Triangle Numbers on Ulam
A number n is said to be a "Triangle Number"
if we can arrange n number of objects into a solid triangle pattern:
(1,3,6 and 10 are triangle numbers)
The n-th triangle number can be
found with n = n* (n+1) / 2.
Therefore, the 3rd tri-number
is = 3*(3+1)/2 = 6
Below are some images of triangle numbers (along
standard and Mersenne primes) plotted onto a square Ulam Spiral grid..
The Tri-numbers show up in a striking spiral in green points.
The image on the right is intended
to be zoomed in on in a graphics package.
see the ulam
prime spiral page.
back to pulchritudinous primes