Squared is to 2, as ____ is to 3 (details).

Cubed

@filmfann Thank you!!! That’s what I said but my mom argued it with me. Now I have verification that I’m right.

Agreed: cubed.

Squared is to 2 as cubed is to 3. This translates into square feet and cubic feet.

Yep, cubed. Squared is two dimensions, hight and width. Cubed is three dimensions, hight, width and depth.

Can I laugh? No? Okay, sorry. Ahem, cubed.

So what did your mother think it was?

The answer is cubed, as already established, but may I now ask:

Cubed is to three as ___ is to four?

Quartic.

@Luiveton What would that be in the ”-ed” form, I wonder? Cubic -> cubed, so quartic -> quarted?

2: Square/squared
3: Cubic/cubed
4: Tesseractic/tesseracted
5: Surfolidic/surfolided

@SavoirFaire 16th century terminology? The only reference I can find to surfolidicism is from Robert Recorde. I call it Penteractic so I can scale upwards, see: http://en.wikipedia.org/wiki/Hypercube

Yeah, “penteract” is fine. It’s also more useful in the long run. I just think that “surfolidic” sounds cooler.

@cazzie to be didactic, squaring leads to areas and cubing to volumes only when the original quantity has a unit of length associated with it. Taking x^n where x is a dimensionless (“pure”) number will yield another dimensionless number. If the quantity does have a unit associated with that is not a length one needs to remember to apply the exponent to that unit as well, be it electric charge or whatever.

I recall being told once that the ancient Greeks insisted on geometric interpretations for what we now express as algebraic equations and that this had the effect of preventing them from developing algebra much further than they did.

@SavoirFaire and @Zyx, that is interesting, I’ve never heard of that term before either.

Well, I live in the real world with space and volume, not a hypothetical world, and I use metrics because they relate better to the real world. I craft, I don’t do theoretical math.

@cazzie the second point I had to make actually is quite crucial beyond the realm of purely abstract mathematics (that about units other than length). Physics, chemistry and engineering will require the solution of equations involving various quantities other than just length as well as the conversion of quantities from one set of units to another. It’s easy to get things mixed up in the course of these computations and one of the most important checks is to make sure the final quantity you end up with is expressed in the right units. I can recall one engineering professor of mine in grad school bemoaning the fact that his undergraduate students didn’t appear to recognize the importance of this. (He also lamented that they wouldn’t appear to be troubled by being many orders of magnitude off; that they had no feel for what a reasonable order of magnitude for a solution would be in given situation, but that’s another issue.)

(And for the first point in my previous post, well I did say I was being didactic.) ;-)

Eeek. You share sad news. Being off by powers of 10 is rather something I would be worried about as well as being sure to write whether I was working in inches or centimeters, cubic feet or cubic meters. As I mentioned, I work in the real world and if I get these things wrong, I could hurt myself or others rather seriously.

@wundayatta I’m not particularly sure what she thought it was, something along the lines of tried?

Cubed. When squaring a number, you simply multiply it by itself twice. When cubing you multiply it by itself three times and so on.