# Euclid's Muse

## your source for INTERACTIVE math apps

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# Search Results for “Tangents”

##### Tridecagon Diagonals, Circles and Tangents
You'll want to start out with the heptagon and work your way up. This one's the same as all the others, just with a 13-sided regular polygon. Observe the tangencies to diagonals of circles centered at intersections of diagonals, when the circles are resized (by dragging). This is a smaller version that works well on most monitors (zoom in with two-finger touch). Bigger version here.

Tags: Tridecagon, diagonals, circles, tangents, intersections, puzzler, intricate, confusing, wow

##### 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

##### 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

##### 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

##### Tangents to Polar Functions
The purple curve has polar equation r=f(θ). A lies on this curve, and B is a point at the intersection of the tangent at A with the line perpendicular to OA. The red curve is the locus of B The grey curve is the curve r=g(θ) rotated by the quantity on the slider. What function g() will rotate to lie on top of the red curve?

Tags: polar-function, tangent, spiral, Archimedes

By Cannon
##### Death Star vs. Endor
An exciting mix of calculus and the hit series Star Wars, explore a problem the mighty empire could've faced with their final attempt to squash the rebellion.

Tags: Starwars, Derivatives, Normal-lines, Draggable, Fiction, Circles, Ellipses, Tangents

##### Circle isotomic
The circle isotomic is the locus of the reflections of a given point in the tangents to the circle. It is easy to convince yourself that it is also the envelope of the circles whose centers lie on the circle and which pass through the given point. The given point is C.  Try dragging it outside the circle.

Tags: isotomic, curve, envelope, limacon

##### Cardioid
Initially you see the cardioid as the caustic curve due to light reflecting in a circle.  (the caustic is the envelope of the reflected rays).  A second view of the cardioid is as the epicycloid formed by a point on the circumference of a disk rolling round a circle of the same radius.  A third view is as the orthotomic (locus of the reflections of the point in the tangents to the curve) of a point on the smaller circle.

Tags: clock