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"quadratic" - 4 of what?

"quadratic" - 4 of what?

"quadratic" - 4 of what?

(OP)
The meaning of the terms quadratic polynomial (Ax^2+Bx+C) and quadratic equation (Ax^2+Bx+C=0) are well known.

Why the root word "quad"? 4 of what?

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RE: "quadratic" - 4 of what?


From Latin, quadratus = square, pp. of quadrare = to square. It is related to quattuor "four".

RE: "quadratic" - 4 of what?

(OP)
I can see the connection.

It brings to mind another question. How did the term "square" come to describe x^2

(because the area of a square is the second power of it's length?)

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RE: "quadratic" - 4 of what?

(OP)
I think by also considering the term cube, the area interpretation must be right.

area of square is L^2
  hence the term quadratic equation
volume of cube is L^3
  hence the term cubic equation

Still kind of bizarre that we use the term "quad" to refer to a square when the aspect of that square we are referring to is the A=L^2 aspect.

Thx. You solved the mystery. No I can look smart in front of my kids (I'll tell 'em I knew it all along).

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RE: "quadratic" - 4 of what?

(OP)
If we wanted to apply same logic to a cubic polynomial, we should describe it by the number of sides of a cube.. something like a duodecatic polynomial?

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RE: "quadratic" - 4 of what?

Or perhaps hexahedratic... (six sides).

BTW, polynomials of a higher degree are named: quartic, quintic, sextic, septic(!), octic, and so on, n-tic polynomials....

RE: "quadratic" - 4 of what?

(OP)
Oh yeah, a cube has six sides. I was thinking of the number of line segments in a cube... 12. Either way I don't think cubic will be replaced in the near future.

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RE: "quadratic" - 4 of what?

It doesn't matter me as long as I split any polynimial into no. of squares and cubeswink. For x5, I would first construct a square of x and I will cube the x2 etc. Let us see if the quantum mechanics makes the physical interpretation easy with those all extra dimensions.

Here is a good paper for the physical interpretation of the polynomials including imaginary numbers. The mind boggling logic by Gauss is worth reading.

http://www.larouchepub.com/eiw/public/2002-18/bruce1/gauss1.html

RE: "quadratic" - 4 of what?

The term quad comes from quadrangle

RE: "quadratic" - 4 of what?

I like 25362's explanation better:
   From Latin, quadratus = square, pp. of quadrare = to square. It is related to quattuor "four".

RE: "quadratic" - 4 of what?

I like 25362's explanation better too. Any explanation with latin just totally befuddles me, so I believe it more!!! winky smile

"Do not worry about your problems with mathematics, I assure you mine are far greater."   
Albert Einstein
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