Filling of the plane with pentagons and hexagons

Filling of the plane with pentagons and hexagons

11-gon and triangle

 

Mapping of regular polygons: octagon

 

√2+1 lines, one being the side of 
the regular octagon.

√ 2

√ 2

 a2 + b2 = c2.
(√ 2+1)2 +(1)2 = c2

Lines of one

 a2 + b2 = c2.
(√2/2)2 + (√2/2+1)2 =c2

Lines of 2

Mapping of regular polygons : hexagon

Mapping of regular polygons : hexagon

Mapping of regular polygons : pentagon

 The lines in a pentagon : one and the golden ratio ,

Mapping of regular polygons :square

 

Mapping of regular polygons :square

Mapping of regular polygons : triangle

 

Mapping of regular polygons

Mapping regular polygons(from my point of view) is mainly about measuring lines and segments of diagonal lines of regular polygons.  It is also about looking for  patterns occurring in regular polygons. In an octagon we can easily find ratios of square root 2, finding ratios and patterns in other polygons is much more difficult.

Lines of one in an octagon

49- gon

 49-gon and heptagon, squared numbers