Divide a Line Segment into a Whole Number of Parts

Geometric Construction with the Compass Alone

Construct segments 2, 3, 4, etc. times as small as AB.

Solution

Pick an arbitrary segment b and, for a given n, construct a segment with length a=nb (Problem #1). Let c be the length of the given segment. Use Problem #10 to find x such that a/b=c/x. x=c/n is the required length.


Problems (Use a compass only)

  1. Multiply a Line Segment by a Whole Number
  2. Reflect a Point in a Line Sgement
  3. Cross a Circle by a Line Segment
  4. Drop a Perpendicular to a Line from a Point
  5. Detect Collinearity
  6. Complete a Parallelogram
  7. Bisect an Arc
  8. Find the Points of Intersection of a Circle with a Line Segment
  9. Build a Square on a Given Side
  10. Find the Fourth Proportional of Three Lengths
  11. Find the Intersection of Two Straight Lines
  12. Divide a Line Segment into a Whole Number of Parts
  13. Find the Center of a Given Circle
  14. Bisect a given line
  15. Mascheroni Construction of a Regular Pentagon
  16. A Compass Only Construction - A Chord Tangent to an Inner circle

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Copyright © 1996-2018 Alexander Bogomolny

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