Marquette University

We saw before that without carefully proving theorems, we may occasionally run into paradoxes. For example, we recently "showed" that 90 equal 89, and thus that 1 = 0.
In the book, on page 60, we cut an 8 by 8 square into four pieces, and then put the four pieces together as a 5 by 13 rectangle. Since 8 x 8 equals 64, and since 5 x 13 equals 65, we seem to create new area out of "nothing," contrary to what we feel is right.
In class we demonstrated the same idea as above, by cutting a 21 by 21 square into four pieces, and then re-assemble it as a 13 by 34 rectangle. Since 21 x 21 equals 441, and since 13 x 34 equals 442, we seem to create new area out of "nothing," contrary to what we feel is right.
In class we showed how to make a professor disappear, as in the pictures

Last updated: March 2006
Comments & suggestions: wimr@mscs.mu.edu