New posts in diophantine-approximation

Why is an irrational number's algebraic complexity the opposite of its Diophantine complexity?

intuition transcendental-numbers diophantine-approximation

Exploiting a Diophantine approximation of $\pi^4$ into giving a series of rationals for $\pi^4$

sequences-and-series analytic-number-theory elliptic-curves sums-of-squares diophantine-approximation

How find the value $\beta$ such $\left|\frac{p}{q}-\sqrt{2}\right|<\frac{\beta}{q^2}$

number-theory diophantine-approximation

An integral for $2\pi+e-9$

definite-integrals exponential-function pi diophantine-approximation

Can we make $\tan(x)$ arbitrarily close to an integer when $x\in \mathbb{Z}$?

calculus real-analysis diophantine-approximation

Does there exist $\ n,m\in\mathbb{N}\ $ such that $\ \lvert \left(\frac{3}{2}\right)^n - 2^m \rvert < \frac{1}{4}\ $?

inequality arithmetic diophantine-approximation

Is there any real number except 1 which is equal to its own irrationality measure?

number-theory irrational-numbers diophantine-approximation

Series and integrals for inequalities and approximations to $\log(n)$

sequences-and-series inequality definite-integrals logarithms diophantine-approximation

Prove $\sum_{n=1}^\infty\frac{\cot(\pi n\sqrt{61})}{n^3}=-\frac{16793\pi^3}{45660\sqrt{61}}$

sequences-and-series complex-analysis number-theory continued-fractions diophantine-approximation

Irrationality of $\sum_{p\in\mathbb{P}} \frac{1}{2^{p}}$

number-theory prime-numbers irrational-numbers diophantine-approximation

Is the sequence $(B_n)_{n \in \Bbb{N}}$ unbounded, where $B_n := \sum_{k=1}^n\mathrm{sgn}(\sin(k))$?

sequences-and-series diophantine-approximation

How was this approximation of $\pi$ involving $\sqrt{5}$ arrived at?

approximation pi golden-ratio diophantine-approximation

$\pi^4 + \pi^5 \approx e^6$ is anything special going on here?

exponential-function approximation pi constants diophantine-approximation

Examples of transcendental functions giving almost integers

real-analysis numerical-methods approximation-theory diophantine-approximation

Does the sequence $\{\sin^n(n)\}$ converge?

real-analysis sequences-and-series convergence-divergence diophantine-approximation

Series and integrals for inequalities and approximations to $\pi$

sequences-and-series inequality definite-integrals pi diophantine-approximation

How to find $\sum_{i=1}^n\left\lfloor i\sqrt{2}\right\rfloor$ A001951 A Beatty sequence: a(n) = floor(n*sqrt(2)).

sequences-and-series summation radicals ceiling-and-floor-functions diophantine-approximation

Fermat's Last Theorem near misses?

number-theory elementary-number-theory diophantine-equations diophantine-approximation

How close can $\sum_{k=1}^n \sqrt{k}$ be to an integer?

sequences-and-series summation radicals approximation-theory diophantine-approximation

Does the sequence $n+\tan(n), n \in\mathbb{N}$ have a lower bound?

sequences-and-series number-theory trigonometry approximation diophantine-approximation