Page:Popular Science Monthly Volume 67.djvu/671

Rh right-end which were computed by the Hillsboro Mathematical Club.

This solution is published in the American Mathematical Magazine for May, 1895, where Bell remarks that each of these enormous numbers is 'one half mile long.' A clearer idea of its length may be obtained from considering the space it would take to print it. Each page of this contains 45 lines and in each line about 50 figures may be set, so that one page would permit a number of about 2,250 figures to be printed. To print a number containing 206,545 figures there would be required 92 pages, and to print the nine numbers indicated above a volume of about 830 large octavo pages in this size of page and type would be needed.

It is known that Archimedes speculated regarding large numbers, for his book called Arenarius is devoted to showing that a number may be written that will express the number of grains of sand in a sphere of the size of the earth. It can not be proved that Archimedes was, or was not, the author of the cattle problem, but, as Amthor remarks, the enormous numbers required in its solution render it worthy of his genius and proper to bear his name. Its closing challenge still remains open, for the complete solution has not yet been made. Moreover, it is practically impossible that the long numbers can ever be computed, since the investigations of Bell show that this would require the work of a thousand men for thousand years. The little prairie town of Hillsboro may, however, well exult as a conqueror, for its mathematical club has made the most complete of all solutions of the cattle problem and has proved itself to be highly skilled in numbers.