Late but definitely worth the wait

Okay, so I ran out of green paper but you have to admit that this Sierpinski tetrahedral structure made out of 256 individual tetrahedrons is pretty impressive. Each edge of the structure is 64cm long so I have had to be careful carrying it around school – it just about fits through the doors!

Two of my students also constructed a beautiful topper for our Christmas tree. Again it was done properly using a pair of compasses and consists of equilateral triangles. There are three of the snowflakes taped together to create a sort of pyramid that sits on top of tetrahedral structure.

The topper is another example of a fractal and is called a Von Koch Snowflake. You start with an equilateral triangle and draw three more equilaterals, which have sides a third of the original, in the centre of the three sides. Now do the same on the twelve new sides and repeat as many times as you like as shown in the diagram below.

Our Van Koch Snowflake began with an equilateral triangle of sides 9cm. The next iteration used 3cm equilaterals and we stopped once we’d done the 1cm triangles as this was fiddly enough using a pair of compasses.

Mathematics really is beautiful.

Handmade Christmas Cards Received

I think I only received these three homemade cards for Christmas this year (ok, last year to be accurate) but I only sent shop-bought cards this year so I can’t complain!

This first one is made by Ruth using glass paints on acetate…

The second is a layered image card from Stephanie…

The last one is an embossed card from Sue…

Lovely crafting ladies! They are beautiful, thank you.

How to make a Sierpinski Christmas Tree

This Christmas tree (which is yet to be completed) is inspired by the Sierpinski triangle fractal. The image below shows the progression of the fractal at different levels of complexity.

 

The number of black triangles in each diagram forms the geometrical progression 1, 3, 9, 27, … . It is an example of a fractal, which means that it has a self-similar structure and you can see the same pattern repeated over and over again.

My challenge with Year 10 this year was to take this design into three dimensions and create a fractal Christmas tree. We started with regular tetrahedrons constructed with a pair of compasses and a straight edge. In just an hour the girls managed to create one and a half level 4 fractals each containing 4³ = 64 tetrahedrons. They worked really hard and I promised them that somehow I’d get up to the next level of fractal, which has a total of 256 tetrahedrons in it. My Year 12s and 13s helped but I was only just over half way through at the end of the day and I’m still working on it now!

This is the first one that they created:

So, this is how to do it…

1. Create the nets of four tetrahedrons and sellotape or glue them together to make a larger tetrahedron. Do this by taping three tetrahedron together on the base and adding a fourth one above.

    

2. Remember that fractals require a self-similar structure so you now need to make four of these structures and tape together to make the next stage in the fractal.

    

3. Repeat this process as many times as you like. Create four of the current structures and tape them together in exactly the same way.

I’ll post the finished tree sometime in the middle of next week, then I just have to find an appropriate place to keep it safe. It’s going to be beautiful!

[Here's a link to the finished tree - it's huge!]

Knitted Baubles

These beautiful baubles were created by Lib as part of our Christmas present this year. Now I’m definitely going to have to actually put our Christmas tree up next year. Homemade baubles and homebrewed beer – well done and thank you, Mr and Mrs Haigh!

    

My First Ever Curve Stitching - 1991

It would appear that I started curve stitching at the age of nine…

I really don’t remember doing it and I was very impressed that my work is obviously constructed accurately with a pair of compasses. I found this piece of work, which is dated on the back, in Nan’s collection of keepsakes. She hadn’t kept a huge amount but the bits and bobs she had kept were cherished.

Here are two cards that I had made for her at various times:

    

Ruth made the next one and also painted the beautiful Barn Owl (sorry about the flash) for us to give her one Christmas…