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Search Results for “Circle”

By Phil Todd
Circle isotomic and Conchoid
The circle isotomic with respect to P is the locus of the reflection of P in the tangents of the circle. The Conchoid is the locus of the points a given fixed distance from a point on the circle, and lying on a line through that point and P.

Tags: conchoid, circle, isotomic

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 Phil Todd
Simpson Line and 9 point Circle
The envelope of the Simpson line is seen to be tangent to the 9 point circle and to touch the concentric circle of 3 times the radius.

Tags: pedal-triangle, Simpson-Line, 9-point-circle, circumcircle

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
Epic Circle Trace 3
Four points are located proportionally around a circle, according to four different functions of t. A figure connecting the four points is traced through t. What are the four functions? Look at the .gx source for the answer. Tip: press "go" to animate t at a constant rate from 0 to ∏ and back, looped.

Tags: Proportional-point, function, circle, puzzler, trace, ellipse, sometimes-quadrilateral

By Nick Halsey
Epic Circle Trace 2
A triangle, defined by three points that are located proportionally around a circle by functions of t, is traced as t varies from 0 to 2Π. What are the functions of t, f(t), g(t), and h(t), that define the points D, E, and F, respectively? Hint: one of the functions is _(t) = t.

Tags: Trace, puzzler, circle, triangle, proportional-point, functions

By Larry Ottman
Circle Equation
This app allows you to practice writing the equation of a circle given a graph. (G-GPE 1)

Tags: Geometry, Common-Core, conic-sections, circle, equation

By Phil Todd
Reflection in a circle
Point A is midway between the center and the circumference of a circle.  BC is the reflection of AB in the circle.  What is the maximum angle of ABC?

Tags: circle, reflection

By Nick Halsey
Polar Proportional Point and Circle Puzzler 3
A circle is centered at the origin and its radius is defined by the distance between the origin and a point, P. P is defined by a polar function, u(t), and is located at the current value of t. Adjust t, or animate it by pressing ”go”. What is u(t)? Look at the .gx source for the answer. Hint: if you look closely, u(t) can be seen in dark gold. It is a particular ”polar flower”.

Tags: Polar-function, proportional-point, circle, radius, flower, puzzler

By Saltire Team
Morph a circle into a line
A morphing operation can be defined between any pair of parametric curves, open or closed. This app shows morphing a circle into a line segment.  Try moving the location of the destination line segment relative to the start of the circle’s parametrization by dragging the red dots to get different morph curves.

Tags: morph-circle-into-line, clocks, morph-clock-explained


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