The area of a square is just double its side.
We have:\[\rm x^2 = 2x\]so\[x^2 - 2x = 0\]\[x(x - 2) = 0\]The solutions are 0 and 2, but is it possible to have a square with 0 as its side?

- ParthKohli

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- TuringTest

not really. Some mathematicians have called such objects "degenerate" squares, but you can exclude those kinds of answers when they pertain to physical objects.

- TuringTest

I remember myin's "degenerate circle" question :)

- myininaya

That reminds me of a question I asked about circles.
Can a "circle" with radius zero still be considered a circle?
(x-h)^2+(y-k)^2=r^2
(x-h)^2+(y-k)^2=0
So in other words, can a single point on a graph be seen as a circle with radius 0.

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## More answers

- myininaya

lol. We were thinking the same thing.

- TuringTest

Yes, I borrowed Zarkon's answer because I liked it :)

- ParthKohli

Hmm...

- anonymous

whom are you calling a degenerate?

- ParthKohli

If a point has 0 area, then the point doesn't cover any area... but a point still covers *some* area right?

- ParthKohli

Like infinitesimal, but still, I don't agree with the point that a point has zero area. :p

- ParthKohli

It's not a fair point.

- ParthKohli

Yello.

- jiteshmeghwal9

i don't gt why
\(x^2=2x\)
@ParthKohli

- UnkleRhaukus

a square has two dimensions

- jiteshmeghwal9

I have studied something like that
\(x^2=x \times x\)
\(2x=x+x\)

- ParthKohli

@jiteshmeghwal9 See the top-line of my question.

- TuringTest

a point has no are as it is zero-dimensional, and squares (at least non-degenerate ones) require two dimensions as @UnkleRhaukus said

- TuringTest

no area*

- jiteshmeghwal9

Ohh ! im so stupid i gt it Okay :)

- ParthKohli

So 0 is not a solution for \(x\)?

- TuringTest

in the purely mathematical sense, I would say "yes it is a solution", but as a "square" in the normal sense of the word, or as a physical object, the answer would be "no".

- UnkleRhaukus

if a side length is zero it is not a square

- ParthKohli

Okay, I'm talking about this question.
So, yes, 0 is not an answer to the word problem?

- TuringTest

@UnkleRhaukus @Zarkon termed such objects "degenerate".
I think this is a sketchy question, they should have included the condition that \(x>0\) to avoid the subtleties in the philosophical mathematical implications of a zero-by-zero square.

- UnkleRhaukus

yes zero is not an answer to word problem, however it does solve the equation

- ParthKohli

Math is so idiotic.

- ParthKohli

lol. :)

- UnkleRhaukus

maths is a tool,

- TuringTest

True.^
Professional mathematicians throw out useless concepts just because they are such. They also make their own theorems and definitions depending on what they feel is called for in a given situation. For example, many great mathematicians have \(defined\) \(0^0=1\)
there is no objective mathematical proof of this, but sometimes it is convenient to do such things. These guys just make it up as they go along basically :P

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