Euclid's Muse

your source for INTERACTIVE math apps

Search Results for “curve”

By Phil Todd
Maximum Area Triangle
The app uses a physical model to find the largest area triangle whose vertices lie on a smooth closed curve (defined by the red control points). The triangle defined by the tangent lines at the vertices is displayed, along with its medians. What do you notice about the maximum?

Tags: maximum-area

By Phil Todd
Inverted Trammel 2
Archimedes trammel draws an ellipse if used properly. Turning the trammel upside down gives a curve which is certainly not an ellipse.

Tags: Trammel-2

By Duncan
Roll one disc around the outside of another to create a curve...

Tags: epicycloid

By Duncan
Rolling Parabola
If you roll a parabola along the ground, what curve does its focus trace out? It might look like a parabola, but is it?

Tags: parabola, catenary, focus

By Duncan
Function composition challenge 6
Find f(x) such that f(sin(x)) matches the mystery curve.

Tags: function-composition, trigonometry

By Duncan
Function composition challenge 3
Can you find the function f, so that f(sin(x)) matches the grey curve?

Tags: function-composition, algebra-2

By Duncan
And the envelope please...
What is the phantom curve you see when you look at a set of lines, perpendicular to a set of chords through a common point in a circle?

Tags: envelope, circle, ellipse, hyperbola

By Phil Todd
Cam with reciprocating roller follower
Alter the parameters of the output curve and follower geometry, and see the cam shape change.

Tags: cam, sine

By Phil Todd
Rotating Cube
I saw a demo where a foam cube had a knitting needle inserted along the long diagonal, and was rotated by spinning the needle between the palms of the hands. The sides of the cube formed a curve... in fact a portion of a hyperbola, as this video illustrates.

Tags: Hyperbola, cube

By Duncan
Function composition challenge 5
Can you find the function f, so that f(sin(x)) matches the grey curve?

Tags: Function-composition, trigonometry

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