Triangular numbers: Difference between revisions
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tetrahedral-root: 44355.777384073256052620916903 |
tetrahedral-root: 44355.777384073256052620916903 |
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pentatopic-root: 4321</pre> |
pentatopic-root: 4321</pre> |
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=={{header|Wren}}== |
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{{libheader|Wren-fmt}} |
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{{libheader|Wren-big}} |
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<syntaxhighlight lang="ecmascript">import "./fmt" for Fmt |
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import "./big" for BigRat |
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var t = List.filled(30, 0) |
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for (n in 1..29) t[n] = t[n-1] + n |
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System.print("The first 30 triangular numbers are:") |
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Fmt.tprint("$3d", t, 6) |
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for (n in 1..29) t[n] = t[n] + t[n-1] |
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System.print("\nThe first 30 tetrahedral numbers are:") |
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Fmt.tprint("$4d", t, 6) |
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for (n in 1..29) t[n] = t[n] + t[n-1] |
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System.print("\nThe first 30 pentatopic numbers are:") |
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Fmt.tprint("$5d", t, 6) |
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for (r in 5..12) { |
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for (n in 1..29) t[n] = t[n] + t[n-1] |
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} |
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System.print("\nThe first 30 12-simplex numbers are:") |
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Fmt.tprint("$10d", t, 6) |
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var xs = [7140, 21408696, 26728085384, 14545501785001] |
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var digs = 16 |
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for (x in xs) { |
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var bx = BigRat.new(x) |
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System.print("\nRoots of %(x):") |
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var root = ((bx*8 + 1).sqrt(digs) - 1)/2 |
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Fmt.print("$14s: $s", "triangular", root.toDecimal(digs-5)) |
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var temp = (bx*bx*9 - BigRat.new(1, 27)).sqrt(digs) |
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root = (bx*3 + temp).cbrt(digs) + (bx*3 - temp).cbrt(digs) - 1 |
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Fmt.print("$14s: $s", "tetrahedral", root.toDecimal(digs-5)) |
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root = (((bx*24 + 1).sqrt(digs)*4 + 5).sqrt(digs) - 3) / 2 |
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Fmt.print("$14s: $s", "pentatopic", root.toDecimal(digs-5)) |
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}</syntaxhighlight> |
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{{out}} |
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<pre> |
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The first 30 triangular numbers are: |
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0 1 3 6 10 15 |
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21 28 36 45 55 66 |
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78 91 105 120 136 153 |
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171 190 210 231 253 276 |
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300 325 351 378 406 435 |
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The first 30 tetrahedral numbers are: |
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0 1 4 10 20 35 |
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56 84 120 165 220 286 |
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364 455 560 680 816 969 |
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1140 1330 1540 1771 2024 2300 |
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2600 2925 3276 3654 4060 4495 |
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The first 30 pentatopic numbers are: |
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0 1 5 15 35 70 |
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126 210 330 495 715 1001 |
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1365 1820 2380 3060 3876 4845 |
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5985 7315 8855 10626 12650 14950 |
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17550 20475 23751 27405 31465 35960 |
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The first 30 12-simplex numbers are: |
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0 1 13 91 455 1820 |
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6188 18564 50388 125970 293930 646646 |
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1352078 2704156 5200300 9657700 17383860 30421755 |
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51895935 86493225 141120525 225792840 354817320 548354040 |
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834451800 1251677700 1852482996 2707475148 3910797436 5586853480 |
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Roots of 7140: |
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triangular: 119 |
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tetrahedral: 34.00000000000 |
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pentatopic: 18.87664661593 |
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Roots of 21408696: |
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triangular: 6543 |
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tetrahedral: 503.56182697464 |
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pentatopic: 149.06094737527 |
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Roots of 26728085384: |
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triangular: 231205.40556525584 |
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tetrahedral: 5432.00000000000 |
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pentatopic: 893.44245675168 |
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Roots of 14545501785001: |
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triangular: 5393607.15814517232 |
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tetrahedral: 44355.77738407326 |
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pentatopic: 4321 |
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</pre> |