Pascal`s Triangle (answers)
... a) Continue the pattern to determine the fourth, fifth and sixth triangular numbers. b) Relate the sequence of triangular numbers to Pascal’s Triangle. State the nth triangular number in terms of a Pascal’s Triangle term, tn,r. c) Determine a general rule for the nth triangular number. d) Determine ...
... a) Continue the pattern to determine the fourth, fifth and sixth triangular numbers. b) Relate the sequence of triangular numbers to Pascal’s Triangle. State the nth triangular number in terms of a Pascal’s Triangle term, tn,r. c) Determine a general rule for the nth triangular number. d) Determine ...
46 Austrian Mathematical Olympiad
... Let k1 and k2 be internally tangent circles with common point X . Let P be a point lying neither on one of the two circles nor on the line through the two centers. Let N1 be the point on k1 closest to P and F1 the point on k1 that is farthest from P . Analogously, let N2 be the point on k2 closest ...
... Let k1 and k2 be internally tangent circles with common point X . Let P be a point lying neither on one of the two circles nor on the line through the two centers. Let N1 be the point on k1 closest to P and F1 the point on k1 that is farthest from P . Analogously, let N2 be the point on k2 closest ...
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.