Triangular numbers: Difference between revisions
Added XPL0 example.
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tetrahedral: 44355.77738407326
pentatopic: 4321
</pre>
=={{header|XPL0}}==
Some "interesting" loss of precision in the Pow function....
<syntaxhighlight lang "XPL0">real T(13, 30);
proc ShowRoots(X);
real X, SR, CR1, CR2;
[Format(1, 0);
Text(0, "Roots of "); RlOut(0, X); CrLf(0);
Format(7, 13);
Text(0, " triangular: ");
RlOut(0, (sqrt(8.*X + 1.) - 1.) / 2.);
Text(0, "^m^jtetrahedral: ");
SR:= sqrt(9.*X*X - 1./27.);
CR1:= Pow(3.*X + SR, 1./3.);
CR2:= Pow(3.*X - SR, 1./3.);
RlOut(0, CR1 + CR2 -1.);
Text(0, "^m^j pentatopic: ");
RlOut(0, (sqrt(5. + 4.*sqrt(24.*X + 1.)) - 3.) / 2.);
CrLf(0); CrLf(0);
];
proc Print(Str, Places, R);
int Str, Places, R, N;
[Text(0, Str); CrLf(0);
Format(Places, 0);
for N:= 0 to 29 do
[RlOut(0, T(R,N));
if rem(N/6) = 5 then CrLf(0);
];
CrLf(0);
];
int R, N;
[for N:= 0 to 29 do
T(1,N):= float(N);
for R:= 2 to 12 do
[T(R,0):= 0.;
for N:= 1 to 29 do
T(R,N):= T(R,N-1) + T(R-1,N);
];
Print("The first 30 triangular numbers are:", 4, 2);
Print("The first 30 tetrahedral numbers are:", 5, 3);
Print("The first 30 pentatopic numbers are:", 6, 4);
Print("The first 30 12-simplex numbers are:", 11, 12);
ShowRoots(7140.);
ShowRoots(21408696.);
ShowRoots(26728085384.);
ShowRoots(14_545_501_785_001.);
]</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: 119.0000000000000
tetrahedral: 34.0000000017903
pentatopic: 18.8766466159280
Roots of 21408696
triangular: 6543.0000000000000
tetrahedral: 503.5611663345480
pentatopic: 149.0609473752660
Roots of 26728085384
triangular: 231205.4055652560000
tetrahedral: 5431.9999386465400
pentatopic: 893.4424567516850
Roots of 14545501785001
triangular: 5393607.1581451700000
tetrahedral: 44355.7773765584000
pentatopic: 4321.0000000000000
</pre>
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