# Tagged Questions

For questions related to approximations

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### Relation between Simpson's Rule, Trapezoid Rule and Midpoint Rule

I am studying numerical approximation and verifying $S_{2n} = \frac{1}{3}\left(T_n +2 M_n\right)$. ($S_n$ refers to Simpson's Rule approximation, $T_n$ refers to Trapezoid Rule approximation and $M_n$ ...
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### Asymptotic number of unlabeled graphs

A rather tight lower bound $c(n)$ of the number of unlabeled digraphs of order $n$ (loops allowed) seems to be $$c(n) = 2^{n^2}/n!$$ because there are $2^{n^2}$ labeled graphs, almost all of them ...
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### Math behind a “fling”? (i.e. on a mobile touch device)

I'm working on a game which relies on "flinging" an object. That is, click and hold on the object, and then drag and release it, and it continues on the path you were dragging it. Of course, the most ...
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### Can the trigonometric functions be expressed, explained, or proven in terms of arithmetic?

I'm trying to wrap my head around sine, cosine, and tangent. I'm aware that they're commonly defined in high schools as ratios of the various parts of triangles set in the unit circle, but that's not ...
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### Approximating log of factorial

I'm wondering if people had a recommendation for approximating $\log(n!)$. I've been using Stirlings formula, $(n + \frac{1}{2})\log(n) - n + \frac{1}{2}\log(2\pi)$ but it is not so great for ...
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### What is the proof of the rules of significant figures?

I wanted to know how do we know that the rules that we follow when doing arithmetic with significant figures are correct? Like why when adding or subtracting we keep the same number of decimal places ...
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### Calculating the divisor, known to be small, of two Stirling approximations of the logarithmic Gamma function without overflows

Earlier, I asked a question on MathOverflow regarding how one might analytically approximate a function of the form: $f(n) = \prod_{i=1}^{n-1} (1-ai)$ for $a \ge 0$, $(ai) < 1$, and $n > 10^5$ ...
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