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[[Pascal's triangle]] is a triangula array of numbers which is well-known in mathematics. The number at the n-th row and r-th column in the array is the value of combination :<texcode> {n \choose k} </texcode> or <texcode> \binom{n}{k} </texcode>.
More detailed explanation, you may read wikipedia.
* '''[https://en.wikipedia.org/wiki/Pascal%27s_triangle Pascal's Triangle in Wikipedia]'''
We draw Pascal's triangle using MetaFun and Lua. It can be done by the help of Hans.
First, we define a function to calculate the combination with Lua.
== lua code for calculation ==
The functions MP.p_ncr(n,r) and MP.p_ncr_x() are provided for better and simpler code.
<context source=yes mode=mkiv>
\startluacode
local function fact (n)
if n <= 0 then
return 1
else
return n * fact(n-1)
end
end
local function ncr(n,r)
return fact(n)/(fact(r)*fact(n-r))
end
userdata.P = {
fact = fact,
ncr = ncr,
}
function MP.p_ncr(n, r)
mp.print(ncr(n,r))
end
function MP.p_ncr_x()
mp.print(ncr(mp.scan.pair()))
end
\stopluacode
</context>
== Drawing Pascal's triangle with lines ==
There are 3 different ways of calculating the value of combination tt.
<context source=yes>
\startMPcode
numeric n,r,u,dx,dy,tt,final; u := 1.8cm;
path p, q;
pair A,now;
A := dir(210)*u;
dy := ypart A;
dx := -2*(xpart A);
for n=0 upto 4:
for r=0 upto n:
% tt := lua("mp.print(P.ncr(" & decimal n & "," & decimal r & " ))");
% tt := lua.MP.p_ncr(n,r);
tt := runscript("MP.p_ncr_x()") (n,r) ;
now := n*A + (r*dx,0);
dotlabel(textext("$\displaystyle {" & decimal n & "\choose" & decimal r & "} = "& decimal tt & "$"),now);
draw (now+A) -- now -- (now+A+(dx,0));
endfor;
endfor;
\stopMPcode
</context>
== Drawing Pascal's triangle of numbers ==
<context source=yes>
\startMPcode
numeric n,r,u,dx,dy,tt,final; u := 1.2cm;
path p, q;
pair A,now;
A := dir(210)*u;
dy := ypart A;
dx := -2*(xpart A);
for n=0 upto 8:
for r=0 upto n:
% tt := lua("mp.print(P.ncr(" & decimal n & "," & decimal r & " ))");
% tt := lua.MP.p_ncr(n,r);
tt := runscript("MP.p_ncr_x()") (n,r) ;
now := n*A + (r*dx,0);
label(textext("$" & decimal tt & "$"),now);
endfor;
endfor;
\stopMPcode
</context>
Created page with " Pascal's triangle is a triangula array of numbers which is well-known in mathematics. The number at the n-th row and r-th column in the array is the value of combination..."
[[Pascal's triangle]] is a triangula array of numbers which is well-known in mathematics. The number at the n-th row and r-th column in the array is the value of combination :<texcode> {n \choose k} </texcode> or <texcode> \binom{n}{k} </texcode>.
More detailed explanation, you may read wikipedia.
* '''[https://en.wikipedia.org/wiki/Pascal%27s_triangle Pascal's Triangle in Wikipedia]'''
We draw Pascal's triangle using MetaFun and Lua. It can be done by the help of Hans.
First, we define a function to calculate the combination with Lua.
== lua code for calculation ==
The functions MP.p_ncr(n,r) and MP.p_ncr_x() are provided for better and simpler code.
<context source=yes mode=mkiv>
\startluacode
local function fact (n)
if n <= 0 then
return 1
else
return n * fact(n-1)
end
end
local function ncr(n,r)
return fact(n)/(fact(r)*fact(n-r))
end
userdata.P = {
fact = fact,
ncr = ncr,
}
function MP.p_ncr(n, r)
mp.print(ncr(n,r))
end
function MP.p_ncr_x()
mp.print(ncr(mp.scan.pair()))
end
\stopluacode
</context>
== Drawing Pascal's triangle with lines ==
There are 3 different ways of calculating the value of combination tt.
<context source=yes>
\startMPcode
numeric n,r,u,dx,dy,tt,final; u := 1.8cm;
path p, q;
pair A,now;
A := dir(210)*u;
dy := ypart A;
dx := -2*(xpart A);
for n=0 upto 4:
for r=0 upto n:
% tt := lua("mp.print(P.ncr(" & decimal n & "," & decimal r & " ))");
% tt := lua.MP.p_ncr(n,r);
tt := runscript("MP.p_ncr_x()") (n,r) ;
now := n*A + (r*dx,0);
dotlabel(textext("$\displaystyle {" & decimal n & "\choose" & decimal r & "} = "& decimal tt & "$"),now);
draw (now+A) -- now -- (now+A+(dx,0));
endfor;
endfor;
\stopMPcode
</context>
== Drawing Pascal's triangle of numbers ==
<context source=yes>
\startMPcode
numeric n,r,u,dx,dy,tt,final; u := 1.2cm;
path p, q;
pair A,now;
A := dir(210)*u;
dy := ypart A;
dx := -2*(xpart A);
for n=0 upto 8:
for r=0 upto n:
% tt := lua("mp.print(P.ncr(" & decimal n & "," & decimal r & " ))");
% tt := lua.MP.p_ncr(n,r);
tt := runscript("MP.p_ncr_x()") (n,r) ;
now := n*A + (r*dx,0);
label(textext("$" & decimal tt & "$"),now);
endfor;
endfor;
\stopMPcode
</context>
