(A technical) mathematics question...

scouse_dave · 09:15 AM

so i got to thinking about Pythagorean Triples. that is to say a set of 3 positive integers; x, y, z where:

x

2 + y

2 = z

2; [x, y, z (= Z > 0]

say, for example, [x,y,z] = [5,12,13]

then it occured it to me about generalising the theory to that of an unspecified positive index. to clarify, let us examine the equation:

x

n + y

n = z

n [x, y, z, n (= Z >0]

so, what gives? i wonder if anyone could shed any light on this with perhaps a mathematically rigourous proof either way...is it true or not? feel free to use proof by induction or whatever means you see fit. the use of galois theory, ring sets and fractals, whilst not essential, may be useful.

lawson · 10-25-2002, 08:52 AM

not sure what you're going for since the pythagorean triples only work for certain values, isnt a true equality, and is

2

2=

3 while your new equation is

n

n=

n but then again you've surely taken more math than me and have some grand idea.

.5(x+y)* root2 gives an estimation for small numbers, ha

sawdust restaurants · 10-25-2002, 08:56 AM

Hey, there were qualifications in my original post for a reason. Obviously you'd have had to study Nietzsche in some depth to be able to answer it; it wasn't pissing in the wind, it was just looking for a needle in a haystack.

The answer to your question, by the way, is 42.l

JPK · 10-25-2002, 08:59 AM

I haven't done math in forever so I must be wrong, but just by an example it seems that your idea wouldn't work.

Let's take an easy triple [3,4,5]

3

2 + 4

2 = 5

2

but

3

3 + 4

3 = 27 + 64 = 81 is not equal to 5

3

so there.

(please correct me if I'm wrong :-/ )

scouse_dave · 09:16 AM

Quote:

Originally posted by PhantomFM
not sure what you're going for since the pythagorean triples only work for certain values, isnt a true equality, and is 2 2=3 while your new equation is nn=n but then again you've surely taken more math than me and have some grand idea.

well...sure, it isn't a true equality in the sense it isn't satisfied for ALL values of [x, y, z]...however, i never implied that it was. that's the difference between the two horizontal lines for 'is equal to' and the three for 'is always equivalent to".

ummm, in pythagorean triples, all indices are exactly 2. The 'z' or 'c' component is not raised to the power of 3. so....i don't know what you're saying really....?????

the equation:
x

n + y

n = z

n

is the generalised form of the special case:
x

2 + y

2 = z

2, which we know as pythagoras' theorem.

JPK · 10-25-2002, 09:12 AM

Quote:

Originally posted by scouse_dave

ummm, in pythagorean triples, all indices are exactly 2. The 'z' or 'c' component is not raised to the power of 3. so....i don't know what you're saying really....?????

you made a typo in your first post.

scouse_dave · 09:18 AM

Quote:

Originally posted by JPK
I haven't done math in forever so I must be wrong, but just by an example it seems that your idea wouldn't work.

Let's take an easy triple [3,4,5]

32 + 42 = 52

but

33 + 43 = 27 + 64 = 81 is not equal to 53

so there.

(please correct me if I'm wrong :-/ )

well, two things
1. i didn't say that the general formula was true in the first place...it was a simply a proposition. i.e. i wanted people to decide for themselves whether or not it was true or not.

2. the fact that [3,4,5] works for the power of 2 doesn't mean it should work for the power of 3. that's almost irrelevant. the [x,y,z] in each case don't need to be the same. what i'm saying is...can you find 3 integers that fit the equation to the power 3, or 4, or 5, or 37, or whatever.

so maybe that 34

12 + 52

12 = 56

12...ya know?

i'm not looking for number crunching here...it might take you, i dunno, literally a whole evening to find one set that matches

scouse_dave · 10-25-2002, 09:15 AM

Quote:

Originally posted by JPK
you made a typo in your first post.

aack, so i did

scouse_dave · 10-25-2002, 09:17 AM

Quote:

Originally posted by sawdust restaurants
Hey, there were qualifications in my original post for a reason. Obviously you'd have had to study Nietzsche in some depth to be able to answer it; it wasn't pissing in the wind, it was just looking for a needle in a haystack.

i'm just poking fun, man...

your question did seem a lil specialised...

sawdust restaurants · 10-25-2002, 09:18 AM

Quote:

Originally posted by scouse_dave
i'm just poking fun, man...

your question did seem a lil specialised...

True. Itz all good. And I am thoroughly lost here, by the way.

scouse_dave · 10-25-2002, 09:22 AM

*waits for deviousj*

he'll solve it !!!

JPK · 10-25-2002, 10:10 AM

I told you it I might be wrong!

now I'll let the real math geeks try to solve it

10-25-2002, 07:53 AM	#1
scouse_dave Minion of Satan Location: Manchester Posts: 5,089	(A technical) mathematics question... so i got to thinking about Pythagorean Triples. that is to say a set of 3 positive integers; x, y, z where: x2 + y2 = z2; [x, y, z (= Z > 0] say, for example, [x,y,z] = [5,12,13] then it occured it to me about generalising the theory to that of an unspecified positive index. to clarify, let us examine the equation: xn + yn = zn [x, y, z, n (= Z >0] so, what gives? i wonder if anyone could shed any light on this with perhaps a mathematically rigourous proof either way...is it true or not? feel free to use proof by induction or whatever means you see fit. the use of galois theory, ring sets and fractals, whilst not essential, may be useful. Last edited by scouse_dave : 10-25-2002 at 09:15 AM.

10-25-2002, 08:52 AM	#2
lawson Apocalyptic Poster Location: raleigh Posts: 4,176	not sure what you're going for since the pythagorean triples only work for certain values, isnt a true equality, and is 2 2=3 while your new equation is nn=n but then again you've surely taken more math than me and have some grand idea. .5(x+y)* root2 gives an estimation for small numbers, ha

10-25-2002, 08:56 AM	#3
sawdust restaurants Fucking Creep Location: On the East Coast Posts: 5,992	Hey, there were qualifications in my original post for a reason. Obviously you'd have had to study Nietzsche in some depth to be able to answer it; it wasn't pissing in the wind, it was just looking for a needle in a haystack. The answer to your question, by the way, is 42.l

10-25-2002, 08:59 AM	#4
JPK Ownz Location: Ste-Foy, Quebec, Canada Posts: 525	I haven't done math in forever so I must be wrong, but just by an example it seems that your idea wouldn't work. Let's take an easy triple [3,4,5] 32 + 42 = 52 but 33 + 43 = 27 + 64 = 81 is not equal to 53 so there. (please correct me if I'm wrong :-/ )

10-25-2002, 09:22 AM	#11
scouse_dave Minion of Satan Location: Manchester Posts: 5,089	waits for deviousj he'll solve it !!!

10-25-2002, 10:10 AM	#12
JPK Ownz Location: Ste-Foy, Quebec, Canada Posts: 525	I told you it I might be wrong! now I'll let the real math geeks try to solve it