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Search Results for “radius”

By Nick Halsey
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.

Tags: Circles, radius, proportional-position, puzzler

By Duncan
incircle radius
The radius of the incircle of a 3,4,5 triangle is 1. How about other Pythagorean triangles?

Tags: Pythagorean, incircle, radius, geometry

By Phil Todd
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

Tags: linkage, symmetry, curve

By Faith
Soda Cantastrophy
Download app to see the effects of changing radius and rate of change on the area.

Tags: circle, radius, circumfrance, rate-of-change, related-rates, draggable

By Nick Halsey
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”.

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

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 Nick Halsey
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”.

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

By Phil Todd
Incircle Radius
Can you relate the incircle radiusto the area and perimeter of a triangle?

Tags: incircle, NWMC

By Phil Todd
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 Archimedes Twins, and have the same radius. Can you work out what this radius is in terms of the radii of the purple circles?

Tags: Archimedes, Twins, circle, tangent

By Phil Todd
An Arbelos Theorem
The large circle in the diagram has radius 1.  Circles centered at A and B are tangent and each tangent to the large circle.  (The shape in between the circles is called an arbelos after the Greek for a cobbler's knife, which it apparently resembles.) BC is tangent to circle A and AD tangent to circle B. EF and GH are perpendicular to AB. Can you show that they are equal? Can you find an expression for their length in terms of the radius of circle A? Are they the same size as Archimedes "twins"

Tags: archimedes, arbelos, puzzler


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