Heritage

I have recently found myself in a surplus of “baby” yarn left over from baby showers and baby-doll-loving cousins. There are four balls of bulky white and blue yarns and a half of a skein of this very thin, soft yellow yarn. In the daze following the completion of the bubbly crocheted piece, I realized I had seen that particular shade of yellow somewhere before.

Yellow.  (Yes, I did feel like Arthur Dent for a while.)

The weight of the yarn intrigued me as well. The baby blanket my grandmother had crocheted for me was yellow, but it wasn’t that fine of a yarn.

Then it hit me. It wasn’t my baby blanket, it wasn’t made by my grandmother and it wasn’t crocheted.

It was a baby blanket made by my great grandmother and it was knit. Though I’m not sure when it appeared there or for whom it was made, I found it safely tucked away in my mother’s linen closet one afternoon and became instantly enamored by it. She had made it in a tight gauge with squares; yellow borders around white stockinette spaces with sheep drawn in embroidery with black yarn.

Generally I don’t think that stockinette makes for a good blanket and embroidering a pattern onto it I like even less. You see both sides of a blanket, and there is no way to make the back side of an embroidered stockinette anything look pretty.

So why do I like this blanket?

Honestly, the fact that my great grandmother made it plays a big role. Also, no matter how hideously unlike the front the back may be, it is at least neat. The sheer cuteness of the little lambs doesn’t hurt, either.

Remembering that blanket, I went to my cup of many knitting needles and pulled out a pair of size 2  and just started knitting up a swatch of the yellow yarn.

It was a perfect match. I didn’t even have to look.

There is no way to describe how I felt, holding those knitting needles and that swatch in my hands. I had knitted with my mom before. I had crocheted with my grandma. My great grandmother left this world before I ever had the chance to do needlework with her but in that moment it was as if she were right there beside me clinking her needles together and crunching on an ice cube with me.

 

Understanding Imaginary and Complex Numbers

How can a number be “imaginary”?

First of all, we know that the imaginary number, i, is defined as being the square root of negative 1.

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We know that the square root of a number is something that when squared, or multiplied by itself, gets that number. Say two; two multiplied by two is four, so the square root of four is two. This process is backward, as you might have noticed; you know the answer before you can look for it. But is that the whole answer? What else when squared gives you four?

Negative two.

A negative number multiplied or divided by another negative number gives you a positive number. Squaring any negative number will give you the same positive number as the square of the absolute value of that number.

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The square of a negative number can never be a negative number and the square of a positive number can never be a negative number. The square of zero, as anything multiplied by zero, is still zero.So what is the square root of a negative number, if it can’t be positive, negative or zero?

Imaginary.

i is represented by a letter because it can’t be represented by a number. It is an invented concept that we (the culmination of human civilization) have come up with to help us move forward.

There may be some measure of faith when it comes to mathematics. Mathematicians find themselves hitting brick walls, then “invent” ways through them only to find later that those inventions were more like discoveries and insights a little deeper into the workings of the universe.

Basic Math Using i

i+i = 1*i+1*i = (1+1)*i = 2*i

i-i  = 1*i – 1*i = (1-1)*i  = 0

i*i = sqrt(-1)*sqrt(-1) = -1

i/i= 1

Complex Numbers

Complex numbers are numbers with both real and imaginary components. The general form looks like this:

a*i+b

where both a and b represent real numbers.

a = Re(a*i+b)                     read “a is the real part [of a*i+b]“

b = Im(a*i+b)                    read “b is the imaginary part [of a*i+b]“

Note:

5 = 0*i + 5                                                                      (example cn.01)

i = 1*i + 0                                                                        (example cn.02)

2*i = 2*i+0                                                                     (example cn.03)

Any number can be written as a complex number, but where 5 can be written as a complex number, 2*i is explicitly a complex number.

Okay, so now you know how to write complex numbers. How do you use them?

Addition/Subtraction

The one thing that you always need to remember is that the general form of a complex number is the closest thing you can come to adding a real number to an imaginary number.

5+i = 1*i+5                                                        (example ca.01)

5 + i + i = 2*i + 5                                             (example ca.02)

5+5+i = 1*i + 10                                             (example ca.03)

Notice a pattern? Associative Property to the rescue!

5+i+i                                                                   (example ca.04)

=(5+i)+i

= (i+i) + 5

= 2*i+5

5+5+i                                                                  (example ca.05)

=(5+i)+5

= i+ (5+5)

= 1*i+10

5+5+i+i                                                              (example ca.o6)

=(5+i)+(5+i)

=(i+i)+(5+5)

=2*i+10

(3*i+5)-(-2*i+4)                                              (example ca.07)

=(3*i+2*i)+(5-4)

=1+5*i

Multiplication

This is basically just foiling, treating i as a variable even though it technically isn’t. Thought it would never come in handy? Wrong.

(5+i)*(5+i)                                                          (example cm.01)

=5*5 + i*5 + 5*i + i*i

=25+5*i+5*i+(-1)

=10*i + 24

(1+2*i)*(3+4*i)                                                (example cm.02)

=1*3+ 1*(4*i) + (2*i)*3 +(2*i)*(4*i)

(2*i)*(4*i)

=(2*4)*(i*) thanks to the associative property of multiplication

=8*(-1) = -8

=3 +4*i + 6*i + (-8)

=(4+6)*i +(3-8)

=10*i -5

Note that on example cm.02 I took a part of the problem and solved it independently from the rest of the expression. If you ever have trouble doing all of your work on one page or all at once, it is useful to remember that you can use scrap paper and solve individual parts of a problem that is too complex to tackle in one go. Just remember to do it responsibly.

Division/Fractions

(10*i+5) / (5)                                                (example cd.01)

=(10*i/5)    +    (5/5)

=(10/5)*i     +    (5/5)

=2*i+1

(10*i-5)/(2*i+1)                                           (example cd.02)

This is not so simple without special tools. We need to factor. This is going to be broken up into three basic stages.

First, we’re going to assume that the solution is going to be a complex number that we’re going to need to solve for the real and imaginary parts of.

(2*i+1)*(a*i+b) = (10*i-5)                    cd.o2.1

(2*i)*(a*i) + (2*i)*(b) + (1)*(a*i) + (1)*(b) = 10*i -5

2*a*i*i + 2*i*b + a*i +b  = 10*i-5

(2*b +a)*i +(b-2*i)  =10*i -5

Second, we’re going to separate out the real part and the imaginary parts and solve them separately to get two equations in terms of “a” and “b”.

Re((2*b +a)*i +(b-2*i) )=Re(10*i -5)

2*i*a*i  +1*b   = -5

b-2*a = -5                                cd.02.2

Im((2*b +a)*i +(b-2*i)) = Im(10*i -5)

2*i*b + 1*a*i =10*i

a+2*b =10                                cd.02.3

Third, we’re going to treat the two equations we found in step 2 as a system of equations to solve for “a” and “b”.

b=2*a-5      is a way to re-write  equation cd.02.2

a+2*(2*a-5)=10     rewrites cd.02.3 substituting 2*a-4 in for b

a+4*a-10 = 10

5*a = 10+10

a=20/5 =  4                                      cd.02.4

b=2*a – 4

b=2*4-5

b=10-4=3                                         cd.02.5

(10*i-5)/(2*i+1) = (4*i+3)

Do you want to know what would have made this process so much easier?

Complex Conjugates!

This is one of the most important parts of a complex number; the complex conjugate of a number, (generally written as that number with a line drawn over it, but written here as underlined), is the same magnitude but has an imaginary part of opposite sign. Complex conjugates are a special tool created to make your life easier!

a*i + b   = b – a*i   = (-a)*i +b                                             (example cc.01)

Re(ai+b)=Re(ai+b)

Im(ai+b)=-Im(a*i+b)   and Im(ai+b)=-Im(ai+b)

Note:

a*i+b   *  a*i+b                                              (example cc.02)

= (a*i+b)*(b-a*i)

=(a*i)(b) + (a*i)(-a*i) +(b)(b) + (b)(-a*i)

=ab*i – ab*i  + (b)(b) + (a)(a)(-1)(i)(i)

=b^2  +  a^2

=Re(a*i+b)^2 + Im(a*i+b)^2

(a*i+b) / (c*i+d)                                             (example cc.03)

=(a*i+b)(d-c*i) / (c^2 +d^2)

which is useful because it not only cuts down on how many steps it takes to solve something, but makes messier fractions more manageable.

(7i-5)/(2i+3)                                                              (example cc.04)

=(7i-5)(3-2i)/(4+9)

=(21*i-10*i+14-15) /13

=(11*i-1)/13

=(11/13)*i +(-1/13)            <- (can you imagine doing that the other way?)

(10*i-5)/(2*i+1)                                                (example cd.02 revisited)

=(10*i-5)(1-2*i)/(4+1)

=(10*i-5 -2*10*i*i +10*i)/5

=(20*i +15) /5

=(4*i + 3)             <- (So much easier to find with specialized tools,no?)

The Complex Plane

The complex plane is very similar to the Cartesian Plane, except instead of the y axis you have the imaginary axis and instead of the x axis you have the real axis.

Generally, to plot (a*i+b), go up “a” and right “b” (down/left for respective negative values).

• Say a  and b are both positive: go up “a” and right “b”, (or down “a” and right “b” for the complex conjugate)
• Say a is negative but b is positive: go down “a” and right “b”, ( or up “a” and right “b” for the complex conjugate)
• Say both a and b are negative: go down “a” and left “b”, ( or up “a” and left “b” for the complex conjugate)

Special Note: There is also another way to write complex numbers, using exponents of the natural number, but this isn’t as important until calculus and will be revisited therein. Feel free to investigate on your own if you are curious.

Related articles

• Here be (mathematical) dragons (3quarksdaily.com)
• A Trip to Mathematics: Part IV Numbers (wpgaurav.wordpress.com)
• Absolute Value (mathematics) (egrejeen.wordpress.com)
• What is i^i? (superconductor.voltage.com)

Fail

As you can tell from the utter lack of recent posts, that I have failed at my grand scheme quite badly.

I would continue with more to say on the subject, but I don’t really feel like writing right now.

I just received two job offers from two different companies asking me to do the same kind of job. One was a scam. I don’t know if the other was, too… but even the job description sounds like one.

Yes, please give us your banking information and we’ll use you to launder any money coming into our business, (with all the assurances that it was completely legal, of course). We wire to you and then we wire from you to us. For your troubles, we’ll give you 6-10%.

What part of that doesn’t scream illegal? I can’t believe these companies, preying on the unemployed who are out there looking for legitimate and HONEST employment. It’s despicable!

No thank you. I’m an honest person looking for a chance to work and make a living, and I’m the only one I want messing around with my accounts.

cheating

It’s really late.

I really just want to pass out right now. My head is pounding and my thoughts refuse to organize themselves into a coherent idea.

I really wanted to cheat today. I did cheat. I posted an old image that I drew up and was willing to leave it at that.

I thought I had nothing else to give today, but looking back over that picture made me think.

This is cheating.

This made me think of the wedding I’m planning.

Boyfriend and I sat in WalMart for three hours for the sake of Black Friday shopping. Yes, there was much Christmas carol singing on my part,(I hate having to wait until after thanksgiving so I use all of the time I can). Beyond the caroling, there was a lot of joking and some surprisingly serious discussion.

This wasn’t the first time that we’d talked about getting married. Before I’m sure I was ready for marriage, we had a running joke that he and the groomsmen would wear kilts (for my pleasure, of course). He already had me look over an entire website of engagement/wedding rings to get a feel for what I’d like. We both agreed we wanted to live together before we were married. We’ve even talked names for kids!

Us getting hitched is kinda old news, but we’re still not formally engaged.

In Walmart that day, he moved the ring my grandmother gave me over to my left hand. Does that count as an engagement? It does to me, but I sincerely doubt that this would do it for our parents.

That is the problem with starting a new tradition: reconciliation.

We’re a pair of functional atheists, getting married. This is breaking new ground as far as our families are concerned. He has a church but isn’t a believer and I’m a believer but don’t endorse “holy” people or churches.  Who is supposed to wed us? Where?

The questions keep piling up, but answers seem few and far between. We both believe in marriage and are taking it very seriously, but it’s hard to separate what it is we believe in from what we find ridiculous and over-done.

Why You should learn Algebra

Very few children like mathematics, especially as they move forward into learning algebra. They will hit a wall, get frustrated and ask “Why do I have to learn this? Will I ever use this in real life?”  Unfortunately, adults tend not to have a response to these questions. It is common sense that you should know mathematics, but I know I haven’t run across a single person who has been able to make an argument that responds with these inquisitive and disgruntled children. To be completely honest, the reason why most adults don’t have an answer to this is because they asked these same questions when they were children and still haven’t found a satisfactory answer to it.

These questions have now existed for generations; it seems like quite a daunting task at this point, but it’s easier that you’d think.

Algebra is a tool. You aren’t learning algebra to learn algebra. You are learning algebra to learn how to simplify problems, how to group a set of problems and, most basically, how to think. It teaches you how to think quantitatively and how to rationalize relationships between two or more things.

Main Aspects of Algebra People have Trouble with:

•  Using letters to replace numbers.  This is an important concept, especially if you want to learn calculus, geometry, probability, statistics or how to write proofs.
• Using and understanding inequalities. This should be a basic concept; everyone understands 1<2, etc.  The problem comes in the combination of inequalities and either algebra or absolute values or both. This is important if you want to learn calculus or write proofs. (geometry?)
• Using equations with multiple variables. This is also important, and as basic as using letters to replace numbers as far as foundations go; it’ll be built upon in calculus, geometry, probability, writing proofs, sciences such as physics or chemistry or biology and computer programming.
• Using piece-wise functions. Piece-wise functions will be used most often with inequalities and graphing, and later in probability functions; it is a way of thinking about functions that you should try to master just because it will be useful. It will follow you to probability, calculus and writing proofs.
• Using matrices. I’ve always hated and struggled with matrices and I made the mistake of marginalizing them, only to hate myself later. They are vital if you ever need to learn linear algebra, cryptography, computer programming or computational physics.
• The ability to draw and read graphs of equations. If you are a visual learner, this should be easier for you to understand than just staring blankly at equations. If you aren’t, it is still a useful skill that will be vital if you want to continue on to calculus, probability,statistics, or sciences such as physics and chemistry. (Graphical computer programming comes to mind, too!)
• Understanding complex numbers. This is a tricky one, and most people think that there isn’t any real-world use for them; but there is. Theoretical physics (studying the workings of atoms and their parts) has found that sometimes the universe can only be explained mathematically by using complex numbers. Not that you will use them for this, in particular, but they will continue to come up in calculus, linear algebra, writing proofs and, again, theoretical physics.
• Understanding powers. This is an extension of multiplication; basically a way of simplifying multiplication. Like most simplifications in mathematics, though, they come with their own special rules. I would suggest that for each new rule for using powers, think back to what that means in terms of what you already understand. This will come back to haunt you in calculus, probability, statistics and sciences such as chemistry or physics.
• Understanding how to factor a polynomial. This truly becomes easier with practice and the diversity of approaches you become comfortable with.  It is increasingly more important in calculus. Useful in writing proofs and sciences such as chemistry and physics.
• Understanding exponents and logarithms.  exponents and logarithms come in handy in analyzing graphs of data later in life. They also give you a kind introduction to the concept of inverse functions.  -all forms of statistics (from the social sciences to the physical sciences), investments and sciences like chemistry and physics
• Understanding how to re-write an equation into different forms. This is perhaps the most important concept you can get from algebra: knowing what you have and how to re-organize what you already know. Applications extend to geometry, calculus, probability, statistics, linear algebra, computer programming and sciences such as chemistry and physics.

Algebra is a tool. It isn’t a goal, it is the means toward a goal. It isn’t meant to be confusing. It is a way to simplify even harder concepts. Everything that is taught in an algebra class is building the students up to the next set of concepts.

So, what is the answer to the original questions?

“Why do I have to learn this?” You have to learn this so that you can learn the next concept.

“Will I ever use this in real life?” No, but if you don’t learn this – if you give up now – you won’t be able to understand more complex concepts taught in this class. For the more here-and-now and grade-oriented: because if you don’t learn this by the time the next concept is introduced, your grades will only drop.

It’s hard to swallow, but it is absolutely key for students to understand this basic fact: they are in this for the long haul and should buckle down and just keep at it.

The worst thing you can do is give up or believe that you can’t do it because you can and you will, if you just keep at it.

 

Related articles

• Algebra on Demand is HERE – The Khan Academy (aodandmore.wordpress.com)
• Probability is not the best the goal for undergraduate math education (superconductor.voltage.com)
• Why Kids Hate Math (vuotkho.wordpress.com)
• Free Algebra Webinar (nchomeschoolinfo.wordpress.com)

Websites

There are three websites that either I use every time I get on the internet (that isn’t checking my email or updating my status on facebook), or would like to.

www.writing.com

Writing.com is a great writing community. In it, new members and new writers are a priority; if you have a short story or an essay or poem that you want critiqued and rated fairly by people who love writing , this is the site for you.

There are tiers of membership that can be bought either with on-site points or through cash donations. Higher tiers have access to create different kinds of items and have more memory space. (They can only dish out so much of their servers to freebies.) It is important to note, though, that a new member can be granted an upgrade by a collective of older members who find them worthwhile. This is both a great __ tactic for them, because it hurts to see all that extra space and special entry types go away, and it allows the newer person to see and experience all that they’re missing out on.

(If you’re wondering how often that happens, it has happened to me at least once and I’m only regular there in spurts.)

What also makes Writing.com great is the community aspect of it. You can read short stories and poems and books, you can develop your analytical skills or even just talk to the author by reviewing, you can follow your favorite authors, you can practice with different prompts they have available, there are contests and group-writes called campfires. That site has EVERYTHING a writer could ever dream of.

Also, if you’ve ever been to writing.com before … and were unable to stand the horrid yellow background… IT’S CHANGED! Now it’s white. Much easier on the eyes, if you ask me.

www.ravelry.com

I’ve been crocheting since I was eight. I’ve been knitting since I was eighteen. This is the best online community for similar yarn enthusiasts. Yes, there are other websites which focus on knitting, crocheting, sewing and such. Those tend to be websites of companies that sell products or services to knitters, and focused more on how to use their products than providing a community to interact with fellow crafters in.

 

unhealthy

There is a very troubled 15 year old girl out there.

She is the life of the party and soul of her softball team. When she was a kid, she wanted to be a baby-sitter her whole life; she loved kids that much. She’s whacky and a chatter box and will be anyone’s friend that lets her.

What’s troubling her, then? She has her family, she has her friends, and everyone loves her; she was even in the homecoming court. What makes her life hard, beyond the normal high school drama and all-too-common body image issues, is how she’s coping with the deaths around her.

The first set of deaths were truly horrifying. The gruesome murder of that family rocked the entire community, but she actually knew the victims. She would frequently walk down to their house to visit and play. It took her a week to recover enough to go back to school. She’s seeking counseling, still; a year later.

Much less immediate to her was the very recent death of a friend’s mother. Another gruesome murder, this time the woman was shot by her ex-husband. It’s actually a murder/suicide, but it happened on the other side of the country.

Didn’t go to school for a day.

Who knows, maybe she’ll skip school tomorrow. Make it two.

There is a considerable toll that death takes for the young, for those who have little experience with it and hadn’t ever really considered how short their own life could be.

Mortality is a hard thing to swallow.

Murder is even harder.

All of the people in this world that have been taken from me passed – naturally? I suppose you’d call it; most from old age, who went silently in their sleep, and a few from freak accidents. No one brutally murdered anyone that I knew.

So, maybe she can’t help it. Maybe there is no real coping mechanism for having someone rip a person out of your life, let alone four times over. It just scares me that she is hiding from the world like that. She’s focusing on herself; how she feels, who’s going to get murdered next, how that would affect her, is she next… and who could blame her?

Those are tough things for a 14-15 year old to be going through; but then, her friends are more deeply traumatized than her. They must be. One lost her whole family and had to spend time with their murderer, the other was finally going to see her mom again- then she was dead. What she is going through pales to what they must be going through, but she has no thought of them. If she did, she would be putting on a brave face and trying to help them get through their pain.

The reason why she is so affected by these things- her beautiful, kind heart and endless empathy- is exactly why she would be the perfect person to help them get through it. She understands. She loved them, too. She is horrified and scared and doesn’t know what to do. You don’t need an adult who isn’t going through all of this to explain to you how you’re feeling, and you don’t need to talk to a brick wall. You need to talk to the other people involved; you need to discuss what you’re all going through. You need to find closure and come to grips with the world around you, and you need your friends to see you through to the other side.

Her parents obviously don’t agree, as they continue to let her skip school and sulk. They would rather see her fall to pieces than have to be “the bad guy”.

Goals

If there’s one thing I’ve learned in my long life of consistently NOT setting goals, it’s that it is EXCEEDINGLY difficult to nigh IMPOSSIBLE to achieve something by accident. I would go so far as to say that “accidental achievement” should not only qualify as an oxymoron, it should define the category.

It took me a long time to figure this out. (What can I say? I learn the hard way.)

This year I’m turning my life around. I will refuse to sit around and wait for good things to come my way and I will NOT  just throw effort into something without thinking it through or planning.

I want to lose weight.

I looked up what my weight should be according to my body mass index. I’m dieting and exercising in a healthy and well-researched manner so as to lose my goal amount. I’m also charting my success. This not only helps me to stay true to my dietary restrictions and claims of increased exercise, but it also helps me track my success. It always feels good when I can write down that another five pounds have melted away seemingly overnight. (Does anyone else find that weird? Days pass by and absolutely no difference… then boom! and goodbye five pounds? Is fat/water weight quantized? If you’re smiling at /disgusted by the misuse of scientific terms, congrats! you’re a physics nerd.)

I want to knit hats.

The key to my success was NOT, as I claimed in my earlier post, that I cheated. Yes, starting at the top allowed me to feel more comfortable about when I was going to start/stop the rounding of the top of the hat. My greatest problem in the past, I knew, had been in deciding where that critical point should fall. It wasn’t always that the hats weren’t wide enough; but I invariably started closing the hat too soon. Starting at the top allowed me to discover this for myself without fear of failure.

The cheating? It was necessary, too. For any of you non-knitters who might be reading this, it is not easy to start knitting outward from a single point; it looks messy and loose and wrong. Crocheting the center is the only way I can think of starting a knit hat at the top without leaving an awkward point. (Knitting from a point, neatly, would require a narrow tube which slowly expands in a conical manner.)

Now that my confidence has been restored and my method proven, I just need to polish it. My next hat (*cross fingers*) will be successfully knit from the bottom up. There will be row counting. Gauge will be considered in all things. I will make minor improvements in the rate of increases, as there is an odd last little bump of an increase that looks like an afterthought (because it was). Thankfully, that is filled out when the hat is worn.

I want to become a better writer.

Guess what actions I’m taking to reach that goal! Yeah, that’s right. This blog isn’t entirely innocent. I’m not writing this every day because I want to; not because I have something to say every day, and certainly not because I enjoy sharing my thoughts on things. I write to keep in practice and to explore my voice. My old friend and I haven’t seen one another in a while.

Sammy’s Snowflake Hat is Complete!

Done! 10:00 January 4th, 2012

Wow. What I came here for … and Hats!!!

Not World of Warcraft.

I don’t enjoy games that you have to be constantly paying for. I prefer one-time-only fees, and internet games i generally just don’t believe in giving money to. There are exceptions, of course. With Wizard101 I did pay 20 bucks for expansions… and have recently found that the investment has been exhausted and I’m just more hooked. I don’t want to be a WOW zombie who breathes and eats and works to WOW. Besides, my computer isn’t shiny enough for games like that, and life is too short to spend that much time with something that can’t teach you anything or love you back.

What I came here for:

This is what it feels like to walk into a room and remember that there was a reason for doing it, but can’t remember what that might have been for the life of you…

Oh yeah! My immediately previous post. I haven’t watched Adventure Time in a while, sadly. I think that just came out as nostalgia in reaction/analysis/report form; if you’ve been through college or just a good English class, you know what it’s like to be locked into paper-writing mode.

On a more personal note, I’m nearly finished with Sammy’s Snowflake Hat!

For a brief history of my life … also known as the collection of hats that weren’t… I have tried (at least) five times to make Boyfriend a hat. Not just any kind of hat – a KNIT hat; I crocheted him a black one, it fit perfectly, looked great, matched my navy blue hat…

Not the knit hats.

They all look amazing! If you completely ignore the scale, and how they are grossly disproportionate to the size of Boyfriend’s head. WAY too small… They are my shame. They are my chagrin. I really don’t want to mention the owl hat which a previous post cheerfully declared “almost finished” …but I will because I refuse to live a lie. So, here we go: it wasn’t made in the round, I completely ignored gauge and I think I tried to do an intarsia project with completely the wrong set of techniques. To say the least, if it isn’t sitting in a landfill somewhere, it has been recycled back into my stash.

Sammy’s Snowflake hat? But it sounds like such a success!  What did I do differently?

…I cheated!!!!

That’s right, I don’t even care. Call me names till your face turns blue; turn away and never read my work ever again – I don’t care! I have a beautiful, knit hat in my hands – color work I designed myself and all! and why? because I started the entire thing out, at the top, with a crocheted circle!

It turned out amazing! It’s a bit big on me, and a bit long, but my brother is bigger and taller than me – as is Boyfriend (the theoretical next recipient of such knit-wear). I don’t know if I want to post this hat as a project on Ravelry.com yet. I’m thinking of getting more yarn, restarting the project – first in the same size as I knitted for Sammy (for Boyfriend), then try altering it for a girl. Then I’ll write up a pattern for it and offer it for free. I’m just going to need to practice writing patterns for crochet. Knit patterns are logical. I don’t know how to make a crochet pattern that isn’t, well, visual.

Pictures will ensue – possibly tomorrow; I could have it finished by then.