


How To Build Cycloids
How to Draw an Inverted Cycloid
(It's easier than a regular one)
 Draw a line AB
 Draw a line segment CD equal to the desired
radius of the circle.
 Hold down Shift to select point C and then D.
 Choose Mark Vector from the Transform menu.
 Draw a point E on line AB for the center of the
circle.
 With point E selected, choose Translate from the
Transform menu.
 Choose Translate by Marked Vector and click OK.
 Draw a circle with center E passing through E'.
 Draw a point F not on line AB.
 Repeat steps 68 for point F.
 Draw a point G on the circle FF'.
 Draw the segment FG.
 Hold Shift to select FG and then point E.
 Choose Parallel Line from the Construct menu.
 Construct point H at the intersection of this
line and circle EE'.
 With point H selected, choose Trace from the
Display menu.
 Select point G, circle FF', point E, and line AB
in that order.
 Choose Animate from the Display menu, select
Once, and click OK.
How to Draw a Rightsideup Cycloid
 Draw a line AB
 Draw a line segment CD equal to the desired
radius of the circle.
 Hold down Shift to select point C and then D.
 Choose Mark Vector from the Transform menu.
 Draw a point E on line AB about at the center of
the screen.
 Select line AB and then point E.
 Choose Perpendicular line from the Construct
menu.
 With this line selected, choose Transform  Mark
Mirror.
 Draw another point F on line AB.
 With point F selected, choose Transform 
Reflect.
 Translate point F' by the marked vector CD.
 Draw a circle with center F' passing through F''.
 Draw a point G not on line AB.
 Repeat steps 1112 for point G.
 Draw a point H on the circle GG'.
 Draw the segment GH.
 Hold Shift to select GH and then point F'.
 Choose Parallel Line from the Construct menu.
 Construct point I at the intersection of this
line and circle F'F''.
 With point I selected, choose Trace from the
Display menu.
 Select point H, circle GG', point F, and line AB
in that order.
 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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