> F:= scalarmul(C, m) F := Ĭomment: The eight entries of this vector are the smallest numbers of white bulls, black bulls, yellow bulls, dappled bulls, white cows, black cows, yellow cows, and dappled cows, respectively, that solve Archimedes' cattle problem.Ĭomment: Compute the total number of cattle. > m:=ilcm( denom(C), denom(C), denom(C), denom(C), denom(C), denom(C), denom(C), denom(C) ) m := 3515820Ĭomment: Multiply C by m to obtain a vector with integer entries. Next, we wish to multiply C by a suitable constant so that the resulting entries are integers with no common divisor.Ĭomment: Find the least common multiple of the denominators of the entries of C. Il ny a pas de raison sérieux de croire que le ‘problème de bétail’ qui est associé à Archimède nest pas soluble. Es gibt keinen ernsthaften Grund zu glauben, da das ‘Vieh-Problem,’ das Archimedes zugeschrieben wird, unlösbar ist. Comment: Load the Linear Algebra library. There is no serious reason to believe that the ‘Cattle problem’ ascribed to Archimedes is unsolvable. The input is in blue, the output is in red, and comments are in black. > C:= B Comment: Every solution of the homogeneous system is a scalar multiple of this one vector C. Archimedes' Cattle Problem (Computer Output) Below is a session of Maple, a symbolic algebra program, used to solve the first part of Archimedes' Cattle Problem. ![]() ![]() It has intrigued mathematicians of modern times since Gotthold Ephraim Lessing discovered a Greek manuscript containing a 44 line poem in the Wolfenbüttel (northern Germany) library in 1773. Thus the dimension of the nullspace of A is one, and so A has rank seven.Ĭomment: Pick out the sole entry of the set of basis vectors of the null space of A. The cattle problem, a difficult problem of indeterminate analysis, is generally attributed to Archimedes. > B:=kernel(A) Comment: The result is in the form of a set with one basis vector. Comment: Load the Linear Algebra library.Ĭomment: Enter the 7x8 coefficient matrix A.Ĭomment: Find a basis for the nullspace of the matrix A. ![]() P A R T )īelow is a session of Maple, a symbolic algebra program, used to solve the first part of Archimedes' Cattle Problem. The cattle-problem including the solution of Wurms problem by Amthor in Zeitschrift fr math. Archimedes' Cattle Problem (Computer Output)Ĭ O M P U T E R.
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