Thursday, August 18, 2016

Fibonacci and Lucas and crochet

Over the years I've made soooo many scarves and in a few of them I've used the Fibonacci sequence. You may have heard the term Fibonacci numbers. Well, about a dozen years ago I researched this and wrote an article on it. I thought it might be interesting to revisit it so here it is again. 

Fibonacci and Crochet
©2004, 2016 Sandra Petit,
What exactly is Fibonacci?

Well, Fibonacci is not a WHAT, but a person. His name was actually Leonardo of Pisa, or Leonardo Pisano, also called Leonard Bigollo. Bigollo means traveler. According to what I’ve read, he called himself Fibonacci, short for Filius Bonacci. I think he did this to make it hard for us to look him up. LOL He was born in Italy in 1170, and died in 1250. That makes him a ripe old 80 at his death, depending on the actual date of birth.
So why do we care anyway?
Well, Fibonacci was a famous mathematician and he wrote some well known books such as Liber abaci. Until this time folks in Italy used Roman numerals. Ever try to add and subtract Roman numerals? Major pain. In this book, which was basically a primer in our current ten based (decimal) number system, he posed problems which were to be worked out by the reader. One of these problems gave birth to the now famous Fibonacci numbers.
In the Fibonacci sequence you add two numbers to get the third in the sequence, as I’ve done below. Note that Fibonacci excluded 0 in Liber abaci. I don’t know when it was added, but somewhere, somehow it was. This did not change the sequence since 0 + anything is that number.
0 + 1 = 1
Sequence: 0, 1, 1
1 + 1 = 2
Sequence: 0, 1, 1, 2
1 + 2 = 3
Sequence: 0, 1, 1, 2, 3
2 + 3 = 5
Sequence: 0, 1, 1, 2, 3, 5
3 + 5 = 8
Sequence: 0, 1, 1, 2, 3, 5, 8...
And so on. Those are the Fibonacci numbers. Of course, this can go on indefinitely, but for the purposes of crochet, there is a limit to how far we want to go. Even for an afghan we would hardly go over a certain number of rows. Can you imagine working 17711 rows or rounds?
Here are the first two dozen numbers so you can see what I mean. The sequence quickly escalates.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657
The Fibonacci sequence of numbers is quite useful for planning a pleasing-to-the-eye sequence of colors. It can help you in designing your crocheted items. Yep. It’s true.So you’re tapping your foot and wondering again, WHY do I care?
For example, squares. Given you have a round 1" x 1" square, and your gauge doesn’t change, you place two of these side by side. That’s the first two numbers (because you obviously can’t have a square 0" wide). The next number is two. You can place a 2" square on top of the two 1" squares. Now you have a square with sides 2" + 1". That would be 3, right? Place that 3" square on one of the sides. Now you have a new side with a 3" and a 2" square. The next number in the sequence is...5. So each new square has a side which is as long as the sum of the last two squares added. Say that real fast three times. Not easy, is it? Makes you sound like the Scarecrow in the Wizard of Oz. Remember that your tension has to be even so your gauge is correct, or it won’t work.
Another way to use the sequence is in determining the length of your afghan. If it is 34" wide, you can make it 55" (the next number in the sequence) long. Or is it’s 55" wide, you can make it 89" long. 21" x 34". You see what I’m saying. Does that mean you HAVE to make it 55" long if it is 34" wide. No. It is just one way of determining a length that might give a nice look. It is by no means the ONLY way.
There is another set of numbers we can also use. These were defined by the French mathematician, Edouard Lucas (1842-1891). As I understand it, he gave the name Fibonacci Numbers to the above sequence. Then he developed his own sequence. He began with 2, 1 rather than 0, 1. Then continued in the same manner as Fibonacci, adding the two digits to get the next. You get a different list of numbers, of course.
2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123
Just because I think it’s cool, note this. From the Fibonacci list, take one number, skip a number and add the next number. Your answer will be the the number between those two numbers on the Lucas row. For example, on the Fibonacci row start at the second 1, skip 2, add 3. 1 + 3 = 4, which is the number in the middle of 1 and 3 on the Lucas row.

Let’s see how else we might use this number sequence in our crochet projects. By the way, an afghan 47 x 76 would, to me, be perfect for a twin size bed. (The two numbers in the Lucas sequence)
One way we make our projects unique is in the colors we choose. Stripes is an oft used method of alternating colors. Why not try using the Fibonacci or Lucas numbers to vary the colors? There are so many different ways to do this.

Two rows of blue, one of white, three of red, four of white, seven of purple, then you might start over or go backwards. That’s the Lucas sequence. Of course you can choose different colors as well. How about the colors of the rainbow?
Rainbow Over You, God’s Blessings In View  - red, orange, yellow, green, blue, indigo, violet.
In case you’re wondering, indigo is the shade of color between blue and violet. According to (definition #3) it is: "The hue of that portion of the visible spectrum lying between blue and violet, evoked in the human observer by radiant energy with wavelengths of approximately 420 to 450 nanometers; a dark blue to grayish purple blue."
How else might you use the Fibonacci or Lucas numbers in your crochet? You could vary the stitches on each row. You might do 1 row of sc, 1 row of dc, 3 rows of sc, 5 rows of dc.
Or you could use different stitches. 1 sc, 1 puff, 2 sc, 3 puffs, 5 sc, 8 puffs ...
You can substitute any other stitch for the sc and puff. Try it with the cross-stitch or the front post stitches or any other. Of course if you are using a pattern with alternating stitch types on one row you have to make sure your foundation chain is correct.
If you’re varying the length of your stitches, as in making sc in one row and dc in the next, you will be able to see the change easier if you use different colors. However, you will still see a difference even if you use the same color. You might consider using the same color but an entirely different sort of stitch.
You don’t have to go the entire sequence either. You could choose two numbers from the sequence. Say 3 and 5 and alternate those. 3 cross-stitches, 5 dc, 3 cross-stitches, 5 dc and so on...
There are just any number of ways to use this sequence with a beautiful result.
There is one other sequence of numbers I read about but it is not very useful in crochet. It is called the Golden String, or the Infinite Fibonacci Word or the Fibonacci Rabbit Sequence.
The sequence is:   1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 ...

How do you get the numbers? Good question. I’m not sure I understand that myself, but here’s how I think it is done.
You start with 1 and 0. That’s easy enough to remember since we work with a decimal system.
Now rather than adding the numbers as you do in Fibonacci, you follow the rule.If the last digit is a 0, make the next digit a 1. If it’s not, then make the next digits 10
Let’s see if that works.
First numbers are 10. The last number in that sequence is a 0, so you add 1.
Sequence 101.

Now the last number is a 1, so you add 10.
Sequence: 10110
Now the last number is a 0, so you add 1
Sequence: 101101
Yep, that seems to work.
Since you can’t do ZERO rows of crochet, it’s not very helpful but I would feel remiss if I didn’t mention it since it is associated with the Fibonacci and Lucas numbers.
So there ya go. Fibonacci, Lucas, and Crochet.

Happy crocheting!

FAQ - Part 1

Doing a little housecleaning and was going through my FAQ. I can't actually make changes to the web site right now because I got a new computer and my old program doesn't work on it. The company has told me they no longer support that edition so still figuring that out. (I still have it on my old computer hard drive.)

Anyway, I thought I'd just post the FAQ and maybe you'll find something new and interesting. Some of it is specific to me and some is just general information, but all are my own opinions.

©2016 Sandra Petit
Do you do link exchanges? Yes and no. I ignore all those e-mails I receive that say "I put a link to your site on my site and I will be waiting for you to link to me." or "I linked to you. You have xx amount of time before your link is removed." Go for it. Link to my site if you find it useful. If I find your site useful, I’ll link to you too.
Why didn’t you answer my e-mail? You say you answer all e-mails. Well, I wrote you once and you didn’t answer! I do answer every e-mail I receive, even if it is to say I can’t help you. Sometimes e-mail goes into my spam box and I don’t see it. I get hundreds of spam items in each of my half dozen accounts so I rarely go through it unless I’m expecting something. Other times I do answer an e-mail and the e-mail I send out is returned to me as undeliverable. I usually will try once more, but then I give up. I don’t have time to keep trying to answer the same message over and over again. Also, sometimes a person will send me a message through a form, but not include their e-mail. I certainly understand the precaution of not handing out your e-mail address to just anyone, but I can’t provide an answer if I don’t have your e-mail.
If you don’t get an answer to your question within a few days, try again. I answer my mail daily unless bad weather or bad health prohibits me using the computer. Oh, and if you reply to my reply, please include the text of my answer as I get a lot of mail, and I don’t always remember your exact situation.
Can I send you something I’ve made so you can tell me what I did wrong? No. Your best option for help with a pattern is the designer or publisher of that particular pattern.
I can’t find this pattern. Can you help me? I’m sorry, but no. Unless it is a pattern I am interested in myself, I will just tell you to do a web search, which is what I would have to do myself. My search engine of preference is Google. I might also suggest you put a message on a message board or join a crochet list. When more eyes are looking, the chance of finding what you’re looking for is better.
I am trying to work a pattern and am having trouble. Can you help me to figure it out? Your best option for help with a pattern is the designer or publisher of that particular pattern. If that is not possible, I am very happy to help when the problem is one I can solve without actually working the pattern. I cannot make the items you are making in order to help you and sometimes it’s hard to tell the problem without doing so. I cannot take you row by row through your project though I’d love to do that if I had the time. If I can help, I will. If I can’t, then I’ll make a suggestion as to where you can find the answer – which is almost always the designer or publisher.
Can I send you a pattern, so you can re-write it for me in plain English? No.
Do you take donated yarn? Thank you for the thought, but no. I no longer take donated yarn.

Happy crocheting!

Wednesday, August 17, 2016


I was looking over my videos at YouTube today and made a reference list of them. I thought I'd share the list with you all so here it is. The numbers are how many videos in that topic. I took out the words "how to" so the more descriptive word would be listed.

adjustable ring - magic ring
alternative to the slip knot
back cross stitch
back popcorn stitch
back post double crochet (bpdc)
berry stitch
blueberries square
bobble stitch
bullion block stitch
Continuous join as you go (4)
crochet on the double (5)
cross stitch square
change yarn color in every stitch
crochet basics ((3)
cross stitch on afghan stitch
Diagonal Box stitch
Difference between puff, bobble and cluster
double crochet
double crochet decrease
double crochet increase
double crochet increase and decrease
double yo yo
filet cancer ribbon (6)
filet crochet
Filet crochet - fleur de lis
Filet crochet vertical 2012
finding the next chain
foundation single crochet
front cross stitch
front popcorn stitch
front post double crochet (fpdc)
front post triple crochet cross stitch (faux cable)
golden loop – gauge
Granny's daughter
half double crochet
herringbone half double crochet
hooks, yarn and other supplies for crocheting
into the turning chain
invisible finish off
Jacob's Ladder (2) (afghan)
Jacob's Ladder scarf (2)
Jeff's Sampler (5)
join new color / changing color
joining squares with a reverse sc
joining squares with a sc
joining squares with a slip stitch
joining squares with a whipstitch
joining squares with sc, ch 3
Lil's Knot
linked triple crochet
long double crochet
long single crochet (spike stitch)
Making a ring using chain stitches
measure a square or rectangle
More crochet basics (4)
parts of a chain in the foundation chain
picot stitch
plastic canvas bookmarkers
puff stitch
pull yarn through many loops on hook
rectangle granny (5)
reverse single crochet
Reversible granny square
Ripple (2)
ruffled scarf (2)
saltines - 2 round granny squares
sc2tog, dc2tog – decrease
simple fringe
Simple Hat (3)
single crochet
single crochet left handed
slip knot
slip stitch
spider stitch
spider stitch scarf
straight box stitch
surface crochet
swatch samples with different hooks
triangle (2)
triple yo yos
triple crochet (treble crochet)
triple crochet decrease
triple crochet increase
triple ripple
tunisian crochet (2)
turn your work
V stitch
work between stitches
work into a space
working along opposite end of the foundation chain
working in the round
working into a ring and how to make a ring
working into the same stitch, an increase
X stitch
Y stitch
yo yo

Happy crocheting!