Beautiful equations

[nammynake]

Interesting article on the physiological response to 'beautiful' equations.

http://www.bbc.co.uk/news/science-environment-2615...

Post your favourites here. Here's one of mine:

Edited by nammynake on Saturday 15th February 10:11

[TwigtheWonderkid]

There's something very pleasing about the simplicity of:

X squared -1 = x+1 times x-1.

(sorry, don't know how to format it to show it in proper equation form.)

I always started with this equation when I explained algebra to my kids when they were younger.

[Simpo Two]

TwigtheWonderkid said:

X squared -1 = x+1 times x-1.

That's almost a palindrome.

Can you have an algebraic palindrome?

[zb]

[skeeterm5]

Simpo Two said:

That's almost a palindrome.

Can you have an algebraic palindrome?

a + b = b + a ?

S

[grumbledoak]

Euler's Equation is pretty cool.

e^{i pi} + 1 = 0

[Simpo Two]

grumbledoak said:

Euler's Equation is pretty cool.

e^{i pi} + 1 = 0

I'm getting the hang of this.

Simpo's Equation:

e^{i pi} = -1


Whichever you use, 'e' is as I recall 2.718 and 'pi' is 3.142 so 'i' should be pretty easy to work out... or did I miss something?

[nammynake]

Simpo Two said:

I'm getting the hang of this.

Simpo's Equation:

e^{i pi} = -1


Whichever you use, 'e' is as I recall 2.718 and 'pi' is 3.142 so 'i' should be pretty easy to work out... or did I miss something?

Simple at first glance but try taking the natural log of both sides...

[V8LM]

Golden ratio: Phi = (1 + sqrt(5)) / 2

Or written another way x^2 - x - 1 = 0

Or a / b = (a + b) / a

1 / Phi = Phi - 1

Phi = 1 + 1 / (1 + 1 / (1 + 1 / (1 + 1 / ....

Edited by V8LM on Sunday 16th February 07:55

[Halmyre]

E=mc^2

and then there's

[FunkyNige]

ash73 said:

How can an equation be beautiful?

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show."

So it's not what it does that has beauty, it's how it does it. For example, the e^(i pi) + 1=0 above isn't a massively useful equation but it does contain the five most important numbers in maths, set together in a fairly straightforward way from a pretty complicated derivation has a form of beauty.

[Shaoxter]

Not an equation, but:

[tobinen]

I always liked the Mandelbrot set:

[nammynake]

Shaoxter said:

Not an equation, but:

69 + c. What does the "c" represent...?

[Zad]

Halmyre said:

E=mc^2

and then there's

"God made the integers; all else is the work of man"

Most people think those equations are the work of JC Maxwell, but they are actually the work of Oliver Heaviside. Maxwell came up with them in quaternion form, which almost nobody could understand, including Heaviside. Heaviside was so frustrated by this that he decided to check them and convert them to the more usable vector form you see above. It is especially impressive that his first step was to start to learn mathematics. Heaviside's various contributions to modern communications are absolutely immense, yet he is still comparatively unknown.

[Migx]

I am feeling quite ignorant. maybe i should go to sleep.

[Zad]

ash73 said:

How can an equation be beautiful?

In addition to the philosophical words above, the Julia set (a sub-set of the Mandelbrot set):



For c=-0.8+0.156i

[Halmyre]

nammynake said:

Shaoxter said:

Not an equation, but:

69 + c. What does the "c" represent...?

The 'c' slings its hook for definite integrals. Or something like that.

[Shaoxter]

nammynake said:

69 + c. What does the "c" represent...?

(13^2 + c) - (10^2 + c) = 69

[nammynake]

Shaoxter said:

(13^2 + c) - (10^2 + c) = 69

Oh the shame! You are, of course, correct.