EUCLID CHALLENGE

Successful Response by Milton Mintz

May 10, 2002

Page 5: Trisection of Any Angle by Straightedge and Compass

 

Example Angle: 30º

  1. Draw line XY.

  2. Draw line GH perpendicular to line XY, intersecting line XY at point B.

  3. On line GH, from point B, towards point H, mark 4 segments; at the  end of the 3rd segment, mark point D; and at the end of the 4th segment, mark point D’.

  4. Center, point B, radius BD, draw an arc, intersecting line XY at points K and L, and line GH at point D.

  5. Center, point B, radius BD’, draw arc K’L’, intersecting line GH at  point D’.

  6. Bisect arc KD, mark point E---45°.

  7. Bisect arc ED, mark point F---22 1/2°.

  8. Bisect arc FD, mark point I---11 1/4°.

  9. Draw example angle ABC, 30°, with points A and C on arc KL
    Extend line BC to intersect arc K’L’ at point C’---A,C,C’---15    °.

  10. Bisect arc DC, mark point O (1/4 of angle ABC---7 1/2°

  11. Bisect arc DO, mark point P (1/8 of angle ABC)--- 3 3/4°.

  12. Draw line BP, extended to intersect arc K’L’ at point P’---3 3/4°.

 

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© Copyright 8/3/2000 Milton A. Mintz. All rights reserved.