Triangular numbers are figurate numbers
because they represent counting numbers as a geometric configuration of equally spaced points.
Playing with figurate numbers
can help making triangle and other geometric number-shapes.
Even without such investigations, early experience playing oware can provide both visual and tactile foundations for more formal explorations of certain mathematical ideas, including figurate numbers
and their properties, iterative and self-referential processes, and cellular automata.
This is exemplified in the student notes booklet of the "Euler Enrichment Stage" in a section that deals with figurate numbers
We pick up from there and use another neat way of adding lists of numbers to find a way of getting general formulae for figurate numbers and use Gauss's method to check it
The same technique can be applied to any other sequence of figurate numbers.
If in the previous issue of AMT (page 15) you didn't try to test Fermat's declaration about figurate numbers being used to express any number, then you might be in a better position to do so now, having found a few more types of figurate numbers with which to play.
So pick any number and find it to be a figurate number itself, or the sum of two or more of them.
Its definition is linked in history to our investigation of figurate numbers.
Figurate numbers were a concern of Pythagorean geometry, (I just love these links between numbers and shapes
What might the gnomons for the next shaped figurate numbers be?
We'll use his technique to revisit figurate numbers next issue