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Monday, April 6, 2009

Imaginary Numbers

Quick: What is an imaginary number?

Oh, sure, you could cheat and use Wikipedia, or--even better--Simple Wikipedia. But do you recall the definition of an imaginary number from your Algebra class (or, at least, Calvin and Hobbes)?

An imaginary number is the square root of a negative number (which, since a negative number times a negative number is always positive, is impossible). But imaginary numbers are very helpful when you're solving for an equation and you find you need to get the square root of both sides of an equation and one of them happens to be negative:

Solve for x:
x2 = -72

If you're still reading, I guess you either find math fascinating--as I do--or you trust me to get to some kind of point worth suffering through the horror of math. Or, you've been skimming and not really paying attention.

If you're no longer reading, I'm glad you at least stopped by. <smile>

I must admit that I still get a little woozy and sick to my stomach when someone asks me how many purple beads are in the pile if 3/4 of them are red, 25% of the rest are black, 14 are white, and x orange beads were given to Bobby last Saturday when Susie took 1/18 of the total for a lemonade stand where she sells a glass of juice from concentrate for $4.13, and ice is another 7% if you want it on Thursdays.

Cherish has a very interesting post on our aversion to math which is often linked to school teachers.
[Edit: Sorry, I forgot to add my "mild profanity" disclaimer.]

I'm not sure if my dad helped give me an interest in math by insisting that he show why 34-17=17; I certainly didn't appreciate it at the time because I just wanted the answer. But his patient--and infuriating--demonstrations of how math really makes sense have helped me.

I hope I can do the same for my children with a few less tears.

Hmm... I guess today was a Math Monday.

 ~Luke Holzmann
Filmmaker, Writer, Expectant Father


Unknown said...

And when the teacher started talking about imaginary numbers, I went off into the imaginary world in my head...

Melonie said...

You know, I didn't expect a REAL math post on this one. When I read the title on Blogger I figured it was going to be about the "money" involved with the bailouts.

Um. Oops.

I don't even remember the term "imaginary numbers" being used in my math classes. Guess that tells you how long it's been since I was in a math class...even in college. (Did I just make myself really old?)

chapman55k said...

I am a math guy (I do it for a living), but my love for math goes back to one teacher who had a gift for making it exciting. I have talked about this with a lot of people and am amazed at how the "charisma" of the math teacher often had as much to do with a mathematician's love for the subject as the math itself.

Luke Holzmann said...

Jessica, you're hilarious! <smile>

Melonie, I didn't even have to do math in college, so it's been a long while for me as well. And, honestly, I'd be hard pressed to remember much of what I learned. So, sure, you may be old, but we're all heading that way more and more every day. <smile>

Ken, I really liked your followup post. And that video cracks me up. Glad you got a kick out of it too <smile>.


Rosslyn said...

Luke, thanks for the post.

After reading the article you linked, I have only one addition (heh heh) to the author's comments. Mental math is important, but calculation gets a bum rap, especially in the lower grades.

I'm no expert, but I remember what I liked about calculation when I was little. Kids like to be good at stuff and to get stuff right. Calculation is easy. So if a student gets plenty of positive reinforcement, "drill and kill" can become "drill and thrill." This is harder for classroom teachers because they don't have time to "ooh" over every correct addition worksheet. We homeschoolers have that luxury.

I'm also very conscious of the female aversion to math, so I'm trying to make sure my daughter develops a positive attitude.

Luke Holzmann said...

Rosslyn, that is an excellent point. I wonder how many other subjects are driven out of us because we simply don't experience enough encouragement and praise.


Anonymous said...

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Luke Holzmann said...

Lisa, may your adventures in math continue to be a joy <smile>.


MamaGeph said...

I am struggling through a college algebra class, and all I have to say is: BLEGH! I want to retreat into my nice, cozy lit bubble.

Luke Holzmann said...

MamaGeph, hang in there! I know it can be overwhelming at times.



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