The best plot twists happen when a writer asks the question, “What if?” Poets play this game when seeking the perfect word. Scientific discoveries begin with “what if?”

A sure sign of a captain idea — one that quickens the imagination — is when it sprouts more ideas. As I studied the number pattern that lead to this graphic, I began to wonder.

Coloring only the odd triangles means I left the even triangles white. Even numbers are those which can be divided by two without having a remainder. What if I leave numbers which can be divided by three white? What about leaving out those divided by four? Five?

What you see below is the answer!

A sure sign of a captain idea — one that quickens the imagination — is when it sprouts more ideas. As I studied the number pattern that lead to this graphic, I began to wonder.

Coloring only the odd triangles means I left the even triangles white. Even numbers are those which can be divided by two without having a remainder. What if I leave numbers which can be divided by three white? What about leaving out those divided by four? Five?

What you see below is the answer!

This line of investigation generated more “what if” questions. What about hexagons? Squares? Diamonds (should I say, “Rhombii”)?

Which divisor do you prefer: two, three, four, or five? What shape is your favorite: triangle, hexagon, square, or rhombus?