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Author
tthsqe

Joined: 20 May 2009
Posts: 724
tthsqe
and http://journal.frontiersin.org/Journal/10.3389/fnhum.2014.00068/full

I personally find the equation
Code:
`1 + e ^ (i pi) = 0    `

to be ugly and unharmonious almost in a contrived way. Much better is the relation
Code:
`e ^ (i x) = cos(x) + i sin(x)    `

Now that is an equation that has some beauty and symmetry to it.

Whachall think?

Quote:
The participants rated Srinivasa Ramanujan's infinite series and Bernhard Riemann's functional equation as the ugliest.

I wouldn't take this too seriously without knowing the precise formulations of these results.
15 Mar 2014, 09:20
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17279
revolution
I think the form:
Code:
`e ^ (i pi) + 1 = 0    `
is a nicer way to put it.

I don't find it ugly. Indeed quite the opposite in some ways because it is both simple and mysterious. Powers with negative results, roots of negative numbers, irrational numbers, imaginary numbers, addition, multiplication, exponentiation, transcendental functions and arithmetic identities all come together and produce a simple looking result that is in fact very complex (pun intended).
15 Mar 2014, 10:11
cod3b453

Joined: 25 Aug 2004
Posts: 619
cod3b453
My answer is basically the same as revolution's with the addition of rationals 0/1 - both also important numbers. I agree the special case is not practical but it is more meaningful in the way it relates so many areas of mathematics and the fact it can be expressed in such a short form is quite impressive.
15 Mar 2014, 11:29
sid123

Joined: 30 Jul 2013
Posts: 340
Location: Asia, Singapore
sid123
I find the equation beautiful but the proof is ugly.
Lol Taylor Series. XD
Some people have really thought crazy stuff from another form of the equation which gives 0 from e^i× + 1 where x = Π.
Code:
`e ^ (i x) = cos(x) + i sin(x)    `

This,

Is a more beautiful way to represent it.
BTW Riemann's sums are worse. *Had almost made my brain double fault during the calc class.*
15 Mar 2014, 12:22
Xorpd!

Joined: 21 Dec 2006
Posts: 161
Xorpd!
Rather shocking that the functional equation for the Riemann zeta function was considered ugly in the study. Titchmarsh gives 7 (actually more than 7) methods of establishing that result in chapter 2. The results seem to be more a measure of what happens when social scientists play scientist.
15 Mar 2014, 18:25
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17279
revolution
pi i = 0

Let me "prove" it:
Code:
```e ^ (pi i) + 1 = 0

e ^ (pi i) = -1

e ^ (2 pi i) = 1 (Squaring both sides)

e ^ (2 pi i) = e ^ 0

2 pi i = 0 (log base e of both sides)

pi i = 0 (divide both sides by 2)    ```
Now we go back and show that this result is perfectly correct.
Code:
```e ^ (pi i) + 1 = 0

e ^ 0 + 1 = 0 (because pi i = 0 as shown above)

1 + 1 = 0

2 = 0    ```
17 Mar 2014, 01:33
cod3b453

Joined: 25 Aug 2004
Posts: 619
cod3b453
Got to admit, saw this and couldn't see the error until I wrote "ln" variation on the 4th line
17 Mar 2014, 17:12
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