equations, illustrated by an account
of a Popular Puzzle and its Solution," by Mr. Eric H. Neville, in the Proceed-
ings of London Mathematical Society, Series II, Vol. 14, Part 4. I will just add
that covering is possible if the ratio of the two diameters exceeds .6094185, and
impossible if the ratio is less than .6094180. In my case above, where all five
discs touch the center, the ratio is .6180340.
- THE THREE FENCES
To divide a circular field into four
equal parts by three fences of equal
length, first divide the diameter of
circle in four parts and then describe
semicircles on each side of the line in
the manner shown in the diagram.
The curved lines will be the required
fences.
- SQUARING THE CIRCLE
If you make a rectangle with one side equal to the diameter, and the other
three times the diameter, then the diagonal will be something near correct. InM