Mr Pie

### Questions (111)

 131 Is the blue area greater than the red area? 32 Are there any other methods to apply to solving simultaneous equations? 19 Is the aim of this Tic-Tac-Toe puzzle possible to achieve? 18 On proving that $\sum\limits_{n=1}^\infty \frac{n^{13}}{e^{2\pi n}-1}=\frac 1{24}$ 12 The most complex formula for the golden ratio $\varphi$ that I have ever seen. How was it achieved?

### Reputation (7,602)

 -2 On proving that $\sum\limits_{n=1}^\infty \frac{n^{13}}{e^{2\pi n}-1}=\frac 1{24}$ -2 On the conjecture that $1-\frac 13 + \frac 16 +\frac 1{10} -\frac 1{15}+\cdots = 1\frac 19$ -2 On expressing $\frac{\pi^n}{4\cdot 3^{n-1}}$ as a continued fraction. -2 On conjectured continued fractions and $e$

 20 A quick way, say in a minute, to deduce whether $1037$ is a prime number 15 Is the blue area greater than the red area? 12 Conjectures that have been disproved with extremely large counterexamples? 8 Proving $\left(1-\cos^2x\right)\left(1+\tan^2x\right)=\tan^2x$ 8 If $1^2+2^2+3^2 + …+ 10^2=385$ , then value of $2^2+4^2+6^2 + … + 20^2$

### Tags (122)

 45 algebra-precalculus × 31 20 primality-test 36 elementary-number-theory × 24 18 conjectures × 39 28 number-theory × 50 17 prime-numbers × 41 23 proof-writing × 28 17 geometry × 8 22 inequality × 9 16 notation × 7