Tagged Questions
6
votes
1answer
124 views
Finding near-integers in a range
I have a (transcendental) constant $\alpha$ and a fixed parameter $\varepsilon>0.$ I'd like to find all positive integers $n<\ell$ for which $\|n\alpha\|<\varepsilon,$ where $\|x\|$ is the ...
1
vote
1answer
123 views
How do I determine appropriate rational approximations to a sum of square roots in order to bound the error accumulation?
I have two numbers, $A$ and $B$, that are sums of integer multiples of a set of square roots of small primes (and 1) and their products:
$A = a_0 + a_1\sqrt 2 + a_2\sqrt 3 + a_3\sqrt 5 + a_4\sqrt 6 + ...
8
votes
1answer
83 views
Do best lower approximations of a quadratic irrational always form a linear recurrence sequence?
Let $\theta$ be an irrational number and let
$$
{\cal L}= \bigg\lbrace (a,b) \in {\mathbb Z} \times {\mathbb N}^{*} \bigg| \frac{a}{b} \leq \theta \bigg\rbrace
$$
and
$$
{\cal B}= \bigg\lbrace ...
