If the answer of a problem is represented in the form [$]\pi r^2[$] then it is the closed form solution.Yes, eg if we have the equation A = pi r^2 then we can't compute it exactly for most r.
If the answer of a problem is represented in the form [$]\pi r^2[$] then it is the closed form solution.Yes, eg if we have the equation A = pi r^2 then we can't compute it exactly for most r.
You need an algorithm or series expansion to compute pi. Iifinite time to fill it. And that's just the start, you need an infinite long memory for both pi *and* (most values of) r. To compute the square and product you need to apply algorithms that manipulate the representation symbols (0s and 1s for binary representation).If the answer of a problem is represented in the form [$]\pi r^2[$] then it is the closed form solution.Yes, eg if we have the equation A = pi r^2 then we can't compute it exactly for most r.
I got a new Nokia 3310 (orange coloured) for my birthday. Does it support Euclid?If you had a smartphone you would have liked the Euclidia app, it has all kinds of puzzles like that, I use it to kill time on a plane.
Close form solution and how to find approximation of an irrational numbers are two different problems. In such a way to find approximation of [$] \pi [$] or [$]\sqrt 2[$] are similar problem. Solution in the form [$]y = \pi r^2[$] or y = sin x are examples of the solutions in closed form.You need an algorithm or series expansion to compute pi. Iifinite time to fill it. And that's just the start, you need an infinite long memory for both pi *and* (most values of) r. To compute the square and product you need to apply algorithms that manipulate the representation symbols (0s and 1s for binary representation).If the answer of a problem is represented in the form [$]\pi r^2[$] then it is the closed form solution.Yes, eg if we have the equation A = pi r^2 then we can't compute it exactly for most r.
What if A is the payoff function of an exotic option, r is a strike factor, pi is the price of an American out with some special parameter values. Now A is no longer closed form by inductions?Close form solution and how to find approximation of an irrational numbers are two different problems. In such a way to find approximation of [$] \pi [$] or [$]\sqrt 2[$] are similar problem. Solution in the form [$]y = \pi r^2[$] or y = sin x are examples of the solutions in closed form.You need an algorithm or series expansion to compute pi. Iifinite time to fill it. And that's just the start, you need an infinite long memory for both pi *and* (most values of) r. To compute the square and product you need to apply algorithms that manipulate the representation symbols (0s and 1s for binary representation).If the answer of a problem is represented in the form [$]\pi r^2[$] then it is the closed form solution.
Wow, that very fasioable! Research show it going to be the best selling phone in 2018, Hugh expectations!I got a new Nokia 3310 (orange coloured) for my birthday. Does it support Euclid?If you had a smartphone you would have liked the Euclidia app, it has all kinds of puzzles like that, I use it to kill time on a plane.
I don't agree. Just because you have a cute symbol [$]\pi[$] does not make it closed form. It is a transcendental number and even Archimedes uses approximation. In mathematics, a transcendental number is a real or complex number that is not algebraic—that is, it is not a root of a nonzero polynomial equation with integer (or, equivalently, rational) coefficients. The best-known transcendental numbers are π and e.If the answer of a problem is represented in the form [$]\pi r^2[$] then it is the closed form solution.Yes, eg if we have the equation A = pi r^2 then we can't compute it exactly for most r.
I bought it because it does what I want, + cheap + none of that fancy crap. Too much consumer brainwashing going on.Wow, that very fasioable! Research show it going to be the best selling phone in 2018, Hugh expectations!I got a new Nokia 3310 (orange coloured) for my birthday. Does it support Euclid?If you had a smartphone you would have liked the Euclidia app, it has all kinds of puzzles like that, I use it to kill time on a plane.