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## ParthKohli 3 years ago 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?

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1. 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.

2. TuringTest

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

3. 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.

4. myininaya

lol. We were thinking the same thing.

5. TuringTest

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

6. ParthKohli

Hmm...

7. anonymous

whom are you calling a degenerate?

8. ParthKohli

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

9. ParthKohli

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

10. ParthKohli

It's not a fair point.

11. ParthKohli

Yello.

12. jiteshmeghwal9

i don't gt why $$x^2=2x$$ @ParthKohli

13. UnkleRhaukus

a square has two dimensions

14. jiteshmeghwal9

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

15. ParthKohli

@jiteshmeghwal9 See the top-line of my question.

16. TuringTest

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

17. TuringTest

no area*

18. jiteshmeghwal9

Ohh ! im so stupid i gt it Okay :)

19. ParthKohli

So 0 is not a solution for $$x$$?

20. 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".

21. UnkleRhaukus

if a side length is zero it is not a square

22. ParthKohli

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

23. 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.

24. UnkleRhaukus

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

25. ParthKohli

Math is so idiotic.

26. ParthKohli

lol. :)

27. UnkleRhaukus

maths is a tool,

28. 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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