# Search Results for “Proportional-point”

##### Polar Proportional Point and Circle Puzzler 2

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, s(*t*), and is located at the current value of

*t*. Adjust

*t*, or animate it by pressing ”go”. What is s(

*t*)? Look at the .gx source for the answer.

*Hint: if you look closely, s(t) can be seen in dark purple. It is a particular ”polar flower”.*

##### 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”.*

##### Polar Proportional Point and Circle Puzzler

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, r(*t*), and is located at the current value of

*t*. Adjust

*t*, or animate it by pressing ”go”. What is r(

*t*)? Look at the .gx source for the answer.

*Hint: if you look closely, r(t) can be seen in dark blue. It is a particular ”polar flower”.*

##### Double Transforming Pentagons

Two pentagons are nested within a third, regular pentagon (ABCDE). They are each defined by a point on each side of ABCDE; these points are proportional along their sides at functions of*. Determine the function of t that represents the proportionality of each point. Notice that both pentagons are congruent to ABCDE when*

**t***= 0 and*

**t****= 1.**

*t*##### Example: Clock

From "Creating HTML5 Apps with Geometry Expressions." Download the GX file to see how this app was made.##### 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.

##### 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.*

##### 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.