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// Learn more about F# at http://fsharp.org
// See the 'F# Tutorial' project for more help.
open MathNet.Numerics
open System.Numerics
//create a fractional approximation of pi
let rec series n q =
seq {
yield q * 4N / n
yield! series (n + 2N) (q * -1N) }
let pi = series 1N 1N |> Seq.take 100 |> Seq.reduce (+)
printf "pi: %s \n\n" (pi.ToString())
//caluclate a sqrt for BigRationals
let BrSqrt (x:BigRational) =
if x.IsOne || x.IsZero then
x
else
let mutable temp = BigRational.FromInt(1)
let precision = 100
while temp.Numerator.ToString().Length < precision do
temp <- ((x / temp) + temp) / BigRational.FromInt(2)
temp
let rec factorial n =
match n with
| 0 -> BigInteger(1)
| 1 -> BigInteger(1)
| _ -> BigInteger(n) * factorial (n - 1)
let rec doubleFactorial n =
if n % 2 = 0 then
match n with
| 0 -> BigInteger(1)
| 2 -> BigInteger(2)
| _ -> BigInteger(n) * doubleFactorial (n - 2)
else
match n with
| 1 -> BigInteger(1)
| _ -> BigInteger(n) * doubleFactorial (n - 2)
//get volume of n-ball
let volumeSphere radius dimension =
if dimension % 2 = 0 then
let ik = dimension/2
let result = (BigRational.Pow(pi,ik) / BigRational.FromBigInt(factorial ik)) * BigRational.Pow(radius,2*ik)
result
// ((pi ** (float)k) / (float)(factorial k)) * (radius ** (float)(2 * k))
else
let ik = (dimension - 1) / 2
let k = BigRational.FromInt((dimension - 1) / 2)
let twok1 =2*ik+1
let two = BigRational.FromInt( 2)
let one = BigRational.FromInt(1)
let kp1 = ik+1
let top = (BigRational.Pow (two,kp1)) * (BigRational.Pow (pi, ik) )
let bottom = BigRational.FromBigInt( doubleFactorial twok1)
let r = top / bottom
let result = r * (BigRational.Pow(radius,twok1))
result
// hypercube volume
let volumeCube length dimension =
BigRational.Pow(length, dimension)
// hypercube diagonal
let diagonalOfCube length dimension =
length * BrSqrt(dimension)
[<EntryPoint>]
let main argv =
//dimensions to check
[ 1205 .. 1207 ]
|> List.iter(fun e ->
//volume of smaller cubes
let vcube = volumeCube (BigRational.FromInt(1)) e
//colume of outter spheres
let vsphere = volumeSphere (BigRational.Parse("1/2")) e
//diagonal of smaller cubes
let diagcube = diagonalOfCube (BigRational.FromInt(1)) (BigRational.FromInt(e))
//inner cricle radius
let innercircleradius = (diagcube - BigRational.FromInt(1)) / BigRational.FromInt(2)
//inner circle volume
let innercirclevolume = volumeSphere innercircleradius e
//large cube volume
let bigcubev = volumeCube (BigRational.FromInt(2)) e
//diff between circle and cube
let diff = innercirclevolume - bigcubev
let vsphereint = BigRational.ToBigInt(vsphere)
let diffint = BigRational.ToBigInt(diff)
let innervint = BigRational.ToBigInt(innercirclevolume)
let radint = BigRational.ToBigInt(innercircleradius)
printf "dim: %i " e
printf "incircrad: %s " (BigRational.ToBigInt(innercircleradius).ToString())
printf "bigcube: %s " (BigRational.ToBigInt(bigcubev).ToString())
printf "inv: %s " (innervint.ToString())
printf "diff: %s\n" (diffint.ToString())
)
System.Console.ReadLine() |> ignore
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