Square root 3 and 2

 

The nonagon, square root 3 and 2.

49-gon

49-gon and heptagons

25-gon and pentagons

 25-gon and pentagons

19-gons

 

19-gons

(6n+7)*3

 (6n+7)*3

14,21

(6n+3)*3 series

(6n+3)*3 series

(6n+5)*3 series

 (6n+5)*3 series

CUBES

 

CUBES

Pentagons and squares filling of the plane

 Pentagon and square filling of the plane,

Construction of geometric drawings

 There are many ways of constructing/drawing geometric pictures.

This one is based on a repetition of a  image . This image is then pasted in some particular points , in this case on the defining points of a regular polygon.

A lot of this images have been constructed before and are sometimes called polygon dissections. It is quite common in geometric drawing to reach to the same image using different ways of thinking.

Hexagons

Pentagon and 1/2 square root 3

 

Numbers:

Phi: (√(5) + 1) ÷ 2

1.53884176859

0.19320903898

0.09318924785

Nonagons (6n+3)

 

21-gons (6n+3)

 

The 6n+3 series

 What do the numbers 3,9,15,21,27,33,39,45,51,57,63,69,75,81,87,93,99... when it comes to regular polygons have in common?

hexagon art

Hexagon art

Construction of a nonagon with compass and marked ruler

 A visual construction of a regular nonagon with compass and marked ruler (neusis construction of a nonagon).

Start with a hexagon and triangle as a base, 

The nonagon

 Connecting the crossing points of nonagons (dot to dot)

54-gon

 54-gon

9-gon, 18-gon, 27-gon, 54-gon

9-gon, 18-gon, 27-gon, 54-gon

13-gon

 13-gon

13-gon

13-gon

Nonagon art

Nonagon art

Filling of the plane with pentagons and hexagons

Filling of the plane with pentagons and hexagons

11-gon and triangle

 

Mapping of regular polygons :decagon

Mapping of regular polygons :decagon

Mapping of regular polygons : dodecagon

Mapping of regular polygons : dodecagon 

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 ,

20°

 

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

14-gons

 

Decagons

Decagons

Heptagons

 

Heptagons

15-gon art design , 4n+3

 15-gon art , 4n+3

The nonagon and the square root 3

The nonagon and the square root 3

 

The nonagon and lines of 1 , 2 and square root 3. The circle in red has a radius of square root 3.