ParthKohli
  • ParthKohli
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?
Mathematics
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SOLVED
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katieb
  • katieb
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TuringTest
  • 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
  • TuringTest
I remember myin's "degenerate circle" question :)
myininaya
  • 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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myininaya
  • myininaya
lol. We were thinking the same thing.
TuringTest
  • TuringTest
Yes, I borrowed Zarkon's answer because I liked it :)
ParthKohli
  • ParthKohli
Hmm...
anonymous
  • anonymous
whom are you calling a degenerate?
ParthKohli
  • ParthKohli
If a point has 0 area, then the point doesn't cover any area... but a point still covers *some* area right?
ParthKohli
  • ParthKohli
Like infinitesimal, but still, I don't agree with the point that a point has zero area. :p
ParthKohli
  • ParthKohli
It's not a fair point.
ParthKohli
  • ParthKohli
Yello.
jiteshmeghwal9
  • jiteshmeghwal9
i don't gt why \(x^2=2x\) @ParthKohli
UnkleRhaukus
  • UnkleRhaukus
a square has two dimensions
jiteshmeghwal9
  • jiteshmeghwal9
I have studied something like that \(x^2=x \times x\) \(2x=x+x\)
ParthKohli
  • ParthKohli
@jiteshmeghwal9 See the top-line of my question.
TuringTest
  • 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
  • TuringTest
no area*
jiteshmeghwal9
  • jiteshmeghwal9
Ohh ! im so stupid i gt it Okay :)
ParthKohli
  • ParthKohli
So 0 is not a solution for \(x\)?
TuringTest
  • 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
  • UnkleRhaukus
if a side length is zero it is not a square
ParthKohli
  • ParthKohli
Okay, I'm talking about this question. So, yes, 0 is not an answer to the word problem?
TuringTest
  • 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
  • UnkleRhaukus
yes zero is not an answer to word problem, however it does solve the equation
ParthKohli
  • ParthKohli
Math is so idiotic.
ParthKohli
  • ParthKohli
lol. :)
UnkleRhaukus
  • UnkleRhaukus
maths is a tool,
TuringTest
  • 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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