Best way to determine if number is triangular number?
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I would like to test if an integer is a triangular number, and am wondering what the best way to achieve this is. I am aware that a triangular number is given by
x = n(n+1)/2
And that x is triangular if and only if 8x + 1 is a square.
However, what is the best way to actually test this in Matlab, giving consideration to floating point arithmetic?
I can think of methods like:
check x is an integer find if sqrt(8x + 1) is an integer to some floating point error
but there must be better ways.
More Answers (2)
Azzi Abdelmalek on 6 Sep 2012
Edited: Azzi Abdelmalek on 6 Sep 2012
for n=1:100 %for example
x = n*(n+1)/2;
n=size(result) % you will obtain n=100, which verify the formula
n=1:100 %for example
x = n.*(n+1)/2;y=sqrt(8*x+1)
all(y==round(y)) % if the result is 1, the formula is checked