# Euclid's Muse

## your source for INTERACTIVE math apps

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

##### watts up
Watt's linkage is used to generate approximate straight line motion in automobile suspensions. Aee how it works. (Yes I'm using an alpha copy of GX version 3.2)

##### 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.

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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.

##### Euclids Elements - Book 1 - Proposition 01
The very first proposition, in which Euclid creates a equilateral triangle from a straight line by using two circles.

Tags: Euclid, Elements, Geometry, Equilateral, Triangle

##### Hendecagon Diagonals, Circles and Tangents
Before even attempting to understand this app, take a look at the heptagon and nonagon versions. It’s the same situation here, circles centered at intersection points of diagonals within the hendecagon. Drag the green points to resize the circles. Resize the circles so that they are tangent to at least 4 diagonals at the same time (this case is possible in at least two positions for each circle). How many instances can you find on this one? Notice a trend with this and the other versions? Now that you've got this one, check out the final installment, the tridecagon version.

Tags: Hendecagon, tangents, circles, diagonals, puzzler

##### Pedal Triangles
The loci of the midpoints of the sides of pedal triangles form ellipses as the pedal point moves around a circle.

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##### Tangential Circles
Can you come up with a formula for the radius of the third circle?

Tags: pappus, apollonian-circles

##### Circles, Tangents, and Heptagon Diagonals
Two circles are centered at intersection points of diagonals of a regular hepatgon. It turns out that circles centered at intersection points in regular polygons (particularly interestingly with polygons of odd numbers of sides) can be tangent to many other diagonals of that polygon. Try resizing the circles by dragging the green points. How many diagonals can each circle be tangent to? Ready for more? Check out the nonagon version!

Tags: Heptagon, circles, tangents, diagonals, geometry

##### proof without words
A proof that the locus of the center of a circle tangential to two nested circles is an ellipse.

Tags: ellipse, focus

##### September Problem
The radii of the small circles add up to that of the large circle. Why?

Tags: incircle, triangle