kitchen table math, the sequel: James Tanton on quadratics

## Wednesday, April 20, 2011

I just interviewed Philip Keller, and he pointed me to James Tanton's website and books.

The prefix quad- means “four” and quadratic expressions are ones that involve
powers of x up to the second power (not the fourth power). So why are quadratic
equations associated with the number four?

A quadrangle has one side four units longer than the other. Its area is 60 square units. What are the dimensions of the quadrangle?

If we denote the length of one side of the quadrangle as x units, then the other must be x+4 units in length. We must solve the equation: x(x+4) = 6, which is equivalent to solving the quadratic equation x^2 + 4x - 60 = 0.

Solving quadratic equations, even if not derived from a quadrangle problem, still
involves the geometry of four-sided shapes. As we shall see, all such equations can
be solved by a process of “completing the square.”

#### 1 comment:

Catherine Johnson said...

Tanton defines a fraction as an "answer to a division problem."

I prefer "a fraction is a number."