Triangular numbers: Difference between revisions
Added Go
Thundergnat (talk | contribs) m (Add summation of Teterahedrals to Pentatopics formulas, rearrange formulas a bit) |
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;* [[Pascal's_triangle|Related task: Pascal's triangle]]
=={{header|Go}}==
{{trans|Wren}}
{{libheader|Go-rcu}}
{{libheader|bigfloat}}
I've had to use a third party library to calculate cube roots as the big.Float type in the standard library doesn't have a function for this. The results (to 24 d.p) are the same as the Raku example with the exception of the tetrahedral root for the largest integer which differs in the last three places.
<syntaxhighlight lang="go">package main
import (
"fmt"
"github.com/ALTree/bigfloat"
"math/big"
"rcu"
)
func main() {
t := make([]int, 30)
for n := 1; n < 30; n++ {
t[n] = t[n-1] + n
}
fmt.Println("The first 30 triangular numbers are:")
rcu.PrintTable(t, 6, 3, false)
for n := 1; n < 30; n++ {
t[n] += t[n-1]
}
fmt.Println("\nThe first 30 tetrahedral numbers are:")
rcu.PrintTable(t, 6, 4, false)
for n := 1; n < 30; n++ {
t[n] += t[n-1]
}
fmt.Println("\nThe first 30 pentatopic numbers are:")
rcu.PrintTable(t, 6, 5, false)
for r := 5; r <= 12; r++ {
for n := 1; n < 30; n++ {
t[n] += t[n-1]
}
}
fmt.Println("\nThe first 30 12-simplex numbers are:")
rcu.PrintTable(t, 6, 10, false)
const prec = 256
xs := []float64{7140, 21408696, 26728085384, 14545501785001}
root := new(big.Float)
temp := new(big.Float)
temp2 := new(big.Float)
one := big.NewFloat(1)
two := big.NewFloat(2)
three := big.NewFloat(3)
four := big.NewFloat(4)
five := big.NewFloat(5)
eight := big.NewFloat(8)
nine := big.NewFloat(9)
twentyFour := big.NewFloat(24)
twentySeven := big.NewFloat(27)
third := new(big.Float).SetPrec(prec).Quo(one, three)
for _, x := range xs {
bx := big.NewFloat(x).SetPrec(prec)
fmt.Printf("\nRoots of %d:\n", int(x))
root.Mul(bx, eight)
root.Add(root, one)
root.Sqrt(root)
root.Sub(root, one)
root.Quo(root, two)
fmt.Printf("%14s: %.24f\n", "triangular", root)
temp.Mul(bx, bx)
temp.Mul(temp, nine)
temp.Sub(temp, new(big.Float).SetPrec(prec).Quo(one, twentySeven))
temp.Sqrt(temp)
temp2.Mul(bx, three)
temp2.Sub(temp2, temp)
temp2 = bigfloat.Pow(temp2, third)
root.Mul(bx, three)
root.Add(root, temp)
root = bigfloat.Pow(root, third)
root.Add(root, temp2)
root.Sub(root, one)
fmt.Printf("%14s: %.24f\n", "tetrahedral", root)
root.Mul(bx, twentyFour)
root.Add(root, one)
root.Sqrt(root)
root.Mul(root, four)
root.Add(root, five)
root.Sqrt(root)
root.Sub(root, three)
root.Quo(root, two)
fmt.Printf("%14s: %.24f\n", "pentatonic", root)
}
}</syntaxhighlight>
{{out}}
<pre>
The first 30 triangular numbers are:
0 1 3 6 10 15
21 28 36 45 55 66
78 91 105 120 136 153
171 190 210 231 253 276
300 325 351 378 406 435
The first 30 tetrahedral numbers are:
0 1 4 10 20 35
56 84 120 165 220 286
364 455 560 680 816 969
1140 1330 1540 1771 2024 2300
2600 2925 3276 3654 4060 4495
The first 30 pentatopic numbers are:
0 1 5 15 35 70
126 210 330 495 715 1001
1365 1820 2380 3060 3876 4845
5985 7315 8855 10626 12650 14950
17550 20475 23751 27405 31465 35960
The first 30 12-simplex numbers are:
0 1 13 91 455 1820
6188 18564 50388 125970 293930 646646
1352078 2704156 5200300 9657700 17383860 30421755
51895935 86493225 141120525 225792840 354817320 548354040
834451800 1251677700 1852482996 2707475148 3910797436 5586853480
Roots of 7140:
triangular: 119.000000000000000000000000
tetrahedral: 34.000000000000000000000000
pentatonic: 18.876646615928006607901783
Roots of 21408696:
triangular: 6543.000000000000000000000000
tetrahedral: 503.561826974636514048196130
pentatonic: 149.060947375265867484387575
Roots of 26728085384:
triangular: 231205.405565255836957291031961
tetrahedral: 5432.000000000000000000000000
pentatonic: 893.442456751684869888466212
Roots of 14545501785001:
triangular: 5393607.158145172316497304724655
tetrahedral: 44355.777384073256052620916889
pentatonic: 4321.000000000000000000000000
</pre>
=={{header|J}}==
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