Mermaid Ragdoll

Having finished the laborious task of making our Christmas cards this morning, I ventured into the unknown this afternoon and made my first ragdoll. The pattern came from my mother-in-law's copy of Jane Bull's Crafty Dolls. It was really straightforward to follow and was fabulously easy for a beginner like me. I sewed the tail and the doll by machine inside out and stuffed the two pieces separately before sewing them together and adding all the details by hand. I can't wait to give her to Jess in the morning and find out what she's going to be called!

Book Review - Project Origami, Thomas Hull

Although there is a second edition of this book out at the end of this month (click here for details) I only just got this one for Christmas. It’s brilliant. Mind you, it is very definitely another one of those books that will appeal to the few of us who really are passionate about both Mathematics and crafting.

 

This book consists of 22 activities to inspire mathematical discovery in the classroom through origami. They range from “folding equilateral triangles in a square” to “rigid folds – Gaussian curvature and spherical trigonometry”. The worksheets and solutions are carefully produced and, at least at first glance, appear to be very useable while the pedagogy and extension sections are really interesting.

 

Although the material is primarily aimed at higher education Mathematics courses such as topology, number theory, calculus and graph theory, many of the activities can be adapted to suit high school Mathematics too. It will just take a bit of creativity, flexibility and plenty of enthusiasm to see them through.

 

Once they have constructed the net of a truncated icosahedron (football), I have often challenged my key stage 4 classes to colour the net so that no two faces of the same colour touch before cutting and folding the net into the 3-dimensional shape. This book has given me some further ideas on this topic and next week I’m going to attempt to introduce my Year 10s to the concept of planar graphs allowing them to demonstrate that four colours are sufficient to colour the ball without like-coloured faces touching.

 

Imagine putting a football (which is made up of 20 hexagons and 17 pentagons) onto the table, stretching the bottom face out and pushing the rest of the ball down flat onto the table so that none of the edges cross. This creates the following planar graph of a truncated icosahedron:

Note that this representation only shows 31 faces as the 32nd shape (the final pentagon) is stretched out underneath all of the others. This new 2-dimensional representation of a football clearly shows which faces touch each other, making the colouring problem significantly easier to tackle. It is easy enough to show that three colours are not sufficient so all they need to do is to colour the diagram with four colours so that no two adjacent shapes are the same colour and the outer hexagons are coloured using only three colours (so that the hidden pentagon can be coloured in the fourth colour). This is a simple exercise that they will have no problems with. It can then be extended to a 3-edge-colouring problem, which is even more interesting!

 

That’s why I keep asking for these kinds of books. They give me so much inspiration and help me to steer clear of hum drum textbook learning once in a while. I know it’s a niche market but while they keep publishing this kind of material I will keep buying it. Sorry David, my quirky library is ever expanding.

Geometrical Quilts

I’ve had this book for a long time having picked it up from a Tarquin stall at a Maths teacher training day some years ago. It was actually the only useful thing I picked up that day but that’s another story.

I love this book although I have never actually made a quilt from it. It’s full of beautiful designs and templates as well as inspiration for Maths lessons. I used two of the designs a few years ago in a Year 9 lesson revising ratio and proportion. Specifically I used the Fibonacci Series and Sierpinski’s Triangle quilts, which made for an interesting lesson for me if not the girls! ‘m often a little over-ambitious with my observed lessons!

Anyway, this book also features such delights as Penrose tiling, an Archimedian Spiral, the Lutes of Pythagoras and Von Koch’s Snowflake. There are so many ways to use them alongside lessons on tessellations, angles, fractals and rotational symmetry, as well as the ratio and proportion that I chose to use them for. One of these days I’m going to get the girls to recreate some of the designs using coloured paper to make amazing displays for room 16. This Maths and Crafting combination is a fascinating and powerful one. Honestly!

Crocheting Adventures with Hyperbolic Planes

Oh yes, I’ve finally got my hands on Crocheting Adventures with Hyperbolic Planes. Unlike Crafting by Concepts and  Making Mathematics with Needlework this does book doesn’t include lesson ideas. However, it is an award winner…

Again, it is a book that thrills me for it’s combination of two of my favourite things in life – crafting and Mathematics. What’s even better, these projects seem achievable even for a beginner like me. There are also interesting sections considering the use of hyperbolic planes in Science, Medicine, Computer Science, Music and Art.

I’m not going to go into too much detail but let’s see how many of these index items you recognise…

absolute geometry	annuli	asymptotic	catenary
catenoid	crochet	curvature	Erlangen program
exponential growth	geodesics	helicoid	hyperbolic geometry
hyperbolic plane	ideal triangle	Klein bottle	knitting
local intrinsic geometry	manifold	minimal surface	Mobius strip
mosaics	naalebinding	non-Euclidean geometry	orbifold
Parallel Postulate	patters	Poincare model	pseudosphere
radius	Riemann surface	simply connected	spherical geometry
Strands	sum of interior angles	torus	tractrix

 

That gives you a good idea of what’s involved and it really is sad how excited that list makes me!

Super-geek!

Look what arrived today!! :¬) This is yet another amazing book for the incredibly niche market that fits me so perfectly. It contains ten academic papers along with the crafting projects. Each chapter contains definitions, experiments and conjectures,  observations, theorems and corollaries, as well as advanced questions and teaching ideas for use with my students. I have the best end of term activities!! So, mostly to indulge the mathematical me, I’m going to briefly run you through the projects and principles.

1. Quilted Mobius Band

This chapter includes work on the Euler characteristic, homology groups, matrices, graph theory and map-colouring problems. The crafting item seems to be of little practical use but this particular topological structure will always hold a special significance to me. David proposed by writing the all important words on a Mobius strip and placing it in a bouquet of flowers for my 26th birthday.

2. Picking up stitches and diophantine equations

Other than the diophantine equations this paper uses algorithms and mathematical modelling as well as considering the existence and uniqueness of solutions to produce bi-directional knitted hats that do not require ‘finishing off’ at the end of the knitting process.

3. The Sierpinski variations: self-similar crochet

The Sierpinski triangle is a fractal consisting of mathematically similar triangles produced using a simple iteration. I’ve taught lessons on ratio and proportion based on the Sierpinski triangle. It also discusses Pascal’s triangle, binomial coefficients and modular arithmetic. It contains a couple of ideas for creating crocheted shawls.

4. Only two knit stitches can create a torus

Combinatorial analysis and curvature are the main discussion points in this chapter. However, they also consider a number of interesting questions such as, “How could the plain torus pattern be altered to change the ratio of the longitudinal and meridianal cycles?”

5. Symmetry patterns in cross-stitch

Whilst creating beautiful stitched patterns using the expected symmetries and transformations, the authors discuss Isometries of the Euclidean plane, group theory and how to use cross-stitch to see that tan(60o) is irrational. I love the two large patterns provided and will definitely make them at some point.

6. Socks with algebraic structure

As yet I have not mastered the art of knitting so it may be some time before I have the ability to tackle algebraic socks but I certainly can appreciate the modular arithmetic involved!

7. Fortunatus’s Purse

There is more fun to be had with topological manipulation in this chapter. The Klein bottle makes an appearance and we must consider colour theorems in the Euclidean plane and antipodal points on shapes such as dodecahedrons and truncated icosahedrons.

8. Knot cables and braids

Again, there are lots of patterns and ideas about knitting braids and cables. In the Teaching Ideas section they suggested that the braid group can provide useful examples that explore algebraic properties such as commutative and associative laws.

9. The Graph Theory of Blackwork embroidery

Eulerian graphs, Holbeinian graphs, multigraphs, Aragonian graphs, four definitions, four theorems and five corollaries, need I say more?! This chapter is a Mathematicians dream and I can’t wait to try this new craft. The final pieces are stunning.

10. Stop those pants!

Ever fancied knitting hyperbolic trousers? Well, now’s your chance. In this chapter the authors discuss the curvature of wearable trousers and how to model both constant positive and constant negative curvature from plastic.

Amazing, an inspirational, thought-provoking book that pushes all of my buttons. The next purchase will be Crocheting Adventures with Hyperbolic Planes but I guess I’d better get on and learn how to crochet first…

Crafting Clutter

Clutter is the curse of a crafter, or at least, it is the curse of this crafter. I find it very difficult to control my buying and I am always on the look out for new crafts to try (which inevitably require new and exciting equipment or materials). It goes without saying that I never turn down anything when it is offered to me…

Just before Christmas I was given a big bag full of fabulous retro fabrics and was very happy to give them a home with all of my newly purchased Ikea bargains. Until tonight, that home has been the lounge floor. I just couldn’t look at them any longer; I had to attempt to organise.

I store my crafting materials in boxes on a bookshelf in the spare bedroom, on another one in the lounge, in magazine racks on a desk in the lounge and in a chest of drawers in the lounge. In short, I need a bigger house with at least one room just for my crafting. It’s hardly a surprise that it quickly ends up in a mess and I can rarely find anything. I’ve done a lot of sorting this evening and was astonished that I needed a whole drawer for “cutting and sticking” and an entire shoebox for my ribbons, many of which are harvested from cards, chocolates and flowers given to me by my students – David’s not the romantic sort!! It’s getting a little ridiculous. I have card, thread, buttons and beads everywhere.

I’m a little ashamed of the amount that I have collected and so have made a late New Year’s resolution not to buy more for some time. I’m not prepared to put a timeframe on this but I do promise to try.

Now that I am almost certain my dear husband will have had enough of reading this post and returned to reading something bird related I shall divulge the second and much more important reason for organising my crafting things today. I needed to sneak a few new crafting books into the house…

These are not all brand new – some are old friends! What you see here is my entire crafting collection. I was given The Happy Hooker, Crafting by Concepts and one of the Compendiums of Cardmaking for Christmas. I bought Quilting In No Time from The Book People in November ( I think) but Kirstie Allsopp’s Craft and Fast Fabric Gifts arrived today. They look fantastic and I’m looking forward to trying out some of the projects. They were heavily reduced on Amazon so I couldn’t resist. I may even try something tomorrow if time allows.

Never any time in September

September is always a big month for me and unfortunately the only thing I get time to do at weekends is craft numerous UCAS references for my form whilst evenings are filled with marking until I find a routine that suits me better. So far this month I have found the odd hour to devote to the cross-stitch kite but I’m now getting really frustrated that I don’t have time for any other projects. I’ve satisfied myself with a little hemming this morning before I head out for a day of sailing!

As a Mathematics enthusiast, I regularly read Plus Magazine, which is a fantastic online publication. When browsing the site the other day, I stumbled across a review for a book that looks brilliant and was swiftly added to my Amazon wish list. I met the woman who’s written the review at a conference at Murray Edwards College back in July. If only I’d known she were a crafter – our conversation would have been much more varied!

Click the picture below to read more…

I have six more early deadline references to write in the next few days then I might just be able to do something about my urge to get crafting again. Fingers crossed.

Exciting Christmas Gifts

Many thanks to my parents-in-law who bought me a couple of excellent books from Search Press. I have one about iris paper folding and another about tea-bag paper folding. These are both crafts that I’ve done before, and thoroughly enjoy, but I was in need of some additional inspiration.
The cards that I’ve made so far were inspired by a good website that I use. It’s also great for the tea-bag papers that you can print at home… Circle of Crafters
I’ll keep you posted with new cards as I get the time to explore the books further.