Wednesday, November 23, 2011

Rolling Regular Polygons around a Circle - (2) Polygonal Epitrochoid




(n = 3, k = 5/2, d = 0)


(n = 3, k = 5/2, θ = 0.5α, d = b)


(n = 3, k = 5/2, P lies on the border of the polygon.)
(The distance from P to the nearest vertex is 1/8 side length.)


(n = 3, k = 5/2, θ = 0.5α, d = 0.5b)


(n = 3, k = 5/2, θ = 0, d = 0.5r)


(n = 3, k = 5/2, θ = 0, d = 1.5r)


(n = 4, k = 4/3, θ = 0.25α, d = 0.5r)


(n = 4, k = 5/2, θ = 0.5α, d = 0.5b)


(n = 4, k = 5/2, θ = 0.5α, d = b + 0.7455a)


(n = 4, k = 11/2, θ = 0, d = 0.5r)


(n = 5, k = 3, θ = 0, d = r + a)


(n = 5, k = 3, θ = 0.5α, d = b + a)


(n = 6, k = 3/2, θ = 0.5α, d = 0.5b)


(n = 7, k = 4/3, θ = α/3, d = 0.5b)


(n = 8, k = 4/3, θ = α/3, d = 0.5b)


(n = 4, k = 8/7, θ = 0.5α, d = 0.5b)


(n = 3, k = 8/7, θ = 0.5α, d = 0.5b)


(n = 3, k = 8/7, d = 0)


(n = 3, k = 12/5, θ = 0, d = 0 ~ r)


(n = 3, k = 12/5, θ = 0, d = 0 ~ r + a)


(n = 5, k = 6/5, θ = 0.5α, d = 0 ~ b + a)


(n = 3, k = 12/5, θ = 0 ~ α, d = r)


(n = 3, k = 12/5, θ = 0 ~ α, P lies on the border of the polygon.)


(n = 2.5, 3.5, 4.5, ..., 32.5, k = 21/20, θ = 0.5α, d = b)


( Mathematical software used: GeoGebra )


Related posts:

Saturday, November 19, 2011

Rolling Regular Polygons around a Circle - (1) Polygonal Epicycloid

(n = 5, k = 3)


(n = 3, k = 5/2)


(n = 6, k = 3/2)


(n = 4, k = 1/2)



n = the number of sides of the rolling polygon
a = the radius of the base circle
r = the circumradius of the polygon



(n = 3, k = 12/5)


( Mathematical software used: GeoGebra )


Related posts:

Wednesday, November 2, 2011

Monday, October 31, 2011

When Sine Met Line (當正弦遇上直線)

Sine met Line in the Hexagon Park last night.


They fell in love at first sight.


Sine is so beautiful even when she twists her body.


Line is so straight even when he relaxes his mind.


They danced together and had a good time.


They felt it was time to tie the knot.


What a colorful night!


( Mathematical software used: GeoGebra )

Saturday, October 29, 2011

Curvilinear Star Polygons (曲線化星形多邊形)

( Click on the image for a larger view. )



( Mathematical software used: Graph )

Tuesday, October 25, 2011

Clown (小丑)



( Mathematical software used: UDAV )

Tuesday, October 18, 2011

Superposing Star Polygons (2) (星形多邊形的疊合 2)

n = 3 ~ 26 (Click on the image for a larger view.)


n = 3 ~ 40


( Mathematical software used: GeoGebra )