Mathematical / geometric art

3 Circles project (oil paintings started end January 2019)

circles circles

Variations on intersections of three circles .... The above picture on the left shows 16 of the possible 165 cases. The above is acrylic on wood, 1.2 x 1.2 m, it's still in progress. I seem to have a lot of unfinished projects on the go right now! The picture on the right is an edited version of a file with 157 cases, which was created using python to write a latex/tikzpicture file. Here is a less pink version (blue lines). There are 8 cases missing from these computer generated files, since 8 can't be drawn with centers only at three allowed points.
I am aiming to paint all 165 variations on this circle theme; also there are many other ways of combining them and interpreting.
These are the first few of the series, which I've been working on starting in January 2019. I've been doing these on 30cm x 30cm (12inch x 12inch) canvas in oil. Doing different themes for groups of them. Each series has a different title. Also planning large works with many of these images on one piece, developing relations and transitions between them.

circles circles circles circles circles
circles circles circles circles circles
circles circles circles circles circles
circles circles circles circles
circles circles circles circles circles

4 circles and more variation

geometric 1

Koln design variations

In Koln cathedral in Summer 2017, I was fascinated by a particular mosaic design on the floor. Here are some of my interpretations.

geometric 1

Celtic knot series and other

geometric 1 geometric 2 geometric 3

Other activities:

Old pages on geometric origami design.
home ed maths club, incorporating a lot of maths arts crafts activities.
math computer game for children - for basic addition, multiplication for young children.

Origami tessellsations

I have recently designed and folded a few tessellations.... These are my own designs/developments; they are very simple, so may well have also been created by other people. The starting point generally comes from someone else, so I will try to credit where I can. The basic starting point is the square twist, which is more or less a kind of "tato" a traditional origami purse, but I believe developed by Kawasaki into tessellations.
My plan is to put up some photos, crease diagrams, and instructions too. If I manage to get anything done, will probably move to another page.
I am particularly interested in sequences of tessellation folds - for example, as below, the square on cross sequence can be continued. You can actually fold one level at a time, that is, after making the precreases, you can fold it to look like the first step, then continue to make it look like the second, and then continue and fold to look like the third picture. So it's not too hard.
I came up with this design myself, though it's very simple, so anyone who has independently already come up with it, no offence intended!

Origami square on cross sequence

Each sheet folded from 15cm square origami tant paper. This sequence can be continued, as explained in the description of the crease pattern. click on image for crease pattern/description
squares on crosses origami squares on crosses origami