Skip to content
Exit presentation

Constructions and Tilings

Start here

A floor by the stairs is tiled with six-sided shapes. No gaps. No overlaps.

Two moves: build with a compass, and tile a floor.

What this track covers

  • Copy a corner. No protractor (angle measurer) needed.
  • The perpendicular bisector. Every point is the same distance from two ends.
  • Split a corner. Two halves that match.
  • A parallel through a point. A line with the same gap everywhere.
  • A triangle from three lengths. Base, arc, arc, join.
  • A triangle from two lengths and the angle between. A second method.
  • What a tiling is. No gaps, no overlaps.
  • Why some shapes fit. Tile corners at one point add to 360°.
  • A square line. A perpendicular, at 90°, through any point.
  • 60°, 30° and 15°. One equilateral triangle, then bisect (halve) the corner.
  • A hexagon. Mark the radius again and again round a circle.
  • The tangram. Seven pieces, each a share of one square.
  • Tiling the whole floor. Which regular shapes fill a point.

Most of this is Chapter 6 of Part II, Constructions and Tilings. The two triangle methods are also in Part I, Chapter 7. Bring a compass.

Jump to lesson

This track

  1. 0 Start here
  2. 1 Copy a corner, no protractor
  3. 2 The line fair to both ends
  4. 3 Split a corner in two
  5. 4 A parallel through a point
  6. 5 Three lengths, one triangle
  7. 6 Two sides, the angle between
  8. 7 Covering a floor with no gaps
  9. 8 The corners must add to 360°
  10. 9 A square line from a point
  11. 10 60°, 30° and 15° with a compass
  12. 11 A hexagon from a circle
  13. 12 The tangram
  14. 13 Tiling the whole floor
  15. 14 Checkpoint: perpendiculars, 60°, hexagons and floors
  16. 15 The big picture
  17. 16 Track quiz

Other tracks