centred polygonal numbers

the Ancient Greeks took to exploring number patterns derived from shape arrangements - possibly pebbles in the sand
Hypsicles of Alexandria (around 170 BCE) seems to have been one of the first
followed by Theon of Smyrna, Nichomachus and (reported at least in) Plutarch (around 100CE)

this work might be used to focus on number patterns but also could involve:

• developing quadratic nth terms
• solving simultaneous equations in 3 unknowns
• proof, involving triangular numbers

these resources focus on the centred polygonal numbers
a geogebra version with sliders

pictures created by Stefan Birkner

pictures created by Claudio Rockini