Excerpt from
"One is one and all is one and evermore shall be so."
I was once preparing a large group of students for the math section of the Graduate Record Exam, an exam taken by college graduates before they apply for graduate school. The following problem was on the sample test:
Many students threw up their hands, some tried muscling through it by hand or with a calculator. Only a couple of students saw right through the problem. Only they had the privilege of being taught, or understanding on their own, the concept of one. I hope that by the end of this chapter, you will join their ranks.
If you understand, truly understand, the number one, you will have a remarkable amount of math at your fingertips. The number one, in one of its infinite variety of forms, is at the root of the solution to an enormous number of math problems, including the one above. To find out what you understand now about the number one, let's start with The Singular Test.
An Exercise from MMMM
An important theme, the difference of squares, comes up in algebra in several contexts. For example, students may have to factor an equation that is the difference of squares, or rationalize a denominator of a fraction containing a radical or an imaginary number. Rarely has the basis for the method been planted in number form. This is based on MMMM's Day Four lesson that includes an exploration of perfect squares.
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