Today, we're going to work a little magic with mirrors!
Instead of using mirrors secretly, however, we're going to use them openly. And instead of stage magic, we're going to play with magic squares.
Numberphile recently posted a great video involving mirrored magic squares. Don't worry if you're not familiar with magic squares, since the video starts with a basic introduction to them:
Inspired by this video, a poster with the screenname rotflmaopmpqxyz developed the following magic square with the same qualities, but using 3 digits and totaling 1,776 in every direction:
UK magician Chris Wardle developed a variation of the magic square in the video, which was posted last year over at Mark Farrar's site. If you mouse over the images, they'll automatically display their rotated versions.
Chris Wardle also created two other interesting magic squares here. Instead of using mirrors, however, these two magic squares rotate. The top one keeps the same total when rotated, and the bottom one changes.
To my mind, however, one of the most impressive mirrored magic square is Werner Miller's Square Bet magic square. This is a 2 by 4 grid that doesn't become a magic square until you hold a mirror up to it. When you do, you get a 4 by 4 square totaling 234 in every direction, even diagonally!
Considering that the creators not only had to take into account the totals, as with all magic squares, but the appearance of the numbers themselves, and how the new number would change in relation to each other, I find all of these to be very impressive!