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**pi_cubed****Member**- From: A rhombicosidodecahedron
- Registered: 2020-06-22
- Posts: 63

This thread is for posting about anything about math.

Math books, sine, recreational mathematics, etc.

e to the i pi plus 1 is zero -Leonhard Euler | a squared plus b squared equals c squared -Pythagoras | Energy equals mass times the speed of light squared -Albert Einstein | i² = -1 | x^2+1=0 x^2=-1 x=i

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 32,465

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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**pi_cubed****Member**- From: A rhombicosidodecahedron
- Registered: 2020-06-22
- Posts: 63

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?

e to the i pi plus 1 is zero -Leonhard Euler | a squared plus b squared equals c squared -Pythagoras | Energy equals mass times the speed of light squared -Albert Einstein | i² = -1 | x^2+1=0 x^2=-1 x=i

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 32,465

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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**pi_cubed****Member**- From: A rhombicosidodecahedron
- Registered: 2020-06-22
- Posts: 63

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

e to the i pi plus 1 is zero -Leonhard Euler | a squared plus b squared equals c squared -Pythagoras | Energy equals mass times the speed of light squared -Albert Einstein | i² = -1 | x^2+1=0 x^2=-1 x=i

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 621

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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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 32,465

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 8,944

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

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**pi_cubed****Member**- From: A rhombicosidodecahedron
- Registered: 2020-06-22
- Posts: 63

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.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 8,944

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

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