(Do you know any math poems?)

**Imaginary Numbers Do the Trick**

by Sue VanHattum

(written on December 15, 2008)

In an email group of 4,000 homeschoolers,

a member wrote:

My son asks, “The square root of 1 is 1,

So what's the square root of -1 ?”

This was my reply to her…

What we call the real numbers

is everything on a number line,

positive, negative, zero.

If you're thinking about those real numbers,

on that number line,

none of the negative numbers can have a square root,

because anything times itself will come up positive

(or zero).

But, once upon a time (for real),

mathematicians dueled

by giving each other lists of thirty hard problems.

The winner got recognition

and perhaps a job.

All this dueling led to

a solution for cubic equations:

these mathematicians

created a formula

that would find the numbers

that would solve a thing

like 2x3-3x2+4x-5 = 0.

But that formula was a problem!

It came up with square roots of negative numbers,

which drove the mathematicians wild.

No, no, no. There is no such thing!

Well, maybe there could be…

and if there is,

what would it look like?

With a wave of the magic wand of imagination,

These mathematicians

made up a new number,

which later got the name i.

(Imagine it written in fancy script.)

i is the square root of -1,

so i squared must equal -1.

i is the first step in creating …

the imaginary numbers.

Picture, if you will, a new number line

of imaginaries

crossing the line of real numbers at 0,

with the real number line horizontal,

and this new one vertical.

(It looks just like x and y axes,

but now it's all one number system,

a bit more complex.)

i sits one step above zero.

Another step up this imaginary number line,

we see 2i,

2i is the square root of -4.

(It is?!

Why yes, 2i times 2i equals 4 times i squared,

and i squared equals -1,

so we get -4.

Cool, huh?)

And on it goes.

Now all of this wouldn't really solve much

if there were no square root of i,

and that seems too weird to think about.

But, once you study trigonometry

(how'd that get in here?!),

the solution to that little problem

is actually quite elegant.

I love the perspective! It's cool to see a math person who sees the poetry in numbers.

ReplyDeleteyou know about T.C. Mits?

ReplyDeleteYes, and I love it! (Or were you asking John?)

ReplyDeleteLillian Lieber, the author of

The Education of TC MITS, wrote another book I'm looking forward to reading,Infinity.