Another view of my piece ...

Here are the images of my final piece:

Finally! A Dodecahedron-shaped Flowery Ball Thing!

Finally, after about two hours of folding and 5 hours of assembling the thing over and over again (until I got fed up and hot-glued it), I have a dodecahedron-shaped flowery ball thing.

It looks pretty much like it was supposed to, except it's a little bit crooked.

Next I'm going to try and make a dodecahedron using modular units from a pattern that I found and modified slightly. It should end up looking sort of floral, like a hydrangea or an agapanthus, hopefully ...

Fingers crossed.

Tetrahedron Form

Here's a tetrahedron form that I'm using in my art work:

It's made from three pieces of thick paper to hold the shape.

Each piece of paper is formed into a modular unit that has pockets and tabs that are able to be interlocked into other units in order to assemble a geometric shape.

Here's one of the parts for my Math & Art work. It's a pinwheel-shaped piece made with eight modular units.

A more successful butterfly ...

An experiment at making a butterfly ....

I don't think it worked particularly well.

Kusudama Piece Unfolded

This is the kusudama when it's unfolded back to a sheet of flat paper.

Kusudama Piece Side View

Kusudama Piece

This piece is called a kusudama.

Math & Art Essay

Here's the link to my Math & Art essay:

Math & Art Essay

The Huzita-Hatori Axioms:

1. Given two lines L1 and L2, a line can be folded placing L1 onto L2.
2. Given two points P1 and P2, a line can be folded placing P1 onto P2. Line equation is F(s) = P1 + s(P2 - P1).
3. Given two points P1 and P2, a line can be folded passing through both P1 and P2.
4. Given a point P and a line L, a line can be folded passing through P and perpendicular to L.
5. Given two points P1 and P2 and a line L, a line can be folded placing P1 onto L and passing through P2.
6. Give two points P1 and P2 and two lines L1 and L2, a line can be folded placing P1 onto L1 and placing P2 onto L2.
7. Given a point P and two lines L1 and L2, a line can be folded placing P onto L1 and perpendicular to L2.

These rules are also known as the Huzita-Justin Axioms, named for Humiaki Huzita and Jacques Justin, and Humiaki Huzita and Koshiro Hatori respectively. They are a set of rules related to the mathematical principles of origami.

Apparently, because these axioms have several solutions, the resulting geometries are stronger than those resulting from compass and straightedge geometries.

Project Focus

I have decided to focus on origami for my essay. I chose this because it’s not an obvious choice, and yet it seems to have much more to do with maths than anybody would usually suspect.

Origami came to my attention for this project because I found an article about Martin Demaine and his son Erik, who both work at MIT. Martin is an artist and sculptor, and Erik is a math prodigy who got into Canada's Dalhousie University at the age of 12 and completed his bachelor's degree at the age of 14.