You know you're a math geek when you spend your Saturday morning at a math competition. Today was the 2006 Michigan Autumn Take Home (M.A.T.H.) Challenge. I wasn't exactly looking forward to it because these tests always have a way of showing you just how much you don't know. We had 3 hours to tackle 10 problems. I worked with one other person as a team. We did some pretty good work i think. The nicest part of the exam is that as soon as you are done, you can see what the answers were.
I'll leave you with a sample problem: The three points (4,14,8,14), (6,6,10,8), and (2,4,6,8) which are vertices of a cube in four-dimensional space. Find the center of the cube.
Posted by Matthew at October 28, 2006 06:23 PMWoah -- so what's the answer. And better yet, how'd you do?
Posted by: Jeff at October 30, 2006 12:55 PMFiguring the crudest possible way I know how (graph paper) I get (3,9,8,11). There must be a more generalized method.
Posted by: William Clifford at November 4, 2006 08:16 AMoops (3,9,9,11)
Posted by: William Clifford at November 4, 2006 09:08 AMI'd like to see your graph William. I was never much good at drawing things in four-dimensional space.
The trick to finding the center of the cube is to find the midpoint of the longest diagonal of the cube. Luckily the distance formula scales well to a 4D space. The longest distance is between points (4,14,8,14) and (2,4,6,8). That means that the center of the cube is at (3,9,7,11) which is half way between those two points.
Posted by: Matthew at November 5, 2006 05:15 PM