
Nick Halsey uploaded a new app: Double Transforming… 8 years, 2 months ago
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 t. 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…

Nick Halsey uploaded a new app: Pythagorean Theorem… 8 years, 2 months ago

Nick Halsey uploaded a new app: Polar Rose: Mathema… 8 years, 2 months ago
These flowers are constructed with polar rose functions, play with n and d to change the flower’s shape. Download the .gx source to check out the polar function.
A more useroriented version that lets you change the color of the flower and download the image can be found here: http://celloexpressions.com/misc/makeflowers/.

Nick Halsey uploaded a new app: Epic Circle Trace 3 8 years, 6 months ago
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.

Nick Halsey uploaded a new app: Epic Circle Trace 2 8 years, 6 months ago

Nick Halsey uploaded a new app: Polar Proportional … 8 years, 6 months ago
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…[Read more]

Nick Halsey uploaded a new app: Polar Proportional … 8 years, 6 months ago
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 da…[Read more]

Nick Halsey uploaded a new app: Polar Proportional … 8 years, 6 months ago
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…[Read more]

Nick Halsey uploaded a new app: Circle Radius and P… 8 years, 6 months ago
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 anima…[Read more]

Nick Halsey uploaded a new app: Demo 8 years, 7 months ago

Nick Halsey uploaded a new app: Vector Combinations… 8 years, 10 months ago

Nick Halsey uploaded a new app: Squeezing Twisted S… 8 years, 11 months ago

Nick Halsey uploaded a new app: Twisted Savonius Wi… 8 years, 11 months ago
The Twisted Savonius Wind Turbine has promising applications for rooftop usage, but its high cost has kept it unfeasible for widespread adoption. The Twisted Savonius Geometric Modeling project explored the geometric properties of the turbine’s shape, and proposed a more efficient method of construction and geometric design as a result.
This…[Read more]

Nick Halsey uploaded a new app: The Three Primary T… 8 years, 11 months ago
The three primary types of wind turbine, the Savonius VAWT, the Modern HAWT, and the Darrieus VAWT, are animated as if in operation.
I first created this model in Geometry Expressions two years ago and after sharing it on Wikipedia it became quite popular and has been reused in many places. I decided to create an updated version, which…[Read more]

Nick Halsey uploaded a new app: The Three Primary T… 8 years, 11 months ago
The three primary types of wind turbine, the Savonius VAWT, the Modern HAWT, and the Darrieus VAWT, are animated as if in operation.
I first created this model in Geometry Expressions two years ago and after sharing it on Wikipedia it became quite popular and has been reused in many places. I decided to create an updated version, which…[Read more]

Nick Halsey uploaded a new app: Chord Angle Theorem 8 years, 11 months ago
The chord angle theorem states that in an inscribed triangle (ABC) where A is the center of the circle and BC is a chord, and BDC is an inscribed triangle on the same chord, angle BDC must equal one half of angle BAC. Try changing the angle and moving point D and observe the theorem’s truth.
Note: the measure of angle BDC is being constantly r…[Read more]

Nick Halsey uploaded a new app: Cyclic Quadrilatera… 8 years, 11 months ago

Nick Halsey uploaded a new app: Geometric Top View … 8 years, 11 months ago

Nick Halsey uploaded a new app: Simple Similar Tria… 8 years, 11 months ago
Drag points A, B, and C to change the size and shape of the blue triangle, and its white counterpart that is similar (constrained by proportional SAS). Drag the Red point D to change the ratio in sizes.
Observe the multitude of calculated output lengths and angles, and how they match the proportion value, proving similarity, regardless of the…[Read more]

Nick Halsey uploaded a new app: Tridecagon Diagonal… 8 years, 11 months ago
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 13sided 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…[Read more]
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