Euler Identity

[Guille]

Magnificent and absolutelly incredible, it is the one magical equation in mathematics that no one, not even anti-mathematicians, dare to disagree with or dislike.

The identity is a special case of the euler formula:



because when x=π then cosπ=-1 and sinπ=0. So we come to it:



And to show the relationships between all the mathematical constants, we obtain the most beautifull object done in mathematics tat I'v ever seen, it is to mathematics what the mona lisa or giocconda is for painting, and bethoven's symphony nº 9 to music, it is:



What do you think about it? What could it's significance be? How important should it be for the TOE?....Any other comment?

[AntonioLao]

This expression proves the existence of directed straight lines, one positive and one negative. When they collide, the result is zero.

[Guille]

This expression proves the existence of directed straight lines, one positive and one negative. When they collide, the result is zero.

Do you mean directed straight lines in spatial reality, i.e. geometry, or in just mathematical representations (maybe graphs?)?

[AntonioLao]

Do you mean directed straight lines in spatial reality, i.e. geometry, or in just mathematical representations (maybe graphs?)?

Both. I know, I find it very difficult to graph zero, but if I graphed 1 and -1, zero is exactly located at the midpoint between 1 and -1.

[Guille]

Both. I know, I find it very difficult to graph zero, but if I graphed 1 and -1, zero is exactly located at the midpoint between 1 and -1.

Interesting, spetially for this: Imagine the graph is the graph of complex numbers, with the horizontal (x) dimension being the real numbers and the imaginary numbers being the vertical (y) dimension. This mean that the midpoint between any two complex numbers is 0. But it doesn't make sense because 0 is the cross point between the two dimension. Or maybe this zeros to whic h you refer to, we can call them "local zeros" in contrast to the other "universal zero"?

[AntonioLao]

the numbers found on the horizontal axis are pure real numbers. The ones found on the vertical axis are pure imaginary numbers. Complex numbers are found anywhere on the 4 quadrants except the two axes mentioned above.

[Guille]

the numbers found on the horizontal axis are pure real numbers. The ones found on the vertical axis are pure imaginary numbers. Complex numbers are found anywhere on the 4 quadrants except the two axes mentioned above.

Up to what I know, all reals and imaginary are included int he set of complex numbers, they are indeed complex numers. What happens is that they are of the form a+0 or 2i+0..... But they ARE counted as complex numbers.

[AntonioLao]

they are of the form a+0 or 2i+0

when the real argument is zero, the complex number becomes pure imaginary. When the imaginary argument is zero, the complex number becomes pure real.
These are respectively found the imaginary axis and real axis.

[Guille]

when the real argument is zero, the complex number becomes pure imaginary. When the imaginary argument is zero, the complex number becomes pure real.
These are respectively found the imaginary axis and real axis.

True, I know. But they do count in the set of all complex numbers.

About Euler's identity, e^ipi is a real number, -1. This means that some combinations of reals and imaginaries can give still realsor imaginaries, not complex numnbers, even when no part of the number is zero.

[AntonioLao]

Euler's identity, e^ipi is a real number, -1.

the math behind Euler's identity is the imaginary exponent of real is real. I have the book that explains a little bit about this. I try to look into it.