Triangular numbers: Difference between revisions
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pentatopic-root: 4321.0 |
pentatopic-root: 4321.0 |
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</pre> |
</pre> |
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=={{header|Mathematica}}/{{header|Wolfram Language}}== |
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{{trans|Julia}} |
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<syntaxhighlight lang="Mathematica"> |
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(* Polytopic number generation function *) |
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Polytopic[r_, range_] := Binomial[# + r - 1, r] & /@ range |
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(* Triangular root function *) |
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TriangularRoot[x_] := (Sqrt[8 x + 1] - 1)/2 |
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(* Tetrahedral root function *) |
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TetrahedralRoot[x_] := N[((3 x + Sqrt[9 x^2 - 1/27])^(1/3) + |
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(3 x - Sqrt[9 x^2 - 1/27])^(1/3) - 1), 18] |
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(* Pentatopic root function *) |
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PentatopicRoot[x_] := (Sqrt[5 + 4 Sqrt[24 x + 1]] - 3)/2 |
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(* Displaying polytopic numbers *) |
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Do[ |
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name = Which[ |
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r == 2, "triangular", |
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r == 3, "tetrahedral", |
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r == 4, "pentatopic", |
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r == 12, "12-simplex" |
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]; |
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Print["\nFirst 30 ", name, " numbers:\n", Polytopic[r, Range[0, 29]]], |
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{r,{2,3,4,12}} |
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] |
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(* Displaying roots of specific numbers *) |
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nums = {7140, 21408696, 26728085384, 14545501785001}; |
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For[i = 1, i <= Length[nums], i++, |
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n = nums[[i]]; |
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Print["\nRoots of ", n, ":"]; |
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Print[" triangular-root: ", N@TriangularRoot[n]]; |
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Print[" tetrahedral-root: ", N@TetrahedralRoot[n]]; |
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Print[" pentatopic-root: ", N@PentatopicRoot[n]] |
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] |
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</syntaxhighlight> |
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{{out}} |
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<pre> |
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First 30 triangular numbers: |
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{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} |
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First 30 tetrahedral numbers: |
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{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} |
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First 30 pentatopic numbers: |
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{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} |
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First 30 12-simplex numbers: |
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{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} |
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Roots of 7140: |
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triangular-root: 119. |
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tetrahedral-root: 34. |
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pentatopic-root: 18.876646615928006 |
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Roots of 21408696: |
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triangular-root: 6543. |
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tetrahedral-root: 503.5618269746365 |
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pentatopic-root: 149.06094737526587 |
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Roots of 26728085384: |
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triangular-root: 231205.40556525585 |
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tetrahedral-root: 5432. |
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pentatopic-root: 893.4424567516849 |
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Roots of 14545501785001: |
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triangular-root: 5.3936071581451725*^6 |
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tetrahedral-root: 44355.777384073255 |
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pentatopic-root: 4321. |
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</pre> |
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=={{header|Nim}}== |
=={{header|Nim}}== |