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16cm squared or 16 square cm?

Warewullf

17:49 / 24.08.03

Ok, I need help settling an arguement between two friends.

Is 16 centimeters squared the same as 16 square centimeters?

Friend A says that 16cm squared is a shape 4cm x 4cm and means the same thing as 16 square cm.

Friend B says that 16cm squared is a shape that's 16cm x 16cm and
16 squared centimeters is 4cm x 4cm

Now, I have the mental arithmetic ability of a month-old yogurt so if this is all horrendesly obvious, I hope you'll indulge me.

w1rebaby

19:03 / 24.08.03

Um. I don't think there is a definitive answer. "Sixteen centimetres squared" sounds, to me, like "sixteen centimetres, squared" i.e. you take a 16cm length and make it into a square 16 centimetres on each side.

But if it's the result of reading out "16 cm2" then it would be a square 4cm x 4cm.

I'd go with the latter since the former is basically me being odd about language.

Warewullf

19:09 / 24.08.03

But is that the same as 16 squared centimeters?

Perfect Tommy

02:15 / 25.08.03

See, I've heard '16cm square' before, which would be a 4x4 square as you say. I've never heard '16cm squared', which to my ears sounds like 'squared' is a verb instructing you to take 16cm and square it.

Now, if you took a single centimeter, and squared it, you'd have a 1x1 square, right? So if you had 16 of those squares, you'd have the 4x4 again.

*blink*

I think this is may be a linguistic rather than mathematical problem...

We're The Great Old Ones Now

08:05 / 25.08.03

'Sixteen square centimetres' is a four by four square - or a two by eight rectangle, or a one by sixteen strip, or some fiendish combination of fractions which yields an area totalling the eqivalent of sixteen one centimetre by one centimetre squares.

'Sixteen centimetres square' is a sixteen by sixteen square.

'Sixteen centimetres squared' would imply a line sixteen centimetres long which is then 'squared' - i.e. matched by three other lines of equal length making a square.

Friend A is full of shit. Ask a maths teacher.

Lurid Archive

12:14 / 25.08.03

I'll confess that I don't have a clue. But...I'm curious as to how people pronounce 16 cm^2 and how A or B reconcile whatever meaning they decide on with the sentence "The area of this circle is 16cm^2."

Point is, I would never use "square(d) centimeters" or "centimeter
square(d)" to mean anything other than cm^2. Keep it simple, I say.

Perfect Tommy

13:01 / 25.08.03

Sam's right on the 16 cm square being 16cm on a side... I wasn't thinking.

aus

13:52 / 25.08.03

I can remember this discussion from maths (I can remember 25 years ago, but I can't remember yesterday) and friend B is correct.

Warewullf

21:15 / 26.08.03

Ok, to clear up the pronounciation, Friend A says that:

16CM2 is pronounced "sixteen centimetres squared" and is the same as sixteen square centimetres. (eg, a shape that's 4x4)

Sixteen centimetres square is a shape that's 16x16

My head hurts.....

Warewullf

21:46 / 26.08.03

Just found this on a forum:

Q: Does a square with sides of 10m have an area of 10m squared or 100 square metres? Or are these the same?

A: To answer this one, remember that square meters and meters squared are two ways to say the same thing.
If you have a square that measures 5 m on each side, its area is:

(5 m) * (5 m) = 25 m^2

which you can say as, "25 square meters" or "25 meters squared."

-Doctors Celko and Doctor Sonya, www.mathforum.org

Lurid Archive

09:24 / 27.08.03

which just goes to show that fridge was, as always, talking a lot of sense. I do think this is the sort of thing that makes maths boring, though I do realise that some people need to have an answer.

And the answer should be that a convention is by its nature arbitrary and that you should adopt one that suits your (current) needs. Having said that, coneventions are supposed to make your life easier, not harder. So, having a convention where misplacing a single letter entirely changes meaning seems unwise to me.

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