# Search Results for “radius”

##### 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.##### incircle radius

The radius of the incircle of a 3,4,5 triangle is 1. How about other Pythagorean triangles?##### 5 bar toy variable radius

The physical pattern drawing toy has a fixed gear ratio of 6:1, giving hexagonal symmetry to the drawings. In software it is easy to make the gear ratio variable. Press the radius button to change the radius of the turntable##### 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”.*

##### Archimedes Twins

The large circle is tangent to each of the purple circles, which are tangent to each other. The radius of the large circle is the sum of the radii of the purple circles. The Yellow circles are each tangent to one of the purple circles, to the large circle and to the common tangent of the two purple circles. The yellow circles are called the**, and have the same radius. Can you work out what this radius is in terms of the radii of the purple circles?**

*Archimedes Twins*