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Exploring Some Geometric Themes

The big picture

Every flattened box on the table now folds back into a box.

Eight ideas about solids and fractals
IdeaHow it goes
Faces, corners, edgesA cube has 6, 8 and 12.
A netA flat plan that folds up. One flat piece per face.
Nets that failOf 35 ways to join six squares, 11 close into a cube.
ViewsFront, top and side. A cone gives a triangle and a circle.
Prisms and pyramidsPrism on n sides: n + 2, 2n, 3n. Pyramid: n + 1, n + 1, 2n.
Sierpinski triangleTake out the middle. Triangles left: 3 times more each step.
Koch snowflakeSides: 4 times more each step. Outline: 4/3 times longer.
Sierpinski carpetTake out the middle ninth. Squares left: 8 times more each step.

Part II, Chapter 4 is Exploring Some Geometric Themes. Read it next and find these ideas in it.

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This track

  1. 0 Start here
  2. 1 Faces, edges and corners
  3. 2 A flat plan that folds up
  4. 3 Six squares, and most plans do not fold
  5. 4 What you see from where
  6. 5 A relation hiding in the counts
  7. 6 A shape inside itself
  8. 7 What each stage really does
  9. 8 The carpet, and fractals around us
  10. 9 The big picture
  11. 10 Track quiz

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