secrets-of-mental-math-malestrom

Chapter 3
New and Improved Products:
Intermediate Multiplication
Mathemagics really gets exciting when you perform in front of
an audience. I experienced my first public performance in eighth
grade, at the fairly advanced age of thirteen. Many mathemagicians
begin even earlier. Zerah Colburn (1804–1839), for example,
reportedly could do lightning calculations before he could
read or write, and he was entertaining audiences by the age of
six! When I was thirteen, my algebra teacher did a problem on
the board for which the answer was 108 2 . Not content to stop
there, I blurted out, “108 squared is simply 11,664!”
The teacher did the calculation on the board and arrived at
the same answer. Looking a bit startled, she said, “Yes, that’s
right. How did you do it?” So I told her, “I went down 8 to 100
and up 8 to 116. I then multiplied 116 100, which is 11,600,
and just added the square of 8, to get 11,664.”
She had never seen that method before. I was thrilled.
Thoughts of “Benjamin’s Theorem” popped into my head. I actually
believed I had discovered something new. When I finally
ran across this method a few years later in a book by Martin