Difference between revisions of "Manuals/calci/Pascal Triangle Fun"
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==Pascal Triangle and Figurate Numbers== | ==Pascal Triangle and Figurate Numbers== | ||
| − | PASCALTRIANGLE( | + | PASCALTRIANGLE(10) |
[https://en.wikipedia.org/wiki/Figurate_number] | [https://en.wikipedia.org/wiki/Figurate_number] | ||
| + | [https://www.mathsisfun.com/algebra/triangular-numbers.html Triangular Numbers] | ||
| + | |||
| + | [https://en.wikipedia.org/wiki/Tetrahedral_number Tetrahedral Numbers] | ||
| + | |||
| + | [https://en.wikipedia.org/wiki/Figurate_number Figurate Number] | ||
| + | |||
| + | <pre> | ||
figuratenumbers=(n,r)=>(n+r-1)!C!r; | figuratenumbers=(n,r)=>(n+r-1)!C!r; | ||
a=[1..10,0..10]@figuratenumbers; | a=[1..10,0..10]@figuratenumbers; | ||
a.parts(10) | a.parts(10) | ||
| + | </pre> | ||
==Lucas, Fibonacci, Golden Ratio Relationship == | ==Lucas, Fibonacci, Golden Ratio Relationship == | ||
Latest revision as of 12:33, 7 August 2020
Pascal Triangle Fun
Sierpiński triangle
//with 32
m=32;
pt=PASCALTRIANGLE(m).$(x=>x%2)
a=pt
.map(
function (r,i)
{
var prefix= (REPEATCHAR(" ",(2*m-(2*i+1))/2).split(""));
return(
prefix
.concat(r.join(", ,").split(","))
.concat(prefix)
)
}
);
(a);
Fibonacci and Pascal Triangle
FIBONNACI(100)
b=PASCALTRIANGLE(100)
b.map(
function calcfib(r,i,d)
{
var fib=0;
var j=0;
for(var xi=i;xi>=0;xi--)
{
fib+=isNaN(d[xi][j])?0:d[xi][j];
j++;
}
return(fib)
}
)
Pascal Triangle and Figurate Numbers
PASCALTRIANGLE(10)
figuratenumbers=(n,r)=>(n+r-1)!C!r; a=[1..10,0..10]@figuratenumbers; a.parts(10)
Lucas, Fibonacci, Golden Ratio Relationship
FIBONACCI(50) LUCAS(50) FIBONACCI(50) .pieces(2) .map(r=>r[1]/r[0]) GOLDENRATIO() LUCAS(50) .pieces(2) .map(r=>r[1]/r[0]) ROUND((GOLDENRATIO())^(1..10)) [(1+√5)/2,(1+√5)/2] ops.on; [(1+√5d100)/2,(1-√5d100)/2]
Pretty Pascal Triangle
m=10;
pt=PASCALTRIANGLE(m)
pt
.map(
function (r,i)
{
var prefix= (REPEATCHAR(" ",(2*m-(2*i+1))/2).split(""));
return(
prefix
.concat(r.join(", ,").split(","))
.concat(prefix)
)
}
);
Now we can use:
PASCALTRIANGLE(10,true)