Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Cycloid
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
== Related curves == Several curves are related to the cycloid. * [[Trochoid]]: generalization of a cycloid in which the point tracing the curve may be inside the rolling circle (curtate) or outside (prolate). * [[Hypocycloid]]: variant of a cycloid in which a circle rolls on the inside of another circle instead of a line. * [[Epicycloid]]: variant of a cycloid in which a circle rolls on the outside of another circle instead of a line. * [[Hypotrochoid]]: generalization of a hypocycloid where the generating point may not be on the edge of the rolling circle. * [[Epitrochoid]]: generalization of an epicycloid where the generating point may not be on the edge of the rolling circle. All these curves are [[roulette (curve)|roulettes]] with a circle rolled along another curve of uniform [[curvature]]. The cycloid, epicycloids, and hypocycloids have the property that each is [[Similarity (geometry)|similar]] to its [[evolute]]. If ''q'' is the [[product (mathematics)|product]] of that curvature with the circle's radius, signed positive for epi- and negative for hypo-, then the [[Homothetic transformation|similitude ratio]] of curve to evolute is 1 + 2''q''. The classic [[Spirograph]] toy traces out hypotrochoid and [[epitrochoid]] curves.
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)