# Gotta love it!!!!

Discussion in 'General Education' started by Aliceacc, Oct 3, 2012.

1. ### AliceaccMultitudinous

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Oct 3, 2012

Yesterday in my Geometry classes, we came across our first quadratic equation of the year. I mentioned that I had no idea why quadratics (which have a variable to the second power) have that name, since "quad" normally means "4." And that someday, when I'm online and bored, I was going to look it up.

Dear Mrs. Aliceacc,
I was bored while on the Internet and decided to look this up. The Website I recieved the information on is
located below though the spaces need to be removed:
Web Site: http:// mathforum. org/library/drmath/view/52572.html

Date: 05/22/99 at 20:40:32
From: Doctor Peterson
Subject: Re: Why is an equation having only two roots, one of which is
raised to 2, called a "quadratic equation"?

second power, not the fourth. But there's another dimension to the
word.

means a square (because it has four sides) and "quadratus" means
"squared." We get several other words from this: "quadrille," meaning
a square dance; "quadrature," meaning constructing a square of a
certain area; and even "square" (through French).

Quadratic equations originally came up in connection with geometric
problems involving squares, and of course the second power is also
called a "square," which accounts for the name. The third-degree
equation is similarly called a "cubic," based on the shape of a third
power. Then when higher-degree equations began to be studied, the
names for them were formed differently, based on degree rather than
shape (since the Romans had no words for higher-dimensional shapes),
giving us the quartic, quintic, and so on. In fact, quartic came
along later; originally a fourth degree equation was called
"biquadratic," meaning "doubly squared," which mixes the two concepts
and is doubly confusing.

So here's a table of names for polynomials and their sources:

degree name shape dimension
------ --------- ------ ---------
1 linear line (1)
3 cubic cube (3)
4 quartic - 4
5 quintic - 5

I don't really care much about the answer. But I LOVE that one of my kids did care enough to find out!

3. ### MrsCMultitudinous

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Oct 3, 2012

The explanation makes no sense to my non-math brain, but I love the initiative and curiousity!

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Oct 3, 2012

Made my day! What a great kid, and I think I learned something!

5. ### moparMultitudinous

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Oct 3, 2012

That shows some extra from this child. They definitely went out of their way to find something out for you!

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Oct 3, 2012

Nice.

7. ### smalltowngalMultitudinous

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Oct 3, 2012

That's awesome, Alice!

8. ### TeacherGroupieModerator

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Oct 3, 2012

So cool that the student was motivated to look it up!

I think math etymologies are fun, but then I'm a word geek.

9. ### MikeTeachesMathDevotee

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Oct 3, 2012

I've been asking myself that question for years but I guess the curiosity never lasted past math class :lol:. Now I know!

10. ### Bored of EdEnthusiast

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Oct 3, 2012

That's pretty much what I always assumed, but the YAY factor is that the student got all into it! YAY!

11. ### applecoreDevotee

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Oct 3, 2012

Extra credit for this student!

12. ### AliceaccMultitudinous

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Oct 3, 2012

Nope, I don't do extra credit. All the more reason to give her a shout out tomorrow though (I tested all day today)-- because she did it simply because she was curious, not for extra credit.

13. ### TeacherGroupieModerator

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Oct 3, 2012

That's not extra credit?

14. ### yarnwomanCohort

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Oct 3, 2012

AWESOME! I love it when students do this!

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Oct 4, 2012

Good point.

16. ### paperlabsRookie

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Nov 2, 2012

I've thought about it just a little and just assumed that multiplying two binomials gives a quadratic. Just as 2x2=4, binomial times binomial equals quadratic. Most math we do with quadratics is based on multiplication (isn't it?) so I didn't think in terms of any other operation such as add or subtract. Since it doesn't seem like anything important, why would I think further?

17. ### cutNglueMagnifico

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Nov 2, 2012

I love it when students are curious enough to go on their own and look up answers but I love it even more that they recognize that adults not only don't know everything but also express this need to satisfy their own curiosity by continuing to learn new information.

The expression of appreciation is worth far more than any points could muster.

18. ### AliceaccMultitudinous

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Nov 3, 2012

Because that's not true.

It becomes a quadratic if you multiply x to the first by x to the first, getting x squared (or x "to the second power" )as a result.

If your binomials are (x ^2 - 5) and (x ^ 2 +7), you're not getting a quadratic, you're getting a 4th degree equation as the product. If they're (x^2 -4) and (x + 6) you're getting a cubic. (x^6 +3) ( x-1) will give you a 7th degree product, and so on. Likewise, you could multiply a monomial by a quadratic and get another quadratic: 4(x^2 - 3x + 2) will give you a quadratic.

It's not about the number of terms you're multiplying, it's about the highest power of the variable contained in each.

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Nov 3, 2012

Good for you for keeping your student so interested!!!!

20. ### pwhatleyMaven

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Nov 3, 2012

I think all word etymologies are fun! I love the history of words, phrases, and sayings, and would love to do a dissertation on "old wive's tale and their origins."

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