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

By Phil Todd
Parabola Polar Line
The locus of the intersection of tangents at the ends of chords of a parabola through a given fixed point is a straight line. This is called the polar line of the given point

Tags: parabola, polar

By Phil Todd
Polar Line
The locus of the intersections of the tangents at the end of chords of an ellipse which pass through a common point is a straight line. A bit of a mouthful, but play with the diagram and it will become clear.

Tags: locus, polar, ellipse, conic

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 Nick Halsey
Epic Circle Trace
A line passes intersects a circle at two points. Each point is located proportionally around the circle in terms of a given function of t. The path of the line’s movement is traced as t varies. Try changing/animating t. Can you figure out how each point is constrained, in terms of t? Look at the gx source file for the answer. Hint: look at the period of the movement, and how it changes as t changes.

Tags: Trace, puzzler, circle, proportional-points, functions

By Nick Halsey
Basic Unit Circle
This very basic representation of the unit circle displays the unit circle with an input for the standard angle θ in degrees (which controls the angle between the hypotenuse and the x axis). The outputs represent the other two sides of the triangle and give their lengths through decimals. A good investigation for geometry students is to have them test out different angles here, then compare the results to those testing the angles with sine and cosine on their calculators. This allows them to visualize the unit circle in a precise diagram rather than simply running inputs and outputs on their calculators.

Tags: Geomtery, Unit-Circle, Sine, Cosine

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
Circle in a trapezoid
When is it possible to draw a circle tangent to all four sides of a trapezoid?  

Tags: trapezoid, inscribed-circle

By Phil Todd
Circle Equation
Try to match a circle defined by its equation with one defined by its center and a point on the circumference. Drag for a hint.

Tags: circle, equation

By Phil Todd
Circle Involute
Find the area of grass accessible to a goat who is tethered to a circular silo.

Tags: Involute, Circle, Goat

By Andrew Zhao
Euclids Elements – Book 3 – Proposition 08
This proposition proves that line AD is longest, ED is shorter, FD is shorter than ED, and CD is even shorter.and that for any line there is only one other line with a point on the circle and a point at D that is equal. (Unless you drag it to somewhere it's not supposed to be) I like it because it’s colorful.

Tags: Euclid, Elements, Geometry, Triangle

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