# Search Results for “Morph-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
##### Cycloid
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
##### Hypocycloid
Rolling a smaller circle inside a larger one draws a hypocycloid

Tags: Cycloid, curve, circle 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. 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 ##### 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.

Tags: 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