Mathematics Degree Programs

I am sure everyone is familiar with one of America's greatest statesman, Benjamin Franklin (1706-1790). Sometimes we forget to credit him for all of his unique diversities; recall that he was a scientist, an inventor, a printer, a philosopher, a musician, and an economist. 

Franklin also liked to dabble in mathematics, and found great pleasure in constructing magic squares at unusual times, such as during the Pennsylvania Assembly meetings. He says he was attempting to avoid the weariness of it all. In a somewhat apologetic tone Benjamin Franklin said that spending time on these "trifles" is time he might have employed more usefully. But although not known as a mathematician himself, Franklin encouraged its study through his essays and his influence in founding the University of Pennsylvania. Shown below is one of Franklin's (almost) magic squares.

Now Franklin's magic square has some quirks of its own. One flaw is that although all of the rows and columns individually add to 260, the sums of each of the two diagonals do not. In fact, they don’t even add up to the same number. See if you can determine what their sums are before I tell you.

The diagonal going from upper left to lower right has a sum of 228, while the other diagonal has a sum of 292. We can salvage something from this though. The sum of 228 and 292 equals 520, and when divided by 2 it equals, you guessed it, 260.

But there is something special about Franklin's magic square that most other magic squares do not possess, a beautiful kind of symmetry.

With the aid of a straight edge draw a line from the center of the box containing the number 1 to the center of the box containing the number 2. Then from that box draw a line to the center of the box containing the number 3. From that to the center of the box containing the number 4, and so on.  

When complete you should see a wonderful design.