MEPX
Chapter 7 of 10All chapters
  1. 1Finding the rule
  2. 2Arithmetic sequences
  3. 3Geometric sequences
  4. 4Sequences worth knowing
  5. 5Primes and factors
  6. 6Writing the nth term
  7. 7Patterns from shapes
  8. 8Recursive rules
  9. 9Patterns outside mathematics
  10. 10Solving pattern puzzles

Chapter 7 of 10

Patterns from shapes

Numbers you can draw.

Triangular and square

Triangular numbers count dots stacked in a triangle: 1, 3, 6, 10. Square numbers count dots in a square. Adding two consecutive triangular numbers gives a square, which is obvious once drawn.

  • The nth triangular number is n times n plus one over two.
  • It also counts the handshakes among n plus one people.

Why drawing helps

Many identities that look like algebra become obvious as a picture. Rearranging dots is a proof, and often a clearer one than symbols.