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Constructions and Tilings

A square line from a point

A shelf must stand at 90° to the wall.

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A line, and a point Q off the line.
Step 1 of 4
  1. A line, and a point Q off the line.
  2. An arc from Q cuts the line at A and B.
  3. Equal arcs from A and B cross at Q and below.
  4. Rule through both crossings. It meets the line at 90°.

The rule

A perpendicular meets a line at 90°.

To draw a perpendicular, you need a segment on the line. Its perpendicular bisector must go through your point. On the line, make the point the middle of the segment. Off the line, pick ends that are equally far from it.

Point on the line: mark A and B, equal steps away. Strike equal arcs from A and B. Rule through both crossings.

Point off the line: strike an arc from the point. It must cut the line twice. Those two cuts are A and B. Bisect AB as before.

Example: a point is 26 mm above a line. A span of 22 mm falls short. A span over 26 mm cuts it twice.

Watch out!

If the arcs do not cross, the span is too short. Set the span to more than half of AB.

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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

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