Manuals/calci/Pascal Triangle Fun

Pascal Triangle Fun

Sierpiński triangle

Sierpierski 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)

[1]

Triangular Numbers

Tetrahedral Numbers

Figurate Number

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)