# Nonstandard topics

- The usefulness of classification
- Ptolemy's theorem
- Proving the finger trick for multiplying by 9
- Proving the finger trick for multiplying 6-10
- Application of the LCM to gear networks
- Strategy for solving tangram puzzles
- Proving that the mean and mode are equal for an arithmetic progression
- Polite numbers
- The number of seconds in six weeks
- Deriving a polynomial from nth differences
- Why do we do the same thing to both sides?
- Proving there are exactly 8 semiregular tessellations
- Investigating cross-sections using GeoGebra
- Deriving formulas for the polygonal numbers
- Deriving the area formula for a regular 5-pointed star
- Pascal's pyramid
- Water pouring proofs
- Sums of angles by paper cutting
- Using a pen to sum interior angles
- Fractal fractions
- Converse of each corresponding angles theorem
- Maximum number of regions created by straight line and planar cuts