VISUAL GEOMETRY

Saturday, June 1, 2024

Visual geometry June24

Visual geometry, geometric drawings ,

Squares and pentagons

3d geometry: heptagon

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

A 3d image created with heptagons

Extended lines of regular polygons

Extended lines of regular polygons.

Looking at the first intersection of the lines extending from regular polygons which has the shape of a geometric star.

The polygons are arranged in a circle and the pattern repeated all around.

All the vesica piscis in those regular polygons are 4 regular polygons short of a full circle (Odd sided polygons) . In a triange for example the vesica piscis has two triangles , when a full circle would have 6. In a pentagon the vesica has 6 pentagons when the full circle has 10.

Triangle

Visual geometry May 24

Visual geometry May24

Geometric sphere

Triangular/hexagonal tessellation

Hexagon dissections

Hexagon dissections and the 6n+3 series

I found the inspiration for this ones looking at https://people.missouristate.edu/LesReid/HS175.html , which can also be found at :

https://en.m.wikipedia.org/wiki/File:Equilateral_pentagonal_dissection_of_regular_octadecagon.svg

which is a pentagonal dissection of a 18-gon.

I made this one with a hexagon at the centre and adding nonagons from the radius lines. I then use parallel lines to find the rest of the points needed to complete the drawing.

The following hexagonal dissections/tessellations are made using the nonagon (9-gon) , 15-gon and 21-gon ( 6n+3 series).

A 3D geometric paper ball designed using the pentagon. Visual geometry.

Design, copy, paste, print, cut and glue.

Multiplication and regular polygons (1)

25 = 5x5

Regular polygons with odd numbers

Regular polygons with odd numbers.

Looking at the diagonals of regular polygons, in this case odd number regular polygons.

Today I'm looking at the 3 smaller regular polygons that can be constructed radiating from the centre, that can be encased with another bigger regular polygon .Diagonal lines and circles are used to find defining points.

Pentagons and squares

Square root 3 and 2

The nonagon, square root 3 and 2.

49-gon

49-gon and heptagons

25-gon and pentagons

19-gons

Wednesday, August 9, 2023

(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,

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