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Search Results for “morph-circle-into-line”

By Phil Todd
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)

Tags: polar, parabola

By Nick Halsey
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.

Tags: Calculus, Derivatives, Functions

By Phil Todd
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)

Tags: ellipse, polar

By Phil Todd
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.

Tags: ellipse, conic, focus

By Duncan
Similar Triangle Incenter
This problem showed up in a math competition. See what you can make of it.  

Tags: incenter, circle, similar-triangles

By admin
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.

Tags: Proof, circles, draggable, real-world, savonius

By Tom Laidlaw
The Goat and the Silo
A solution to the goat and silo puzzle with a rope longer than pi * R

Tags: Goat-and-silo-problem, involute-of-a-circle

By Phil Todd
Coffee Cup Caustic
You can move the light source and observe the changes in the reflected rays which form the caustic.

Tags: caustic, envelope, reflection, circle

By Faith
Soda Cantastrophy
Download app to see the effects of changing radius and rate of change on the area.

Tags: circle, radius, circumfrance, rate-of-change, related-rates, draggable

By Nick Halsey
Circles, Tangents and Nonagon Diagonals
You may want to see the heptagon version before attempting this one Every diagonal within a regular nonagon is drawn. Circles are centered at each intersection of diagonals along a vertical axis (these same constructions can be made nine times around the nonagon). Each circle can be tangent to at least 4 diagonals when the circle is at least 2 different sizes. Unnecessary diagonals have been hidden. Drag the green points to resize the circles. Can you find all 13 positions where a circle is tangent to at least 4 diagonals? Hint: sometimes the circle is not entirely contained within the nonagon. Ready for more? Check out the hendecagon version!

Tags: Nonagons, Circles, Diagonals, Tangents, Puzzler

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