Miscellaneous Math Discussion

pi_cubed · 2020-07-13 14:01:19

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

Jai Ganesh · 2020-07-13 14:23:03

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!

pi_cubed · 2020-07-13 14:42:13

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?

Jai Ganesh · 2020-07-13 14:45:02

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.

pi_cubed · 2020-07-13 15:24:02

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

666 bro · 2020-07-13 15:28:56

pi_cubed wrote:

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

What does an group theory relationship mean?

Jai Ganesh · 2020-07-13 16:44:32

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.

Bob · 2020-07-13 20:24:24

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

pi_cubed · 2020-07-14 05:45:08

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.

Bob · 2020-07-15 06:23:06

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

pi_cubed · 2022-06-15 10:52:19

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)

Bob · 2022-06-15 19:09:10

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 )

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

Math Is Fun Forum

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

Miscellaneous Math Discussion

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

Re: Miscellaneous Math Discussion

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

Re: Miscellaneous Math Discussion

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

Re: Miscellaneous Math Discussion

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

Re: Miscellaneous Math Discussion

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

Re: Miscellaneous Math Discussion

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

Re: Miscellaneous Math Discussion

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

Re: Miscellaneous Math Discussion

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

Re: Miscellaneous Math Discussion

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

Re: Miscellaneous Math Discussion

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

Re: Miscellaneous Math Discussion

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

Re: Miscellaneous Math Discussion

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