Monday, October 13, 2025

Visual representation of Fermat numbers

 Images that show a visual representation of Fermat numbers and how those images can be used to create tessellations and other types of mathematical art.

The images are a combination of  visual geometry and visual number theory with an art component.

The images are based on square grids

The starting point for the Fermat numbers (3,5,17,257...) is a 3x3 square grid.


Wednesday, October 1, 2025

Saturday, September 27, 2025

27-gon neusis construction

 The construction of a 27-gon is based on the general construction methods for 6n+3 polygons.

Starting with the nonagon, 18-gon (double the nonagon) , and we can find the defining lines to construct the 27-gon.


27-gon neusis construction
27-gon neusis construction


Monday, September 8, 2025

Monday, June 2, 2025

Saturday, April 12, 2025

Saturday, February 1, 2025

Thursday, January 23, 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.


Wednesday, January 1, 2025

Monday, November 25, 2024

Visual geometry Nov-Dec24

 


8,24,56,120,248,504,1016,2040,4088,8184,16376
,32760...




Thursday, August 22, 2024

Monday, July 1, 2024

Saturday, June 1, 2024

Visual geometry June24


squares and pentagons
Squares and pentagons


Wednesday, May 29, 2024

3d geometry: heptagon

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

A 3d image created with heptagons
A 3d shape created with heptagons


Friday, May 3, 2024

Friday, January 26, 2024

Square root 3 and 2

 Nonagons and hexagons circular expansion:


Wednesday, August 9, 2023

Tuesday, August 8, 2023

(6n+5)*3 series

 (6n+5)*3 series






Sunday, May 7, 2023

Saturday, February 25, 2023

Pentagons and squares filling of the plane

 Pentagon and square filling of the plane,


Monday, January 2, 2023

Pentagon and 1/2 square root 3

 

Numbers:

Phi: (√(5) + 1) ÷ 2
1.53884176859
0.19320903898
0.09318924785

Monday, December 12, 2022

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?

Friday, October 21, 2022

Thursday, September 29, 2022

Filling of the plane with pentagons and hexagons

Filling of the plane with pentagons and hexagons

Tuesday, September 27, 2022

Tuesday, September 20, 2022

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



Sunday, September 18, 2022

Mapping of regular polygons : hexagon

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 : pentagon

Saturday, September 17, 2022

Mapping of regular polygons :square

 

Mapping of regular polygons :square



Friday, September 16, 2022

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.


Lines of one in an octagon

Wednesday, September 14, 2022

49- gon

 49-gon and heptagon, squared numbers



49-gon

Monday, August 22, 2022

Monday, August 8, 2022

The nonagon and the square root 3

The nonagon and the square root 3
The nonagon and the square root 3

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