47 lines
1.4 KiB
Text
47 lines
1.4 KiB
Text
function Get-Gcd($a, $b){
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if($a -ge $b){
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$dividend = $a
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$divisor = $b
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}
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else{
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$dividend = $b
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$divisor = $a
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}
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$leftover = 1
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while($leftover -ne 0){
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$leftover = $dividend % $divisor
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if($leftover -ne 0){
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$dividend = $divisor
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$divisor = $leftover
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}
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}
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$divisor
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}
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function Is-Heron($heronArea){
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$heronArea -gt 0 -and $heronArea % 1 -eq 0
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}
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function Get-HeronArea($a, $b, $c){
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$s = ($a + $b + $c) / 2
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[math]::Sqrt($s * ($s - $a) * ($s - $b) * ($s - $c))
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}
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$result = @()
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foreach ($c in 1..200){
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for($b = 1; $b -le $c; $b++){
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for($a = 1; $a -le $b; $a++){
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if((Get-Gcd $c (Get-Gcd $b $a)) -eq 1 -and (Is-Heron(Get-HeronArea $a $b $c))){
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$result += @(,@($a, $b, $c,($a + $b + $c), (Get-HeronArea $a $b $c)))
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}
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}
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}
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}
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$result = $result | sort-object @{Expression={$_[4]}}, @{Expression={$_[3]}}, @{Expression={$_[2]}}
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"Primitive Heronian triangles with sides up to 200: $($result.length)`nFirst ten when ordered by increasing area, then perimeter,then maximum sides:`nSides`t`t`t`tPerimeter`tArea"
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for($i = 0; $i -lt 10; $i++){
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"$($result[$i][0])`t$($result[$i][1])`t$($result[$i][2])`t`t`t$($result[$i][3])`t`t`t$($result[$i][4])"
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}
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"`nArea = 210`nSides`t`t`t`tPerimeter`tArea"
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foreach($i in $result){
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if($i[4] -eq 210){
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"$($i[0])`t$($i[1])`t$($i[2])`t`t`t$($i[3])`t`t`t$($i[4])"
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}
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}
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