Mathematics paper cover design

[curious mind 111]

hello, a bit of topic. we're having an exhibition at my university to display outstanding papers. my paper was about my passion for mathematics. I am seeking some ideas to make visitors want to read my paper. I don't want something too childish. I was thinking of making a string model of some equation or possibly fibbonacci sequence, but I didnt find anything on the web. Or maybe i do a painting as the back

 

[fresh_42]

Childish is a personal view. There can be a lot of insight in a "childish" drawing. But what is your paper about? Shouldn't the cover be related to the content? Here's a proposal connected to the Fibonacci sequence:

Source: https://sharoncas.wordpress.com/2012/06/28/non-linear-pattern-web-quest-alg-4c1-7/

 

[curious mind 111]

Thank you for your reply :) My paper is entitled "a passion for numbers" it's about, well, my passion for math. so i was thinking of making a fibonacci spiral with thread or maybe something else but of mathematical significance. something beautiful and artistic.

 

[fresh_42]

The mathematical equivalence to $E = m\cdot c^2$ is Euler's identity
$$e^{i \pi} = -1$$
And here is something funny I once found:
$$2^n+7^n+8^n+18^n+19^n+24^n=3^n+4^n+12^n+14^n+22^n+23^n \text{ for } n =0,1,...,5$$

 

[Jonathan Scott]

something beautiful and artistic.

Try fractals, in particular a "Julia Set".

 

[fresh_42]

I personally like this formula involving the Fibonacci sequence and two other sequences:
$$
\sum_{n\in\mathbb{N}}\frac{F_n}{n}\cdot\frac{L_n}{n}\cdot\frac{1}{(n+1)C_n} = \frac{(2\pi)^2}{\sqrt{5}^5}
$$
where $F_n$ is the Fibonacci sequence, $L_n$ the Lucas sequence and $C_n$ the Catalan sequence. You will find their definitions, e.g. on Wikipedia.

 

[curious mind 111]

Thanks for the great ideas. I'll keep u updated on what i settle on.
Best

 

[pinball1970]

The mathematical equivalence to $E = m\cdot c^2$ is Euler's identity
$$e^{i \pi} = -1$$

Why are they equivalent?

 

[fresh_42]

Why are they equivalent?

They are not literally equivalent. I meant, they are equally famous as THE equation in physics, resp. mathematics.

 

[pinball1970]

They are not literally equivalent. I meant, they are equally famous as THE equation in physics, resp. mathematics.

Good! I was thinking what the hell!? They both have 'e' buts it's a different E!

 

[fresh_42]

Good! I was thinking what the hell!? They both have 'e' buts it's a different E!

Who knows? e is a pretty natural quantity. Maybe someone finally finds a connection.

 

[Frabjous]

What happened in 1874?

 

[fresh_42]

What happened in 1874?

If the family of integral curves of the differential equation $M\,dx + N\,dy = 0$ is left unaltered by the group $Uf \equiv \xi \dfrac{df}{dx}+\eta \dfrac{df}{dy},$ $\dfrac{1}{\xi M+\eta N}$ is an integrating factor of the differential equation. (M.S. Lie, Christiania 1874)

 

[pinball1970]

I was banking on 'trams.'

The integral curve thing did not occur to me...