Recently i saw a proof that perfect squares dont exist,but i dint ubderstand that.can anyone please help me?
2006-10-20 21:50:46 · 14 answers · asked by Red Falcon 1 in Science & Mathematics ➔ Mathematics
here is proof....Proof : Suppose that n is a perfect square. Look at the odd divisors of n.
They all divide the largest of them, which is itself a square, say d^2.
This shows that the odd divisors of n come in pairs a, b, where ab = d^2.
Only d is paired to itself.Therefore the number of odd divisors of n is odd.
This implies that the sum of all divisors of n is also odd. In particular, it is not 2n.
Hence n is not perfect, a contradiction : Perfect squares don´t exist. QED.
2006-10-20 22:01:36 · update #1
of course they exist. perfect squares are essentially numbers that made of the product of another number with itlself
2006-10-20 21:53:33 · answer #1 · answered by Sayan 2 · 0⤊ 0⤋
Actually it is and it isn't. Imagine you had a square that was a 2 X 2. Well we know that squares are made of two triangles. What we use the Pythagorean theorem and calculate the hypotenuses? We would get the equation of 2^2 + 2^2 = c^2. So we get 4 + 4 = c^2. 8 = c^2 and the square root of 8 is irrational. You can not make an irrational line so therefore squares do exist ,but it is impossible to make or draw a perfect square.
2014-04-27 07:06:12 · answer #2 · answered by Anonymous · 1⤊ 0⤋
Perfect squares do exist and are quite common. They are simply whole numbers (integers) that are the squares of another.
eg = 9 and 25 are perfect squares of 3 and 5, respectively.
9 = 3 x 3, 25 = 5 x 5
Any arguments that prove the nonexistence of a perfect square have to have some kind of logical fallacy... Now, I'm no mathmetician logician, but let me give a go debunking the one you quoted... It says (paraphrasing):
"This implies that the sum of all divisors" ... "is not 2n. Hence n is not perfect"
So, first I have to ask - where is it ever stated that a the sum of all divisors of a perfect square has to be 2n? That's not a part of any definition I've ever read! :) That last argument is based on some other facts or conclusions that weren't part of the proof.
2006-10-20 21:59:49 · answer #3 · answered by Gelondil 1 · 0⤊ 0⤋
There seems to be a lot of confusion in the posted answers.
What Red Falcon is asking is : Can a square be a
perfect number? A perfect number n is one for which
the sum of its positive divisors is 2n. Example: 28. If you
add all the positive divisors of 28(including 28) you will get 56.
Red Falcon, what is there about the proof that you
don't follow? The implication in the last statement
follows from the fact that a square has an odd
number of divisors.
2006-10-21 03:48:57 · answer #4 · answered by steiner1745 7 · 0⤊ 0⤋
YES, there are perfect squares although I am unable to explain the maths side of things as uneducated I can show it visually, and believe I have many times in my 360
2006-10-21 00:44:26 · answer #5 · answered by WW 5 · 0⤊ 0⤋
There is hardly a statement in your "proof" which is not self contradicting and together these statements constitute a series of non sequiturs. You may as well be saying there are sometimes five and sometimes less than three altogether.
2006-10-21 00:25:59 · answer #6 · answered by sydney m 2 · 0⤊ 0⤋
Yes, they do exist.
I studied mathematics and saw the proof that perfect squares they exist in one of my books.
2006-10-20 22:09:55 · answer #7 · answered by The Greek Guy 3 · 0⤊ 0⤋
it would be good to see the proof--I imagine it's highly advanced.
the proof that they do exist would depend on the arguments made in the counterproof you are talking about
2006-10-20 21:59:16 · answer #8 · answered by center of the universe 4 · 0⤊ 0⤋
Interesting proof, would have to see it to say for sure. i have seen a proof that parallel lines do eventually meet... strange but true!
2006-10-20 21:55:38 · answer #9 · answered by Jaylaw 3 · 0⤊ 0⤋
Nothin perfect!
2006-10-20 22:04:11 · answer #10 · answered by Anonymous · 0⤊ 0⤋