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North Hollywood High Math Department

Curves


How To Build Cycloids

How to Draw an Inverted Cycloid
(It's easier than a regular one)

  1. Draw a line AB
  2. Draw a line segment CD equal to the desired radius of the circle.
  3. Hold down Shift to select point C and then D.
  4. Choose Mark Vector from the Transform menu.
  5. Draw a point E on line AB for the center of the circle.
  6. With point E selected, choose Translate from the Transform menu.
  7. Choose Translate by Marked Vector and click OK.
  8. Draw a circle with center E passing through E'.
  9. Draw a point F not on line AB.
  10. Repeat steps 6-8 for point F.
  11. Draw a point G on the circle FF'.
  12. Draw the segment FG.
  13. Hold Shift to select FG and then point E.
  14. Choose Parallel Line from the Construct menu.
  15. Construct point H at the intersection of this line and circle EE'.
  16. With point H selected, choose Trace from the Display menu.
  17. Select point G, circle FF', point E, and line AB in that order.
  18. Choose Animate from the Display menu, select Once, and click OK.

How to Draw a Right-side-up Cycloid

  1. Draw a line AB
  2. Draw a line segment CD equal to the desired radius of the circle.
  3. Hold down Shift to select point C and then D.
  4. Choose Mark Vector from the Transform menu.
  5. Draw a point E on line AB about at the center of the screen.
  6. Select line AB and then point E.
  7. Choose Perpendicular line from the Construct menu.
  8. With this line selected, choose Transform - Mark Mirror.
  9. Draw another point F on line AB.
  10. With point F selected, choose Transform - Reflect.
  11. Translate point F' by the marked vector CD.
  12. Draw a circle with center F' passing through F''.
  13. Draw a point G not on line AB.
  14. Repeat steps 11-12 for point G.
  15. Draw a point H on the circle GG'.
  16. Draw the segment GH.
  17. Hold Shift to select GH and then point F'.
  18. Choose Parallel Line from the Construct menu.
  19. Construct point I at the intersection of this line and circle F'F''.
  20. With point I selected, choose Trace from the Display menu.
  21. Select point H, circle GG', point F, and line AB in that order.
  22. Choose Animate from the Display menu, select Once, and click OK.

How to Draw a Prolate or Curtate Cycloid

Follow all the Cycloid instructions, except put point I inside (for a prolate cycloid) or outside (for a curtate cycloid) circle F'F'' on the constructed line rather than at their intersection.

What did you learn from this experiment?

Back to the tutorial index.


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