4x4 Balance (Leaning Tower of Lire)
Brief Description
The Leaning Tower of Lire is a tower of blocks arranged in such a way to maximize the amount of overhang of the top block. Any stackable item will work, but here 4x4’s are used. The tower is made so that for a given block, the center of mass of all the blocks above it is right at the edge of that block. The amount of overhang achieved can be calculated by the series 
where l is the length of each block and n is the number of blocks.
Materials
8 4x4’s
Performing the Demo
To make the tower, stack all the 2 foot 4x4’s straight up. Then move the top block so that half of it is hanging over the edge. Then move the second one from the top so one fourth of it is hanging over the edge. Keep doing this for all the 4x4’s. Starting at the top, the amount that each block hangs over the one below it goes as follows: 12”, 6”, 4”, 3”, 2.4”, 2”, 1.7”, and 1.5”. The blocks are not perfectly uniform, so they will need a little bit more room. When placing the blocks, make sure that the sides on the top and bottom are as smooth as possible. If there are large chips in the wood, try to place it so they are faced towards the side.
Safety and Other Notes
Be careful not to drop any 4x4’s on anybody’s toes. To change up the demo you can also twist each block about the edge of the block beneath it. To do this, start from the top and hold down the block below the one you are rotating. Then, slowly push the end of the block and it will naturally rotate about the center of mass.
