On: BetterExplained: Math Lessons That Explain Concept...

[darkerside]

From: http://betterexplained.com/static/articles/rethinking-arithm...

1 * x^2 = 9

"What transformation (“times x”), when applied twice, will turn 1 into 9?"

That's such a great way of thinking about algebra. The "understood" 1 is equivalent to, e.g., an understood "YOU" in the English language.

[kalid → darkerside]

Beautiful way to put it! We aren't always explicit about the subject of the transformation. Similarly, when working with exponents, I think:

e^ix

is really

1 * e^ix

That is, we're starting with 1.0 and doing a transformation (rotation) on it.