Search Results for “morph-circle-into-line”
Polar Point Parabola
The polar point of a line in a parabola is a common point to the chords defined by the common tangents through the points on the line. (Go to Full Screen if the green points won’t drag)
Basic Derivatives
Drag the point to see how the slope of the line relates to the x value of the point at which it’s tangent to the function. Can you figure out what the function is, based on the values of the x and y coordinates? The slope of the line can also be represented in terms of x; can you figure out what this representation is? This representation is the derivative of the entire function, not just at a single point. This is called the derivative of the function, and can be notated by, for example, the derivative of F(x) = F’(x), although there are many other notations as well.
Polar Point Ellipse
The polar point of a line in an ellipse is a common point to the chords defined by the common tangents through the points on the line. Play with it and the meaning will be clear! (Go to Full Screen if the green points won't drag)
Ellipse as locus of circle center
Take two overlapping circles. Examine the locus of the center of the circles tangential to both. It seems to be an ellipse with foci at the centers of the two circles. Prove it.
Circle Proof
This is the first app ever on Euclid’s Muse! It provides a draggable diagram to help illustrate a mathematical proof. This proof was discovered when modeling the Twisted Savonius style wind turbine from a top view. The full proof can be found here.
Coffee Cup Caustic
You can move the light source and observe the changes in the reflected rays which form the caustic.
