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#1 2020-07-13 14:01:19

pi_cubed
Member
From: A rhombicosidodecahedron
Registered: 2020-06-22
Posts: 115

Miscellaneous Math Discussion

This thread is for posting about anything about math.
Math books, sine, recreational mathematics, etc.


pi³

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#2 2020-07-13 14:23:03

Jai Ganesh
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Registered: 2005-06-28
Posts: 45,956

Re: Miscellaneous Math Discussion

Many years ago, I declared:

Sum of two cubes in two different ways (resulting in a sum which is a positive number) is 91.




Cubes numbers can be both positive and negative, aren't they?

Interestingly,




is zero.

Trivial!


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#3 2020-07-13 14:42:13

pi_cubed
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From: A rhombicosidodecahedron
Registered: 2020-06-22
Posts: 115

Re: Miscellaneous Math Discussion

ganesh wrote:

Many years ago, I declared:

Sum of two cubes in two different ways (resulting in a sum which is a positive number) is 91.




Cubes numbers can be both positive and negative, aren't they?

Interestingly,




is zero.

Trivial!

What do you mean by n^3 and -n^3 is zero?


pi³

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#4 2020-07-13 14:45:02

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Miscellaneous Math Discussion

pi_cubed wrote:
ganesh wrote:

Many years ago, I declared:

Sum of two cubes in two different ways (resulting in a sum which is a positive number) is 91.




Cubes numbers can be both positive and negative, aren't they?

Interestingly,




is zero.

Trivial!

What do you mean by n^3 and -n^3 is zero?

I meant sum.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#5 2020-07-13 15:24:02

pi_cubed
Member
From: A rhombicosidodecahedron
Registered: 2020-06-22
Posts: 115

Re: Miscellaneous Math Discussion

I think the group theory relationship in my signature is flawed.


pi³

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#6 2020-07-13 15:28:56

666 bro
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From: Flatland
Registered: 2019-04-26
Posts: 706

Re: Miscellaneous Math Discussion

pi_cubed wrote:

I think the group theory relationship in my signature is flawed.

What does an group theory relationship mean?


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#7 2020-07-13 16:44:32

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Miscellaneous Math Discussion

666 bro wrote:
pi_cubed wrote:

I think the group theory relationship in my signature is flawed.

What does an group theory relationship mean?

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.

Various physical systems, such as crystals and the hydrogen atom, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.

The early history of group theory dates from the 19th century. One of the most important mathematical achievements of the 20th century was the collaborative effort, taking up more than 10,000 journal pages and mostly published between 1960 and 1980, that culminated in a complete classification of finite simple groups.

pi_cubed thinks his signature is flawed.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#8 2020-07-13 20:24:24

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Miscellaneous Math Discussion

hi pi_cubed

I tried X and Y as 2 x 2 matrices, just making up some numbers.  I didn't get the same answer evaluating X' Y' X Y and  Y' X' Y X.  It was a long calculation so I may have slipped up of course.

Did you just randomly make up the relationship, or does it come from something?

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#9 2020-07-14 05:45:08

pi_cubed
Member
From: A rhombicosidodecahedron
Registered: 2020-06-22
Posts: 115

Re: Miscellaneous Math Discussion

bob bundy wrote:

hi pi_cubed

I tried X and Y as 2 x 2 matrices, just making up some numbers.  I didn't get the same answer evaluating X' Y' X Y and  Y' X' Y X.  It was a long calculation so I may have slipped up of course.

Did you just randomly make up the relationship, or does it come from something?

Bob

I think I read an article somewhere about it but I might have remembered it wrong.


pi³

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#10 2020-07-15 06:23:06

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Miscellaneous Math Discussion

I had assumed that ' is being used to mean the inverse of.  But I cannot find any on-line resources that confirm this.

But, if it is, then

(X' Y' X Y) (Y' X' Y X) = X' ( Y' ( X (YY') X' ) Y ) X = the identity = I

Also (XY) (XY)' = I = X Y Y' X' => (XY)' = Y'X'

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#11 2022-06-15 10:52:19

pi_cubed
Member
From: A rhombicosidodecahedron
Registered: 2020-06-22
Posts: 115

Re: Miscellaneous Math Discussion

I just found this and I don't understand why I made this 2 years ago
Anyways, what I meant to say for the group thing is (don't remember exactly what the expression was since it's been 2 years but i'll try):


this doesn't seem useful to me, but I don't know what I was thinking 2 years ago
suggestion: allow putting latex inline with dollars signs (like $this 2^3 \binom{3}{2}$). And the latex tutorial should be more clear that you use [math] tags
Also, did you change your name from "bob something" to Bob?

Last edited by pi_cubed (2022-06-15 10:53:00)


pi³

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#12 2022-06-15 19:09:10

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Miscellaneous Math Discussion

hi pi_cubed

A couple of years ago I discovered that cyber criminals had quite a file of facts about me.  Because I'd used my real name for an on-line account (not this one) they had been able to link together several things about me and tried to use it to blackmail me. (not that there's any real substance to the threat as I'm an innocent soul smile )

Along with a number of other measures,  I decided to to change my username here.  Forgive me for editing your post; but now you know the reason.  Such people do look at this forum and every few days I have to remove potentially dangerous posts from them; members beware!

Now back to group theory.

Consider the two expressions:

Multiply each by XY.

In group theory if Q x P = R x P then Q = R, so the inverse of XY is Y^(-1) X^(-1)

If you look at your expression, you'll see it is just a more complex version of the same thing, so the identity is true.  So you can re-instate it if you wish.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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