Prologue

  • Ontario Grade 8
    • Curriculum and Connections: Patterning and Algebra
      • "Sort and classify quadrilaterals by geometric properties, including those based on diagonals, through investigation and using a variety of tools"
    • Ontario Curriculum
      • 8m40 (Overall Expectations) demonstrate an understanding of the geometric properties of quadrilaterals and circles and the applications of geometric properties in the real world
      • 8m41 (Overall Expectations) develop geometric relationships involving lines, triangles, and polyhedra, and solve problems involving lines and triangles
      • 8m43 (Geometric Properties) sort and classify quadrilaterals by geometric properties, including those based on diagonals
      • 8m45 (Geometric Properties) investigate and describe applications of geometric properties in the real world

Act I

  • Is there a way to fold a triangle so that it can be cut out by using only one cut?

Act II

  • Suggest attempting a simpler problem. Ironically, both of the following are easier.
  • Or maybe watch one failed attempt at cutting a triangle out in one cut

Act III

  • One possible solution for cutting out the triangle in one cut (view as image)

Sequel

  • Try cutting out a parallelogram in one cut. Try other polygons.
  • Can you cut out the letters of the alphabet using this theorem?
  • Check out Erik Demaine's awesome site
  • Numberphile explains the "Fold and Cut Theorem"

https://www.youtube.com/watch?v=ZREp1mAPKTM