Next pictures are related to the equilateral triangle: angles of the regular triangle (in SVG), extreme points of an equilateral triangle with rounded corners (in SVG) and the impossible object Reutersvärd triangle (in SVG).

# Angles of regular polygons

We can draw an equilateral triangle repeating FORWARD and RIGHT commands:

REPEAT 3 [ FORWARD 100 RIGHT 120 ]

More automatization could create the series of regular polygons, also with angles and other annotation, see the gallery and attached LibreLogo source code of the Wikipedia illustration:

# Extreme points

Next triangle is the result of the SVG transition of a mathematical illustration (the original picture was in the Wikimedia Commons category *Top 200 images that should use vector graphics by usage*).

The program of the picture draws 1 inch width outline with rounded corners, and in a second turn, narrow arcs with the appropriate radius.

HIDETURTLE PICTURE “Extreme points.svg” [ FILLCOLOR “SKYBLUE” PENCOLOR “SKYBLUE” PENSIZE 72 RIGHT 30 FORWARD 100 RIGHT 120 FORWARD 100 FILL PENCOLOR “RED” PENSIZE 2 REPEAT 3 [ CIRCLE [70, 70, 9h, 1h, 3] PENUP RIGHT 120 FORWARD 100 PENDOWN ] ]

Note: this illustration helped to find a rare SVG export problem, see the enlarged line end on the right picture and the LibreOffice bug report.

# Reutersvärd optical illusion

One of the best optical illusions, created by the Swedish artist, Oscar Reutersvärd at the age of 18, in 1934. The next program draws the left picture. To get the optical illusion, open the SVG file in LibreOffice Draw, and place two shapes (bottom sides of the first cube) to foreground manually (for example, by Ctrl-Shift-+).

TO tile LEFT 60 REPEAT 2 [ FORWARD 40 RIGHT 120 FORWARD 40 RIGHT 60 ] FILL RIGHT 60 END TO cube colors = [“GOLD”, “TEAL”, “TOMATO”] REPEAT 3 [ PENCOLOR colors[REPCOUNT-1] FILLCOLOR colors[REPCOUNT-1] tile RIGHT 120 ] END PICTURE “Reutersvärd triangle.svg” [ HIDETURTLE PENSIZE 0.1 RIGHT 30 REPEAT 3 [ REPEAT 3 [ PENUP FORWARD 60 PENDOWN d = HEADING HEADING 30 cube HEADING d ] RIGHT 120 ] ]

Note: Using narrow outlines (instead of “invisible” PENCOLOR) limits the SVG rendering problems in low resolution.

I barely try to resolve the little problem redrawing the last cube:

TO tile

LEFT 60

REPEAT 2 [

FORWARD 40 RIGHT 120 FORWARD 40 RIGHT 60

] FILL RIGHT 60

END

TO cube

colors = [“GOLD”, “TEAL”, “TOMATO”]

REPEAT 3 [

PENCOLOR colors[REPCOUNT-1]

FILLCOLOR colors[REPCOUNT-1]

tile

RIGHT 120

]

END

TO lastcube

colors = [“TEAL”, “TOMATO”]

right 120

REPEAT 2 [

PENCOLOR colors[REPCOUNT-1]

FILLCOLOR colors[REPCOUNT-1]

tile

RIGHT 120

]

END

HOME

HIDETURTLE PENSIZE 0.1 RIGHT 30

REPEAT 3 [

REPEAT 3 [

PENUP FORWARD 60 PENDOWN

d = HEADING

HEADING 30

cube

HEADING d

]

RIGHT 120

]

PENUP FORWARD 60 PENDOWN

lastcube