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In mathematics, quadratic means "involving the second and no higher power of an unknown quantity or variable". But the prefix quad- usually describes something that has to do with four, such as quad-core processor, quadrilateral. Why does quadratic describe the second power while quad usually describes "four"?

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28  
Quadratic comes from "quad" meaning square; when you raise something to the second power, you square it. –  medica Feb 11 at 11:40
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@NateEldredge ... or, at least in the case of mathematics, quartic. I can't say I've ever actually heard the word "quadric." –  iamnotmaynard Feb 11 at 16:18
    
@iamnotmaynard: You're right, of course. Brain failure. (Quadric is actually a second-power thing again.) –  Nate Eldredge Feb 11 at 16:24

3 Answers 3

up vote 94 down vote accepted

Because the second power is a square, and a square has four sides. In fact the word square itself comes from quad-, too.

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I like the sound of "squaratic equation," come to think of it. –  Blazemonger Feb 13 at 19:35

Because quadratus is the Latin for "square" due to there being four sides on a square.

The second power of a number is called its square because if we have an integer, and construct a square with that number of items on each side, the total number will be its second power. E.g. a 4×4 square having 16 items:

* * * *
* * * *
* * * *
* * * *

It is also the case that the area of a square with a real number length side, can be measured in terms of the square of that number.

Related language trivia: In the middle of the 16th century, while squared was being used in this sense by some, it had yet to become current, and there was a brief use of zenzic, which means the same thing (via a Latinised, Germanicised, Italian translation from Arabic; it's a convoluted etymology). This form was productive so zenzizenzic meant the 4th power (squared square), zenzicube the 6th (squared cube) and for the 8th power we have zenzizenzizenzic, which is often claimed as the English word with the most Zs in it. It's a doubtful claim though, first there's nothing stopping us from using zenzizenzizenzizenzic to have even more, and second there seems to be about nobody using it any later than 1560 other than in sentences containing the phrase "has the most Zs".

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While the accepted answer got there first, you explain the rationale more clearly. Also, the discussion of zenzic is charming. I once had a math professor who wrote that on the board and asked for speculations on its mathematical meaning. Not one of us guessed it correctly. –  Jonathan Van Matre Feb 11 at 19:52
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All I can think about reading this post is Scrabble. –  emragins Feb 11 at 20:51
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@emragins you wouldn't be the first, but since there's only one z and two blanks, the word is impossible. –  Jon Hanna Feb 11 at 21:03
    
I'm very bad with math. if we have an integer, and construct a square with that number of items on each side, the total number will be its second power. I don't get how this works. If I have a square and each side is the number 2, the total is 8, not 2^2 = 4. If I have a square and each side is the number 3, the total is 12, not 3^2 = 9. How exactly does that number of items on each side get applied? –  teylyn Feb 12 at 0:17
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@teylyn added a diagram to the answer to show what I meant. –  Jon Hanna Feb 12 at 0:20

Quadri-, quadru-, quadr- is a Latin prefix related to the verb quadrare ‘to make square’, quadratus ‘square’ etc. Quad is simply an English shortening of quadrangle, quadruplet etc. So quadri- and quad are actually the same word.

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Well, strictly it comes from making an adjective out of the obsolete English quadrate, that's directly from the Latin quadratus; there was no shortening to quad. –  Jon Hanna Feb 11 at 17:32
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Yes, quad is originally a shortening of the typographic term quadrat (not quadrate). –  fdb Feb 11 at 17:49
    
Quad is found in several different senses which are each shortenings of various cognates. None of them influenced quadratic though, which is < English quadrate < Latin quadratus. –  Jon Hanna Feb 11 at 17:51
    
Ah, you were addressing the other statement in the question. My mistake. –  Jon Hanna Feb 11 at 19:51

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