Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

Friday, 8 June 2012

Yarnbomb disasters!



Who loves a good yarnbomb?


I do!

This year I decided (albeit a little late due the general craziness of life) that I would join in on the fun of International Yarnbombing Day – 9 June 2012. My first EVER yarnbomb adventure!

I decided to draw upon a local festival for inspiration. Annually, on the first weekend in June, our little town holds “Scarecrow Festival”. Every year, people create and display scarecrows in their front yards. There are prizes for most inventive scarecrow and the flea markets make a killing!

With excitement and enthusiasm I raided my yarn stash, my craft cupboards and dragged out the trusty old hot-glue gun for a little added bling. Colour! Lots and lots of colour! And feathers! Piles and piles of them! But I will get to those later.

Before worrying myself with feathers and bling, I wanted a simple tree cozy. Nothing fancy... just a colourful strip wrapped around a huge tree... can’t be too hard right?

Like a demented woman keen on self denial I have, for the last four days, been working my fingers to the bone – literally! One may have described me over the last week to be some kind of [questionably] high functioning insomniac with an unhealthy obsession with YARN!

I calculated the number of stitches that went into the 20 cm wide and 4 metre long strip of crochet fabric to be wrapped around a branch... the whole thing was made in single crochet and chain stitches [weave stitch].

A 20cm square requires 841 stitches (excluding the foundation chain)

1 metre  of this crochet fabric (5x 20 cm) = 4205 stitches

All four metres of this THING = 16,820 stupid stitches!!!

Why did I do this again? Couldn’t I have chosen to make this strip of crochet fabric in a taller stitch?

Oh but wait... I get madder still. Back to the inspiration drawn from the festival... With all of these scarecrows about, I wondered (in this wildly irrational, slightly loopy mind of mine) about the poor little birdies all frightened by the - sometimes ugly, always quirky - Scarecrows of Milton. In come the feathers and the bling!

In total, 53 birds have been made. Each created from a basic HDC circle. They have felt beaks, feathers for wings and beads for eyes, all attached with the assistance of a hot glue gun. Each bird required 5 dots of hot glue. I’m certain I have burnt the tips of my fingers at LEAST once for each bird. That’s 53 little red dots, blisters and cuss words expelled!

Each complete bird consists of 55 stitches (80 including sewing them closed). Let’s see now...

55 x 53 = 2115
OR
4240 including finishing!

In four days, I have made a total of 21,060 complete stitches to create tomorrow’s yarnbomb!


Besides the sheer number of stitches required OMG the mess! Good Lord the mess! My living room, craft room and bedroom all look as if someone has spewed a revolting mix of yarn, brightly coloured feathers and the entire contents of a Diva store (!) every day for the last week – and they didn’t have the courtesy to at least clean it up!

When do the fairies get back from holidays? Maybe I should have paid them more?

The preparation for a yarnbomb has been fun, frustrating, awesome and challenging! Yes, I am poking a little fun at the Scarecrow Festival, but that does not mean that I don’t love it, or our town. On the contrary in fact! It means that I love it so much; that I am willing to put myself through the pain of the last few days to brighten up the place a bit on what is, despite the Festival a wintery weekend!

I think next year I will be more organised, and enlist some help! 

Sunday, 11 March 2012

Tangles, Tantrums and Times Tables

The Anatomy of a Spiral 






For a long time, designing the perfect spiral eluded me. I just couldn't seem to get them right. Sure, I could follow a pattern all-right, but DESIGNING a spiral confused me. I'd get lost on which row I was supposed to be working on and almost always ended up frogging anything that I had managed to do out of sheer frustration.



As usual, I like to be a little difficult and wanted a spiral with more than the usual three or four colours.
I wanted a spiral with eight colours. Again, I went in search of a pattern or image to work from (I'd rather not reinvent the wheel) but found NOTHING.  :(


Being the geek that I am, I've searched high and low for information about the anatomy of a crochet spiral- and the mathematics behind it all, but alas, I kept finding complicated equations for Hyperbolic crochet (not very practical for blankets or garments really - with the exception of a few cool ideas bouncing around in this nutty head of mine -  and the Fibonacci theory; none of which really makes sense unless you are AWESOME at algebra and geometry and can understand what all of those weird little symbols mean.

I searched for patterns, tutorials and numbers and finally came across something that made the anatomy of a spiral "CLICK". Ahhh! So that's it!

I eventually found a tutorial  from the amazing Elisabeth Wetsch of Nadelspiel , (a German knit and crochet cooperative) of a spiral granny square. which is a really cool take on the 'circle to square' that I had been playing with last week. The video is in Deutsch and my German is VERY rudimentary - I only had one year of lessons when I was in the 7th grade and that was a long time ago now. However, my language skills were good enough for me understand most of the video, for what I couldn't understand I just had to wing it.

So I reverted to my mathematics again. 

But where to start???? 

No, no, don't run away.... I couldn't understand anything unless the KISS (Keep It Simple Stupid)  principle applied to everything - All of the sums you need to do are very basic. If you know your times tables and/or can use a calculator, you'll be just fine. 


Step 1: 
Decide how many colours you want in your spiral. 
In my case, I wanted 8 colours. 
My first number is 8. 


Step 2: 
You will need a foundation circle to get you started. You need 3 stitches in your foundation circle for every colour you want to use. 
Multiply the number of colours by 3. 
In my case: 8 x 3 = 24
The stitch count of my foundation circle needs to be 24. 

Step 3: 
Make your foundation circle, applying the law of circle to ensure you get off to a good start. 
In my case, I used a Magic Circle, 
Row 1: 12 SC
Row 2: [INC, SC] x 6 (18sc) 
Row 3: [INC, SC x 2] x 6 (24 sc) slst to join. 
Now, you will notice in almost any pattern that calls for a spiral, the first 2 or three stitches are shorter than the rest. This is why I used Single Crochet as my foundation circle. The increase in the height of the stitches gives the spiral the 'lift' it needs to get out of being a plain old circle. 

Step 4: 
Regardless of how many colours you have chosen, using the equation  above for your foundation circle, when colours are added, each colour is worked in the same manner. 
Row 4: Section 1 - first colour (same as your foundation circle) *Ch 1, SC, HDC, 2DC into next stitch, place a stitch marker or pull up your loop so that stitches are not dropped *
For all additional sections/colours - join new colour into same st as 2DC using slst, then  repeat ** 
I used 8 colours, so each section in Row 4 is repeated 8 times. 






This is the foundation circle with the first coloured row (row 4).
Hahaha I know I know - you can only see 6 colours right??? Look closer. I used the white and rainbow yarn  twice! :) 

Step 5: 
This is the really cool part. You remember the Law of Circle? Increase (inc), 1, increase, 2, increase 3 etc. etc... 
It STILL applies to the spiral! 

What had me confused (before it clicked) was the differentiation between the increase for each section and how it just didn't seem to fit. 

We finished our first coloured row on an INCREASE, and this is our first round that builds upon the spiral,  so each section in your following round should start with ONE stitch into the ch 1 sp, then an INCREASE, then One stitch into the next stitch. I'll give you the example again using the 8 colour spiral. 

Row 5: *2HDC, DC into next st, 2DC into next st,* repeat ** eight (8) times (5 st in each colour)
See how we are applying the law of circle? inc, 1, inc, 1? 

Row 6: *DC into next st, 2DC into next stitch, DC into next 2st's, 2DC into next* repeat ** eight (8) times (7 st in each colour) 
See how we are applying the law of circle? inc, 2, inc, 2? 

Continue in this manner for as long as you like. 

Remember that your rows are worked on top of one another, so you if you want to check your work,  count on a single colour line the spaces between each increase. Your spiral should literally have from the first coloured row to the last (excluding your short stitches), the law of circles applied. You should have 1, inc, 2, inc, 3, inc, 4, inc, 5, inc, etc... all on the one colour. 

Can you see on the image below? 
Looking at the while row and counting backwards from the last increase, there are 5 double crochet's before another increase. Keep going backwards, you will see that there will be 4 Double Crochet before the next increase. 





When you have finished your spiral, as you work  the last row, slowly step down using shorter stitches to bring the spiral back to a true circle. For example, if your next row needs 20 stitch in each colour, work 10 stitches in your tallest stitches (DC in the case of the 8 colour spiral), then 5 stitches in  the next shortest stitch (HDC) then the last 5 stitch in SC, slst to join.

HINT: The only real problem you might incur when working in a spiral, is the entangled trap you set for yourself as you spin your work around! The yarn works itself around each other and can in some cases get so bad that you'll need to cut and rejoin your yarn if you aren't careful.






To avoid at least some of the tangles I've used 2 gift boxes with holes punched in the sides to try and keep the yarn tidy. I have four colours in each box, in order of their placement in the WIP. By keeping half of the yarn in one box, and the other half in another, and sitting with one box either side of my body as I work, the tangles are reduced (I said REDUCED - not eliminated altogether) and there wont be quite as many tantrums on your part.


Don't forget I love to see your work, so if this information has been useful and you have created something special, why not share your work on my Facebook page (there is a link at the top right of this page)?

Happy Crafting!

















Monday, 5 March 2012

Oh Yeah?!!!!

I have a confession to make.

I am a raging bull in a china shop if you even THINK about telling me I cant do something.

I will take the "NO", "IF", or "I bet you cant ......" that comes from your lips and I will run with it, toss it around by the tail, stick a pointy horn into its rear end and yell: "OH YEAH????! WATCH ME!"

Be warned. Don't stand in my way or make a noise if I am trying to do what it is that I have set out to do. You know... that thing you think I cant do? You might get hurt. It doesn't matter if the only person using these terribly negative words is the little devil inside my head. I'll still rip into it like it was a red rag in a bullfighting ring.

So when the little voice in my head said yesterday: "I bet you cant make a circle into a square, into a star, then back to a circle then a square again can you?" What do you think happened?

I DID NOT SLEEP A WINK last night. The yarn was flying the hook was raging and my brain was fried! But guess what! I managed it! Yeah! To that little voice in my head that said "I bet you cant" ..... UP YOURS!




I'll tell you, it's a good thing that this bull doesn't react to the word "dare". You never know what might have happened. Maybe I would have jumped out of an aeroplane with nothing but an umbrella for a parachute; or dived headlong into a river in the middle of the worst drought in history. If the bull reacted to Dares ..... Gah! I'd hate to think!


As you can imagine, I am exhausted tonight, so off to bed with my pretty little head. I'll try to post the pattern up for you all tomorrow.

Sleep tight!





Sunday, 4 March 2012

Accommodating Curves

Turning Circles into Squares

Something has been bothering me for a while now.... the mathematics behind crochet. I noticed in a forum last week that someone was asking about circles in squares- How can they find a way of doing them that enables them to design their own Afghan without using someone else's pattern, and using different sizes throughout. I did some searching on the internet and couldn't find ANYTHING that related to simple mathematics that could help us to design patterns.

It got me to thinking.... what IS the mathematics behind turning circles into squares easily? Could many different sizes be used in the same Afghan?

I've been stewing on this all week and guess what?!!!

The answer is YES!!!!!

We are not talking about hyperbolic crochet or polar angles here -  the mathematics is actually pretty rudimentary. I mean... all you need to know are your 4 times tables and the definition of "median".

FIRST you need to know to begin making circles into squares is ... the "law of circles" .

You can now make your circle as large as you like.... BUT - the stitch count MUST be divisible by four (4).

Image from Whipup

Double Crochet Circles are an easy example because your first row is a multiple of 4:
3x 4 = 12 

A square has 4 corners, to make a square from a circle with a stitch count of 12, a corner will be made in every 3rd stitch.

To keep the work flat, we still need to increase each round by 12 stitches, so we need to increase by 3 stitches in each corner. Easy right?

To make a 1 row DC circle into a square: 
When your circle is complete,  [ch3, dc, ch1, 2x dc] into same stitch (first corner made), dc into next 2 stitches, [2xdc, ch1, 2xdc] into next stitch (corner made), dc into next 2 stitches, corner, dc into next 2 stitches, corner, dc into next 2 st, slst to join.

Can you see the maths happening? 

To make a 2 row DC circle into a square: 
When your circle is complete, [ch3, dc, ch1, 2x  dc] into same stitch (first corner made), dc, hdc, sc, hdc, dc, *corner, dc, hdc, sc, hdc, dc*, repeat 3 times, slst to join.

Here is where it starts to get slightly more involved.... notice how there are now alternative stitches in the "squared" row? this is because in bigger circles, the widest part of the circle needs to be accommodated to achieve a square.

The MEDIAN of the stitches BETWEEN each corner will also be the widest part of the circle, so that is where the shortest stitch needs to be placed.

In the example above, the corner is made into every 6th stitch. The stitch count BETWEEN the corners is 5.

1, 2, 3, 4, 5

The Median is 3. This is where the shortest stitch is placed (Single Crochet). Notice that we have placed a HDC either side of the SC? This helps to accommodate the curve of the circle.

Are you still with me? Lets keep going.....

Making a 3 row DC circle into a square: 
 [ch3, dc, ch1, 2x  dc] into same stitch (first corner made), dc, hdc into next 2 st, sc into next 2 st, hdc into next 2 st, dc, *corner, dc, hdc into next 2 st, sc into next 2 st, hdc into next 2 st, dc*, repeat 3 times, slst to join.

In this example, the corner is made into every 9th stitch. There are 8 stitches between each corner. This means we have a pair of 'middle numbers'.

1, 2, 3, 4, 5, 6, 7, 8

This is why there are 2 SC flanked by 2 HDC.

So there you have it. The basic maths behind turning a circle into a square.

Now to answer the question about joining them in different ways:
THEORETICALLY (I haven't tried it, I avoid working in motifs wherever possible) these 3 sizes alone SHOULD be able to be joined in a few ways:

1 row circle/square made into a 4 patch block could be joined to a 3 row circle/square.

1 row circle/square made into a 9 patch block can be joined to 2 row circle/square 4 patch block.

Summary:
Make your circle.
Divide your stitch count by 4.
Make a corner into the (divisible number) stitch of your circle
Accommodate the curves by using shorter stitches in the middle of the space between 2 corners, and longer stitches towards the corners.


Post Script: 
The Larger your circle, the taller your corners will need to be.
Alternatively, you could add a 2nd row to your square round, still using accommodating stitches, to help keep your edge straight.

I love seeing your creations! Feel free to post pictures of your work on my Facebook page.
Feel free to message me with questions or suggestions.

Happy Crafting!