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 )

Curvilinear Star Polygons (曲線化星形多邊形)

( Click on the image for a larger view. )

( Mathematical software used: Graph )

Clown (小丑)

( Mathematical software used: UDAV )

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 )

Superposing Star Polygons (1) (星形多邊形的疊合 1)

Thirty-Two-Pointed Regular Star Polygons (n = 32)

( Mathematical softwares used: Graph, gnuplot )

Regular Polygons and Regular Star Polygons (正多邊形與正星形多邊形)

A polar representation of the regular star polygon {n/k} (or the regular polygon {n} when k = 1)
can be given by

Example files:

• Download a Graph example file here: Regular Polygons and Regular Star Polygons.
• Download a GeoGebra 3.2 example file here: Regular Star Polygon.
• Download a GeoGebra 4.0 example file here: Regular Star Polygon (for GeoGebra 4).

Cosine Star (3) (餘弦星 3)

( Click on the image for a larger view. )

( Click on the image for a larger view. )

( Softwares used: gnuplot, Ulead GIF Animator, GIMP )

Sine Star (3) (正弦星 3)

( Click on the image for a larger view. )

( Click on the image for a larger view. )

( Softwares used: gnuplot, Ulead GIF Animator, GIMP )

Cosine Star (2) (餘弦星 2)

( Click on the image for a larger view. )

( Click on the image for a larger view. )

( Softwares used: gnuplot, Ulead GIF Animator, GIMP )

Sine Star (2) (正弦星 2)

( Click on the image for a larger view. )

( Click on the image for a larger view. )

( Softwares used: gnuplot, Ulead GIF Animator, GIMP )