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. I just received this email: 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"? People often wonder about the word "quadratic," because they know that "quad" usually means "four," yet quadratic equations involve the second power, not the fourth. But there's another dimension to the word. Although in Latin the prefix "quadri" means four, the word "quadrus" 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) 2 quadratic square (2) 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!

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

So cool that the student was motivated to look it up! I think math etymologies are fun, but then I'm a word geek.

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

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

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.

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?

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.

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.

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."

Alice, all the math stuff is confusing me. But it is remarkable that your student took the initiative to research the question with your asking.