VISUAL GEOMETRY

Monday, June 2, 2025

Visual geometry, april/may 2025

Squares fitted in regular polygons

The process I initially follow , is to start with the regular polygon that I want to insert the squares in, draw a loose point in one of the sides and repeat on the other sides (same length). I draw the squares and move the original point until I find the meeting point of the squares. I use GeoGebra to make the drawings.

6n+3 series, visual geometry

Nonagon

6n+3 series, visual geometry

Visual geometry Jan25

Visual geometry Nov-Dec24

8,24,56,120,248,504,1016,2040,4088,8184,16376

,32760...

Visual geometry Aug-Sep 24

Visual geometry July24

Visual geometry June24

Squares and pentagons

3d geometry: heptagon

A geometric template to create a 3d geometric figure based on the heptagon:

A 3d shape created with heptagons

Visual geometry May 24

Geometric sphere

Square root 3 and 2

Nonagons and hexagons circular expansion:

(6n+7)*3

14,21

(6n+3)*3 series

(6n+5)*3 series

CUBES

Pentagons and squares filling of the plane

Pentagon and square filling of the plane,

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)

Friday, December 2, 2022

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?

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,

A construction of a regular nonagon with compass and marked ruler

Filling of the plane with pentagons and hexagons

11-gon and triangle

Tuesday, September 20, 2022

Mapping of regular polygons: octagon

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

√ 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

Sunday, September 18, 2022

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 : triangle

Thursday, September 15, 2022

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.