Polygonal Number Calculator

This gadget is more cool than any one person can appreciate. We asked our domesticated programmer Andrew to make a fun web app to show the geometric representations of numbers. Then we forgot to tell him to stop. Every so often we see a new feature appear and so we can only assume he is still locked away somewhere working on it. Andrew, if you can read this: it’s ok, you can stop working on this app now.

If you enter a number at the top it will show you various ways it can be represented. So if you put in 35 you can see it as either the 5th generalised pentagonal number or as the sum of two cubes (2 cubed plus 3 cubed). It will also point out that 35 is a semiprime (5 × 7). And goodness knows what else. Click the links to flick between them.

It also works in reverse, so at the bottom you can choose your geometric pattern and request any such number. If you find yourself with the sudden need for a graphical representation of the 9th centred heptagonal number, then this is the web app for you! (It’s 253 by the way.)

Seriously Andrew. You can stop now.

Generate the {{th(m)}}

Link to this pattern