Euclid's Muse

your source for INTERACTIVE math apps

Search Results for “curve”

By Duncan
Pascal's Limacon
Explore this interesting curve by changing lengths, then see the animation which creates the limacon.

Tags: Limacon, Pascal, curve-animation

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

Tags: Cycloid, curve, locus

By Duncan
Lissajous Figure
These were (easy and) fun to create on oscilloscopes in the dark days before computers.

Tags: Lissajous, parametric-curve

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

Tags: Cycloid, curve, circle

By Phil Todd
Four Bar Linkage
You can drag the vertices of the shadow linkage to alter its geometry. Can you create a linkage which draws a figure 8?  How about the letter D?  How close to a straight line can you get? If you like this, you might like my 4 bar linkage clock app.

Tags: 4-bar-linkage, curve

By Duncan
Cubic Spline
Many computer drawing programs use cubic splines to represent arcs. Our diagram shows how a spline can be constructed from 4 control points. We highlight that it is a moving average of two parabolas. These parabolas are exactly the string art parabolas.

Tags: spline, curve, parabola

By Amanda Snodgrass
Sinusoidal Tangent Mirrors
Look at a point on a sinusoidal curve (y=sin(x)) with a tangent line. Then, look at a point on the negative of your sinusoidal curve (y=-sin(x)) that is a mirror image of your first point. Then, notice that these mirror image points have mirror image tangent lines.


By Duncan
Function composition challenge 5
Find f(x) such that f(sin(x)) matches the mystery curve.

Tags: function-composition, trigonometry

By Duncan
Find the Multiple 4
Another mystery curve.  Can you find what multiple of sin(x) it is?

Tags: functions

By Duncan
Function Product Challenge 1
Can you define f(x) so that the red curve lies on top of the grey one?

Tags: functions, function-products, trigonometry

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