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