# Euclid's Muse

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# Search Results for “cycloid”

##### Cycloid is the Brachistochrone
The inverted cycloid is defined by rolling a circle below a horizontal line and tracing the locus of a point on its circumference. You can see the definition by animating theta. You can make the cycloid pass through point B by changing its radius. Now press the Play button to watch the ball roll along the cycloid.  Compare its speed with a ball rolling down a straight line between A and B.

Tags: brachistochrone, cycloid, locus

##### Tautochrone pendulum
By allowing the pendulum to wrap around a cycloid curve, we can constrain its mass to follow another cycloid (this, technically is because the evolute of a cycloid is a cycloid).  As the cycloid is a tautochrone, the pendulums will have the same period no matter what their amplitude. Try dragging one mass close to horizontal, while leaving the other close to vertical.  Do you observe that they have the same period?

Tags: tautochrone, pendulum, brachistochrone, cycloid

##### Mass on a cycloid curve
Regardless of where you start the mass from (it can be dragged), it will oscillate with the same period.

Tags: cycloid, tautochrone

By Duncan
##### Cycloid
If we look beyond the circumference, what path does a point attached to a rolling wheel take?

Tags: Cycloid, curve, locus

##### Tautochrone
The inverted cycloid curve is a tautochrone:  put a marble anywhere on the curve and it will take the same time to reach the bottom. Try dragging the masses to different starting points and observe their behavior.

Tags: cycloid, tautochrone, brachistochrone

##### Beat the Brachistochrone
You can drag the two green points to change the shape of the red track.  Press play to watch a ball roll down the track and another ball roll down the straight line joining the end points. Experiment till you find the fastest track. Then press the Brachistochrone button to see the solution which Newton found. How close did you get to Newton's solution?

Tags: brachistochrone, cycloid

##### supertrammel
Archimedes Trammel has 2 sliders and 1 degree of freedom.  This ”supertrammel” has 3 sliders and still has 1 degree of freedom.  We made one out of wood and enjoyed playing with it. You can play with this electronic reproduction.

Tags: trammel, cycloid

By Duncan
##### Hypocycloid
Rolling a smaller circle inside a larger one draws a hypocycloid

Tags: Cycloid, curve, circle