Mathematics
Re: Mathematics
Anyone have any cool problems they would like to share? I just did a pretty cool one, the proof is easy if you know how to start it but finding the right direction to start in may or may not take some time. I saw this problem before a few years ago and I had to look up the solution, but I tried solving it now again and found another way to do it:
If S can be expressed as the sum of two squares, show that 2S can be expressed as the sum of two squares, and show that 5S can be expressed as the sum of two squares (integers only ofc)
If S can be expressed as the sum of two squares, show that 2S can be expressed as the sum of two squares, and show that 5S can be expressed as the sum of two squares (integers only ofc)
last time i cryed was because i stood on Lego
Re: Mathematics
@Jerom
@GarjaJerom wrote:notification
hy isn't this thread showing in active threads? :(Garja wrote:notification
last time i cryed was because i stood on Lego
Re: Mathematics
Garja wrote:It's off-topic section. Site admin changed that recently.
Site admin as in divinefire? Is he still around? I haven't seen him post in months.
last time i cryed was because i stood on Lego
Re: Mathematics
ovi12 wrote:Anyone have any cool problems they would like to share? I just did a pretty cool one, the proof is easy if you know how to start it but finding the right direction to start in may or may not take some time. I saw this problem before a few years ago and I had to look up the solution, but I tried solving it now again and found another way to do it:
If S is the sum of two positive integers, show that 2S and 5S are the sum of 2 positive integers as well.
I think it's obvious they are sum of 2 positive integers. Maybe you mean something like odd or even?
Correlation doesn't mean causation.
http://www.tylervigen.com/spurious-correlations
"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
http://www.tylervigen.com/spurious-correlations
"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
Re: Mathematics
BrookG wrote:ovi12 wrote:Anyone have any cool problems they would like to share? I just did a pretty cool one, the proof is easy if you know how to start it but finding the right direction to start in may or may not take some time. I saw this problem before a few years ago and I had to look up the solution, but I tried solving it now again and found another way to do it:
If S is the sum of two positive integers, show that 2S and 5S are the sum of 2 positive integers as well.
I think it's obvious they are sum of 2 positive integers. Maybe you mean something like odd or even?
Lol wtf was i writing i meant squares. If S can be expressed as the sum of two squares, show that 2S can be expressed as the sum of two squares, and show that 5S can be expressed as the sum of two squares (integers only ofc)
last time i cryed was because i stood on Lego
Re: Mathematics
I think i meant to write "perfect square" but i wrote positive integer instead
last time i cryed was because i stood on Lego
Re: Mathematics
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Re: Mathematics
iNcog wrote:ovi12 wrote:Garja wrote:It's off-topic section. Site admin changed that recently.
Site admin as in divinefire? Is he still around? I haven't seen him post in months.
it's buckethead
not a bad thing either, can't have new people getting in on all those off topic shitposts lol
What happened to divine? Did he get fired?
last time i cryed was because i stood on Lego
Re: Mathematics
Divine is experiencing real life.
Re: Mathematics
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Reason: on request (off-topic bulk delete)
Re: Mathematics
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Reason: on request (off-topic bulk delete)
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- Jaeger
- Posts: 3107
- Joined: May 16, 2015
- ESO: Hyperactive Jam
Re: Mathematics
Best use of a crawlspace. https://www.youtube.com/watch?v=-k3mVnRlQLU
Re: Mathematics
iNcog wrote:fuck math
https://mathwithbaddrawings.com/2016/07 ... tatistics/
That's statistics not math.
Statistics is the science according to which, on average, every person on the planet has one testicle.
- howlingwolfpaw
- Jaeger
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Re: Mathematics
Dolan wrote:iNcog wrote:fuck math
https://mathwithbaddrawings.com/2016/07 ... tatistics/
That's statistics not math.
Statistics is the science according to which, on average, every person on the planet has one testicle.
So no MATH is used to determine statistics? Pretty sure you need too ADD all the number of people surveyed . Then SUBTRACT the difference of people with 1, zero or more testis, and then DIVIDE the 2 numbers to derive a PERCENT average. That's using math....
The science part is examining each patient to determine their physiology of numerical testis
Re: Mathematics
ovi12 wrote:BrookG wrote:ovi12 wrote:Anyone have any cool problems they would like to share? I just did a pretty cool one, the proof is easy if you know how to start it but finding the right direction to start in may or may not take some time. I saw this problem before a few years ago and I had to look up the solution, but I tried solving it now again and found another way to do it:
If S is the sum of two positive integers, show that 2S and 5S are the sum of 2 positive integers as well.
I think it's obvious they are sum of 2 positive integers. Maybe you mean something like odd or even?
Lol wtf was i writing i meant squares. If S can be expressed as the sum of two squares, show that 2S can be expressed as the sum of two squares, and show that 5S can be expressed as the sum of two squares (integers only ofc)
I thought about it and I have an issue. Say S=2, 2=1^2+1^2. 2S=4, it can't be expressed as an addition of perfect squares, haven't checked for subtraction.
Correlation doesn't mean causation.
http://www.tylervigen.com/spurious-correlations
"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
http://www.tylervigen.com/spurious-correlations
"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
Re: Mathematics
BrookG wrote:ovi12 wrote:Show hidden quotes
Lol wtf was i writing i meant squares. If S can be expressed as the sum of two squares, show that 2S can be expressed as the sum of two squares, and show that 5S can be expressed as the sum of two squares (integers only ofc)
I thought about it and I have an issue. Say S=2, 2=1^2+1^2. 2S=4, it can't be expressed as an addition of perfect squares, haven't checked for subtraction.
2^2+0^2. Addition is sufficient for any number
last time i cryed was because i stood on Lego
Re: Mathematics
@ovi12
(1) Diophantus' identity (a^2+b^2)*(c^2+d^2)=(ac-bd)^2+(ad-bc)^2
Say S=a^2+b^2.
From (1) 2S=(1^2+1^2)(a^2+b^2)=(a-b)^2+(a+b)^2
5S=((1^2)+(2^2))(a^2+b^2)=(a-2b)^2+(2a-b)^2
Ok I got it. Tbh I search a bit on wiki for an equation I didn't know (Diophantus' identity).ovi12 wrote:notification
(1) Diophantus' identity (a^2+b^2)*(c^2+d^2)=(ac-bd)^2+(ad-bc)^2
Say S=a^2+b^2.
From (1) 2S=(1^2+1^2)(a^2+b^2)=(a-b)^2+(a+b)^2
5S=((1^2)+(2^2))(a^2+b^2)=(a-2b)^2+(2a-b)^2
Correlation doesn't mean causation.
http://www.tylervigen.com/spurious-correlations
"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
http://www.tylervigen.com/spurious-correlations
"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
Re: Mathematics
BrookG wrote:@ovi12It's seem like cheating, using zero imoovi12 wrote:notification
Well in the statement of the problem I think I said I allowed any integers, and zero is an integer. I could see why you would call it "cheating" if zero was always one of the squares, but it's not. So I'll state the problem once more with all the restrictions and details in one post:
Show that if S can be written as the sum of two perfect squares (squares of any integers) then 2S can be written as the sum of two perfect squares, and 5S can be written as the sum of two perfect squares.
last time i cryed was because i stood on Lego
Re: Mathematics
Edited my post after a while Also works for pS=x^2+y^2, where p congruent to 1(mod4) from Fermat's theorem, which I saw recently on numberphile.
Correlation doesn't mean causation.
http://www.tylervigen.com/spurious-correlations
"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
http://www.tylervigen.com/spurious-correlations
"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
Re: Mathematics
BrookG wrote:@ovi12Ok I got it. Tbh I search a bit on wiki for an equation I didn't know (Diophantus' identity).ovi12 wrote:notification
(1) Diophantus' identity (a^2+b^2)*(c^2+d^2)=(ac-bd)^2+(ad-bc)^2
Say S=a^2+b^2.
From (1) 2S=(1^2+1^2)(a^2+b^2)=(a-b)^2+(a+b)^2
5S=((1^2)+(2^2))(a^2+b^2)=(a-2b)^2+(2a-b)^2
Congrats, that's the solution I found a few years ago when I couldn't do it. Now I revisited the problem and I came up with this:
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last time i cryed was because i stood on Lego
Re: Mathematics
@BrookG
Also, how did you find that identity?
Yeah Numberphile OP. Did you see the one line proof video? The actual proof, on numberphile2; it's pretty cool.BrookG wrote:notification
Also, how did you find that identity?
last time i cryed was because i stood on Lego
Re: Mathematics
ovi12 wrote:@BrookGYeah Numberphile OP. Did you see the one line proof video? The actual proof, on numberphile2; it's pretty cool.BrookG wrote:notification
Also, how did you find that identity?
I was thinking about the prime as a sum of squares. Googled it. Then on wikia's page on the paragraph of Euler's proof it's the first criterion
Correlation doesn't mean causation.
http://www.tylervigen.com/spurious-correlations
"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
http://www.tylervigen.com/spurious-correlations
"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
Re: Mathematics
Number theory seems the hardest branch to grasp.
Correlation doesn't mean causation.
http://www.tylervigen.com/spurious-correlations
"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
http://www.tylervigen.com/spurious-correlations
"mr.brookg go buy jeans and goto the club with somppuli" - Princeofkabul, July 2018
Re: Mathematics
BrookG wrote:Number theory seems the hardest branch to grasp.
Well it's not hard to understand the questions but it's very difficult to get the solutions. But I think counting problems are the easiest ones to make mistakes in, at least for beginners like me
Have you taken number theory yet?
last time i cryed was because i stood on Lego
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