Solutions - Canadian Mathematical Society
... In other words, a cannot be divisible by 2 or 3 (since 2 and 3 are the only prime numbers which are divisors of 72). How many of the positive integers from 1 to 71 are not divisible by 2 or 3? Of these integers, 35 of the them are divisible by 2 (namely, 2, 4, 6, . . ., 70). Also, 23 of them (namely ...
... In other words, a cannot be divisible by 2 or 3 (since 2 and 3 are the only prime numbers which are divisors of 72). How many of the positive integers from 1 to 71 are not divisible by 2 or 3? Of these integers, 35 of the them are divisible by 2 (namely, 2, 4, 6, . . ., 70). Also, 23 of them (namely ...
THE PROOF IS IN THE PICTURE Theorem: The square root of 2 is
... For each problem in this section, you are given a theorem and puzzle pieces. The goal is to arrange the puzzle pieces in some fashion to prove the theorem. Here is an example (my picture has no explanation, but please explain why your pictures are proofs when you solve the subsequent problems!) • Qu ...
... For each problem in this section, you are given a theorem and puzzle pieces. The goal is to arrange the puzzle pieces in some fashion to prove the theorem. Here is an example (my picture has no explanation, but please explain why your pictures are proofs when you solve the subsequent problems!) • Qu ...
Weber problem
In geometry, the Weber problem, named after Alfred Weber, is one of the most famous problems in location theory. It requires finding a point in the plane that minimizes the sum of the transportation costs from this point to n destination points, where different destination points are associated with different costs per unit distance.The Weber problem generalizes the geometric median, which assumes transportation costs per unit distance are the same for all destination points, and the problem of computing the Fermat point, the geometric median of three points. For this reason it is sometimes called the Fermat–Weber problem, although the same name has also been used for the unweighted geometric median problem. The Weber problem is in turn generalized by the attraction–repulsion problem, which allows some of the costs to be negative, so that greater distance from some points is better.