Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [approximation]

For questions that involve concrete approximations, such as finding an approximate value of a number with some precision. For questions that belong to the mathematical area of Approximation Theory, use (approximation-theory).

Approximations are representations of numbers that aren't exact, for example $\sqrt{2}\approx 1.41$. Such representations may be obtained using differentials (more generally, Taylor's formula), linear interpolation, etc.

4607 questions
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I have found a formula for dividing numbers in easy steps

I found an easy method for division and it depends on some factors. I wanted to find an answer for $1000/101$ with easy steps. My starting point is here. I formulated this method by 2 hours of hard work. It is an infinite series, but taking 4 or 6…
rock-onn
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How much gas does a car use to carry its own gas?

I have always been curious about this one. Since the gas has some weight, the car will have to burn some extra gas to carry it's own fuel around. How can I calculate how much that extra gas is? Assumptions: car lifetime of 300,000km 50lt tank,…
ppp
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Where am I violating the rules?

Being fascinated by the approximation $$\sin(x) \simeq \frac{16 (\pi -x) x}{5 \pi ^2-4 (\pi -x) x}\qquad (0\leq x\leq\pi)$$ proposed, more than 1400 years ago by Mahabhaskariya of Bhaskara I (a seventh-century Indian mathematician) (see here), I…
Claude Leibovici
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approximating a maximum function by a differentiable function

Is it possible to approximate the $max\{x,y\}$ by a differentiable function? $f(x,y)=max \{x,y\} ;\ x,y>0$
mobina
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What's the name of the approximation $(1+x)^n \approx 1 + xn$?

A good approximation of $(1+x)^n$ is $1+xn$ when $|x|n << 1$. Does this approximation have a name? Any leads on estimating the error of the approximation?
Martin C. Martin
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10 answers

How do I Approximate $\log{2}\approx 0.693$ without using the Maclaurin series?

How do I approximate the value $\log{2}\approx 0.693$ without using the Maclaurin series? The book gives the hint: consider $f(x)=e^x-e^{-x}-2x$.
user253631
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2 answers

Approximation vs. Interpolation

Sorry if this is a silly question, i'm just getting back into math after a long time away. My question is regarding approximation and interpolation. In which cases is it appropriate for one technique versus the other. If I have a list of data points…
miggety
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When does $f(a),f(f(a)),f(f(f(a)))...$ produce better and better approximations to $x=f(x)$?

I tried to approximate the solution to $x=f(x)$ for some given $f$, by guessing $x=a$, then I observed that $x=f(a)$ was an even better approximation, and $x=f(f(a))$ and so on was even better, so why does this method work and for which f, is it…
Abdulh Khazzak Gustav ElFakiri
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Approximation by $C^1$ path of a Lipschitz continuous path

I was wondering if the following equality holds: $$\inf\left\{\int_0^1 G(\gamma(t))|\gamma'(t)|dt, \gamma \in X \cap (\text{Lipschitz})\right\}\stackrel{??}{=}\inf\left\{ \int_0^1 G(\gamma(t))|\gamma'(t)|dt, \gamma \in X \cap C^1\right\}$$ where…
Beni Bogosel
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Why some curious almost-identities

I read somewhere that $$e^{\pi\sqrt{163}}$$ is almost an integer and strangely enough this isn't just a random coincidence but rather there exists some general theory http://en.wikipedia.org/wiki/Heegner_number behind the occurences of these almost…
Sidharth Ghoshal
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Simulate a double chance bet with two single bets

If you bet on the result of a soccer match, you usually have three possibilities. You bet 1 - if you think the home team will win X - if you think the match ends in a draw 2 - if you think the away team will win Lets say we have the following…
Sandro
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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 well-known example of flinging is with iPhone and…
Ricket
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How to find an approximation to $1 - \left( \frac{13999}{14000}\right )^{14000}$?

I want to find an approximation to the expression $$ 1 - \left( \frac{13999}{14000}\right )^{14000} $$ I tried by taking logarithm $$ \ln P = \ln\left(1 - \left(\frac{13999}{14000}\right)^{14000}\right) \approx -…
Rescy_
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Given a vector $x\in \mathbb R^n$, how can we find $z\in \mathbb Z^n$ which is closest to a scalar multiple of $x$?

I am looking for how to find integer approximations to scalar multiples of real valued vectors. This is close to the problem of finding a best rational approximation to a real number, but kind of generalized. Given an integer $k$, I would like to…
crf
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How is $\frac{\big(\frac{3}{2}\big)^{99}-1}{\big(\frac{3}{2}\big)^{100}-1}\approx\frac{1}{\big(\frac{3}{2}\big)}$

I read somewhere that $$\frac{\big(\frac{3}{2}\big)^{99}-1}{\big(\frac{3}{2}\big)^{100}-1}\approx\frac{1}{\big(\frac{3}{2}\big)}$$I don't know how to have it. Please let me know how this is approximated.
Silent
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