Question: Length of the medians are integral numbers

September 15 2012 toandhsp 200

0

I created a triangle whose length of the medians are integral numbers. Please comment to me about my code.

> resrart:

ListTools[Categorize]:

N:=5:

L:=[]:

for x1 from -N to N do

for y1 from x1 to N do

for z1 from y1 to N do

for x2 from -N to N do

for y2 from -N to N do

for z2 from -N to N do

a:=sqrt(x1^2+y1^2+z1^2):

b:=sqrt(x2^2+y2^2+z2^2):

c:=sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2):

ma:=sqrt((b^2+c^2)/2-a^2/4):

mb:=sqrt((a^2+c^2)/2-b^2/4):

mc:=sqrt((a^2+b^2)/2-c^2/4):

if (y1*z2-z1*y2)^2+(z1*x2-x1*z2)^2+(x1*y2-y1*x2)^2<>0

 

 and type(ma, integer) and type(mb, integer)and type(mc, integer)

then L:=[op(L), [[0, 0, 0], [x1, y1, z1], [x2, y2, z2],[ma,mb,mc]]]: fi:

od: od: od: od: od: od:

nops(L);

L;

 

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