So, I have three or four projects going at this time, baby blanket, finish the thumb on one mitten and the set is done, a scarf for a friend and lastly, my cabled sweater.
Here is the real problem.....Cables take FOREVER! God! I'll be 50 before this thing gets done. How can I speed this up?
Then, when you have finished that, prove that this is true (sin(θ))^4 +2(sin(θ))^2(cos(θ))^2 + (cos(θ))^4 = tan(θ)cot(θ).



daveballarat's picture

The problem might be in the multi-tasking

I wish I could multi-task but I can't ... well I can to a limited degree...

My dad is the same, and ... the proof is that he never finishes off any project... usually houses, building houses was his hobby but ... he never ever got around to finishing any of them off so they were beautiful, and complete.

I suffer from the same thing... I have noticed over the years. However, my way of forcing myself to complete tasks is by only doing one at the time. I am currently starting a cable sweater. I really really want to start socks but ... I am forcing myself to stick with sweaters for the moment because my success rate with the last Wally hat and the willy warmer was less than encouraging. So with the success of my next project anticipated, I will improve my confidence and success with later projects.

Maybe for you too ... just less projects on the go... and leave the trig to Pythagoreas may be your major source of distraction :)

Istanbul, Turkey


albert's picture

I've spent the past 2 hours pounding a calculator trying to figure out how to center a pattern on a sweater- I don't think I'm up to solving the mystery of your incantation.

scottly's picture

I think you just have to be patient. I've gotten faster at them over time but they still slow me down. I don't mind because the are so much fun to do - they are like magic.

murfpapa's picture

I've heard that cabling without a cable needle is quicker, likely due to not having to fiddle with moving stitches to another needle. I tried it, it works but it was late in the project and I didn't have time to develop a rhythm for the cabling so for me, it was still a bit clumsy in the execution. How wide are the cables?

And, the proof of the equation is "because Mom says it is!" You never said we had to show our work. Surprised to see the equation for the Parkers Sub-subatomic Particle Conundrum in a knitting forum though. Usually we see that stuff in my Thermonuclear Muon Energy Vacuum and Possum Pickle Assimilation group.

mrossnyc's picture

To answer your cable question, I came across a technique a few years ago that sped up a cable project in that it involves skipping the step of putting the stitches on a cable needle. You have to do this carefully, but after a few times it's pretty easy and not as risky as it sounds. Basically, rather than putting the stitches on the cable needle, slip them off the left needle and hold them to the front or back as if they were on the cable needle. Then slip the next group of stitches to the right needle and hold them there. Now go back to the stitches that are not on any needle and slip them correctly back to the left needle. Now slip the group of stitches on the right needle back to the left. At this point, you've made your cable/twist and all stitches are on the left needle in the correct order and you can just knit them in order. I was VERY nervous to try this at first, but it became easy after the first few times. Hope that helps.

Regarding your equation proof, here's what I came up with...

First, the right side of the equation equals 1 since they are inverses of each other:


= (sin(θ)/cos(θ))*(cos(θ)/sin(θ))

which also means that:
= (sin(θ)/sin(θ))*((cos(θ)/cos(θ))

which is also equal to 1.

The left side is a quadratic equation and can be broken down to the Pythagorean theorem, and therefore 1 as well:

Given that the Pythagorean theorem is:

o² + a² = h²


(o² + a²)/h² = 1

where a = the adjacent side of θ

o = the opposite side of θ

h= the hypotenuse of triangle

So, the left side of your equation can be factored out as follows:

=(sin(θ)² + cos(θ)²)*(sin(θ)² + cos(θ)²)

then substituting angle formulas using the variables above:


=((o² + a²)/h²)*((o² + a²)/h²)

and substituting the Pythagorean theorem above, the left side and right side of your equation states:
1 * 1 = 1

How's that, teach?

crmartin's picture

I have tried cables without a needle and I really don't see how it saves time. Maybe I didn't give it enough time. And to the proof, that is what I was going to say! ;-)



Thomasknits's picture

Awesome, I was about to type that out, but you beat me to it. I love computational proofs. Anybody wanna prove my Galois theory homework problems for me?


albert's picture

It's not a theory anymore- oh, wait, that's global waming. Nevermind.

Joe-in Wyoming's picture

Global warming is still a "theory" if you are heavily involved in the energy business in WY. Or a conspiracy to ruin the USofA through some nefarious (insert favorite scapegoat here) plot. At least, if some of the rants you hear in the local news media are to be believed. Good heavens - Do none of these people even BOTHER to think for themselves? Sorry about the mini-rant, BTW. -- Books, knitting, cats, fountain pens...Life is Good.

Books, knitting, cats, fountain pens...Life is Good.

Buck Strong's picture

Very nice! I'd almost let you whisper that proof in my ear....
"A man may fight for many things. His country, his friends, his principles, the glistening tear on the cheek of a golden child. But personally, I'd mud-wrestle my own mother for a ton of cash, an amusing clock and a sack of French porn." Blackadder

To sit with a dog on a hillside on a glorious afternoon is to be back in Eden, where doing nothing was not boring-it was peace.
~Milan Kundera

mrossnyc's picture

Almost? I didn't realize this was a conditional proof...

teejtc's picture

Personally I think the equation is evil... Math is supposed to be done with numbers... literature is supposed to be done with letters.. ne'er should they meet in between :-)

Grace and Peace,

RickeScott's picture

Here's where I learned how to cable without the extra needle:

Faster and a lot more fun! Good luck.

vsidart's picture

Cabling without a needle is totally the way to go. It took some time to learn, but I've gotten to the point that I can c8 without even thinking about it- REALLY speeds up a project!

ksmarguy's picture

Melissa Leapman's book, Cables Untangled, also has wonderful instructions on cables without a needle. It took a bit to get the hang of but once I got the hang of it was so much faster, especially since I am a champ at losing my cable needle between cable rows. Good luck!

TheKnittingMill's picture

I really haven't gotten the hang of cabling sans cable needle. I actually cable faster with the cable needle. Maybe I didn't give it enough of a chance. I do love cables though and I agree with Scott--it IS like magic watching them take shape!

“Now, let us all take a deep breath and
forge on into the future;
knitting at the ready.” -- E. Zimmerman