Figurate numbers: Difference between revisions

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 Most of us are familiar with triangular numbers, such as the arrangement of ten bowling pins in a triangle,
-. . . .
+&nbsp;&nbsp;&nbsp;.<br>
- . . .
+&nbsp;&nbsp;.&nbsp;.<br>
-  . .
+&nbsp;.&nbsp;.&nbsp;.<br>
-   .
+.&nbsp;.&nbsp;.&nbsp;.
 or square numbers,
-. . . .
+.&nbsp; .&nbsp; .&nbsp; .<br>
-. . . .
+.&nbsp; .&nbsp; .&nbsp; .<br>
-. . . .
+.&nbsp; .&nbsp; .&nbsp; .<br>
-. . . .
+.&nbsp; .&nbsp; .&nbsp; .
 but we don't necessarily know how their arithmetic works, or whether we can do the same with, say, pentagons.
 Can we learn something by telling a turtle how to make these numbers? Let's try.