Euclid's Muse

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Search Results for “point”

By Phil Todd
Hyperbola Polar Line
The polar line is the locus of the intersections of tangent lines at the ends of chords of teh parabola through a fixed point. Turns out to be conceptually important - not just a curiosity.

Tags: polar, conic, hyperbola

By Duncan
Chord Product
Examine the product of segments of chords through a common point.


By Duncan
circle intersections
Can you conjecture a formula for the product of the two distances from a point to a circle?

Tags: circle, tangent

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


By Nick Halsey
Spin the Chrome Icon!
This close replica of the logo/icon for Google Chrome, the world's most popular web browser, is built off of a geometric reconstruction of the logo's shape, allowing the logo to "spin" as you drag a point around its edge.

Tags: Google, Chrome, logo, icon, spin, drag

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 Andrew Zhao
Euclids Elements - Book 3 - Proposition 14
Creating a tangent on a circle given point A that is outside the circle.

Tags: Euclid, Elements, Geometry, Circle, Tangent

By Nick Halsey
Rotating Ellipses with Arcs
Now that you know how two ellipses can rotate such that they are tangent to each other and a third larger ellipse (see this app); the next challenge is to figure out how an arc placed on each ellipse can be constrained (with proportional points along the ellipses) such that each arc always covers half of the ellipse and one endpoint is on the tangent point of the two smaller ellipses.

Tags: Ellipses, conics, puzzler, arcs

By Duncan
Newton Raphson 3 iterations
Look at the first three iterations of the Newton Raphson method starting from a point you determine on a function you define. You'll see that when it's good it's very very good and when it's bad its awful.

Tags: root, function, Newton

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