10 most elegant mathematics formulas (2 Viewers)

[Cam O]

Who the hell doesn't love Pythagoras?

 

[darkliight]

Hippasus for a start.

 

[jamesboyd9]

a<SUP>4</SUP>+b<SUP>4</SUP>+c<SUP>4</SUP>+d<SUP>4</SUP>=(a+b+c+d)<SUP>4</SUP> has infinitely many nontrivial integer solutions. The proof of this was published this month and utilises Mazur's theorem that an elliptic curve has at most 16 rational torsion points. (Note this was also used by Wiles to prove Fermat's Last Theorem).

I've attached the article.

um
what?

a<SUP>4</SUP>+b<SUP>4</SUP>+c<SUP>4</SUP>+d<SUP>4</SUP> absolutly does not equal (a+b+c+d)<SUP>4</SUP>

(a+b+c+d)<SUP>4 </SUP>= a<SUP>4</SUP> + ... like a billion combinations of a,b,c & d ... + d<SUP>4</SUP>

what am I missing here?

 

[pLuvia]

um
what?

a<SUP>4</SUP>+b<SUP>4</SUP>+c<SUP>4</SUP>+d<SUP>4</SUP> absolutly does not equal (a+b+c+d)<SUP>4</SUP>

(a+b+c+d)<SUP>4 </SUP>= a<SUP>4</SUP> + ... like a billion combinations of a,b,c & d ... + d<SUP>4</SUP>

what am I missing here?

He's saying for that identity, there are infinitely many non-zero integer solutions.

 

[tau281290]

I think 1 + 1 = 2 is quite remarkable knowing that this is the origin of where all other math equations are derived. The origins of 1 + 1 has been long lost in the histories of thousands of years since human civilisation developed. Nevertheless, perhaps the Neanderthals also employed such a remarkable equation.

































LoL

 

[poWerdrY]

sin²ø + cos²ø = 1

is quite unique

+1

 

[lolokay]

well I wouldn't really call sin²ø + cos²ø = 1 unique..

e^iø = cos ø + i sin ø is pretty cool though

 

[samwell]

dont noe y but i seem to like integration by parts formula.

 

[samwell]

I think 1 + 1 = 2 is quite remarkable knowing that this is the origin of where all other math equations are derived. The origins of 1 + 1 has been long lost in the histories of thousands of years since human civilisation developed. Nevertheless, perhaps the Neanderthals also employed such a remarkable equation.

































LoL

hahahahahah u must be some hilarious guy lol.

 

[shaon0]

Imagine how smart the people are, who came up with these formulae/ideas.

 

[tacogym27101990]

dont noe y but i seem to like integration by parts formula.

integration by parts is just the reverse product rule.
but yeah i think anyone who can come up with these formula's is pretty insane

 

[samwell]

integration by parts is just the reverse product rule.
but yeah i think anyone who can come up with these formula's is pretty insane

I think newtons method is pretty cool how it is derived. The estimation of a root using gradient and fuction. The derivation was a smart thing. Although i dislike Newton's Character he was a smart dude. An application of maths to physics formulas like Newtons law of gravitation.

 

[lilley.matthew]

1. Definately Euler's - especially cause it gives negative logs- and the proof to get there is amazing as well
2. Pi/4=1/1-1/3+1/5-1/7...
3. The integral of sec x - although hardly a formula is an incredibly cool trick
4. 2^n=nC0 + nC1 ... NcN
5. tan a + tan b + tan c = Tan a * tan b *tan c (when a, b, c are in a triangle)

 

[Carrotsticks]

Obviously differenciation by First Principles is the most elegant.

/sarcasm.

 

[Sokolov]

1 + 1 = 2

qed