# Search Results for “puzzler”

##### Circle Radius and Proportional Position Puzzler

Five circles are centered proportionally around an ellipse according to functions of the variable*r*. Each circle’s radius is defined by the same function as its position, of

*r*. Can you figure out the five functions of

*r*which define the five circles? Download the .gx source for the answer.

**Tip**: if you press the ”go” button, r will animate at a constant rate and the ellipse will stay a constant size. If your drag the slider, note that the ellipse is not changing size or position, but the app is zooming in and out in order to display everything within its window most efficiently.

*Hint: one circle’s radius and position are defined by*

**f**(r) = r.##### 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”.*

##### 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.##### 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.*

##### 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.##### 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.