Jun 152013
 

Tip of the Mathberg

The Crochet Lounge Way

Magic Potholders Deciphered

 

I LOVE Magic Potholders and you may, too!

Definition:

A “magic potholder” is a square potholder that is made in one piece (without having to break yarn), on the diagonal, in the round, and folds into double the thickness onto itself before finishing off.

That was a mouthful, but when you hook it, it really is all of the above and more.  Can you tell I am excited to share?

The More

  1. You can take ANY stitch pattern, as long as you make a straight edge for it (to form the square), and make a Magic Potholder!
  2. Using a little bit of mathematics, it can come out the expected size EVERY TIME and we’ll show you how :)
  3. Prefilled tables at your fingertips for your foundation chain/foundation single crochet (fsc) count

The Tip

Use Pythagorean Theorem (yes, Geometry level nomnom) to help figure out the sizing of your finished Magic Potholder!

The Free Pattern

For the faint-hearted at mathematics, here is a pattern to explain by hooking, Butterfly Stitch Magic Potholders.

Butterfly Stitch Magic Potholders 5" & 7" | Free Crochet Potholder Pattern | Crochet Kitchen Essentials

Butterfly Stitch Magic Potholders Backside Stitching 5″ & 7″ – Crochet Kitchen Essentials

The How to

Take ANY Stitch and Making Magic Potholders:
Steps to creating a successful magic potholder with any stitch:

1) Determine your gauge with the chosen hook, yarn and stitch
2) Determine the desired size of the finished potholder e.g. 5″x5″, 7″x7″ so on and so forth
3) Do the math or simply check out the table at the bottom of this post to determine the starting chain length or fsc length taking into consideration how to make the stitch straight edged on the two sides
4) Get ready, set and HOOK the stitch from one end of your foundation chain to the other, adding enough repeats at each end to make a pouch shape.

Quick 30s video of how this pouch is then folded into the Magic double layered Potholder is being uploaded and will be linked here soon.

The Nitty Gritty that isn’t so Detailed

  • A right angle measures 90°, and in this case is the corner of the Magic Potholder.
  • The Legs of the triangle are the sides that form the right angle, denoted as sides b.
  • The Hypotenuse is the largest side in a triangle that is opposite to the right angle.  It is denoted as side c in the Pythagorean Theorem.
  • Since the Magic Potholder is a Square, we will only be talking about the Pythagorean Theorem where side a equals side b (a=b).

 

Tip of the Mathberg - Magic Potholder Pythagorean Theorem Squares | The Crochet Lounge Way

Pythagorean Theorem


The pythagorean theorem states that the sum of the area of the squares created by the two legs of the right triangle (a & b)  is equal to the area of the square with sides the length of the hypotenuse (c).

In our case, the Magic Potholder is a square, so we will be working with the theorem where a is equal to b.

a² + b² = c², and a = b

Here are the steps to find the sides from a given hypotenuse (your foundation chain start):
2a² = c²
a² = c²/2
a = sqrt (c²/2)

The ideal situation is actually determining what end size potholder you want and finding the hypotenuse then converting via your gauge to your starting foundation chain.

The Math:

a² + b² = c², and a = b
2a² = c²
sqrt(2a²) = c

The following table calculates the length of the hypotenuse based on the ending measurement of the sides of the square you would like to make.  It does not include a unit base since it could be used for any unit calculation. In metric, 30.5cm is roughly 12 inches, so the table is made going up to 30.75 for the side.

Determining the Gauge

To determine the gauge, I highly suggest you measure your foundation single crochet or if you must, measure foundation chain with a row of sc to stabilize the chain.  The reason for suggesting using FSC is because it doesn’t stretch/pull out of shape and will stay the same as you stitch across and around it.  I prefer starting all my magic potholders using FSC since it creates a nice straight diagonal or hypotenuse for one side of Magic Potholder.

What is Foundation Single Crochet (FSC)?

FSC is the foundation chain plus a row of sc done in one single row, and is done as follows:

Foundation single crochet (fsc) – ch2, insert hook into 2nd chain from hook, yo draw up a loop, yo draw through 1 (this creates the next foundation chain), yo draw through 2 (this completes the single crochet)
*insert hook into the next foundation chain just created, yo draw up a loop, yo draw through 1, yo draw through 2
Repeat from * until total fsc completed

 The equation so you can make specific calculations to your own gauge.

Ex. Measuring in inches, using worsted weight cotton and an H or I hook, my sc rows can measure 4st to an inch.  Upon determining the hypotenuse of the potholder from the table above, you simply take the hypotenuse and multiply it by the number of stitches per inch to get the number of starting FSC you need.

So to get an 8″ Magic Potholder, you would read the table for 8 inches and see that the hypotenuse will be 11.31in.  To get the number of foundation chain needed to achieve proximity to the 11.31in hypotenuse, you multiply 11.31in to your gauge stitches per inch (here, we’re using 4).

4 stitches/in * 11.31in = 45.24stitches

Obviously, since we can’t stitch a partial stitch, you will then round up or down depending on your heart’s desire :)

The following table calculates the FSC number needed for you – you just need to know what the finished size of the potholder you would like, and using the same base unit (inches or cm, for example), make your gauge to figure out the stitches per unit, and use this table to find out how many starting FSC you would need (or starting chain + 1).

Hooking the Magic Potholder

The only thing remaining for consideration is how to hook the stitch you want on your Magic Potholder.  Some patterns have larger stitch quantities before reaching a repeat.  This will have to work with the size of the potholder you have chosen (unless you want to make it larger or smaller purely based on the number of pattern repeat — which is much easier than the mathberg we are playing with here).

Since the pattern is worked AROUND the FSC, in order for it to start forming the square shape, you need extra stitches in the end fsc on each side in the first round.  If your pattern stands the height of sc, you would use 4sc on each end, if it stands the height of hdc, you would stitch 4hdc on each end.  For more complicated stitches, you can convert the stitch to match – just like the Butterfly Stitch Magic Potholders.  You need to account for the extra stitches at the two ends for your pattern repeat.

On the Butterfly Stitch Magic Potholders, there is an extra 2 stitches at each end of the fsc so when calculating the pattern repeat, you would have to add 4 to the ‘foundation as if it were a flat rectangular piece.

Once you get going, it won’t be such a mystery since all you are doing is going around and around with the fsc as the base of the rectangular pouch you are creating.  When the short side of the rectangle is equal to half of the calculated hypotenuse, you are ready to fold it into your Magic Potholder and stitch it shut into a double layered square.

Enjoy!


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 Posted by at 06:04

  4 Responses to “Tip of the Mathberg – Magic Potholders Deciphered”

  1. I do love your chart and explaining the need for a FSC – along with your including the stitches per inch.

    I love your math, and your application of it is correct; however, your diagram of the Pythagorean Theorem is completely wrong. The hypotenuse is the diagonal of the square and the sides of that *same* square are a and b. You are calling “c” the hypotenuse but showing it as the side of your bigger square. In your example of an 8″ potholder, “a” and “b” are the sides, and “c” is diagonal across your potholder. Please revamp your Pythagorean Theorem diagram to apply to *one* square and not three.

    Thanks so much for this wonderful tool! By the way, I always seem to get a slight rectangular magic potholder… any tips on why that might be? Thanks!

    • Ah, Tammy. The diagram is actually a classic Pythagorean Theorem diagram and shows precisely how a²+b²=c² comes to be with geometry. The area of any square is side². In Pythagorean Theorem, therefore, the two sides a and b would be equivalent. The diagram symbolizes a², b² and c² with a and b being the equivalent sides of the triangle and c being the hypotenuse. If you take the actual units represented by the dots in the diagram, you will find that a² + b² is indeed equal to c².

      When you work the magic potholder, your foundation chain is actually the hypotenuse (c) and you work the rounds until you reach c/2 and it should fold into a nice square. If your magic potholder is slightly rectangular, it could just be the need to adjust your golden loop (this is the loop that you draw up after inserting your hook into the indicated stitch e.g. in a dc, you yo, insert hook into indicated stitch, yo and draw up a loop < - this is your golden loop and the height of it determines the row height). You can pretty much manipulate how a piece turns out by adjusting the golden loop, but need to do it consistently.

      Note that depending on the stitch you are using to create the magic potholder has a height of its own, so if your hypotenuse is not a multiple of that stitch height, it won't turn out as 'square' unless you really manipulate a few rows into fitting the calculations.

      Meanwhile, here are a few links to our friend Pythagoras's Theorem :) http://www.mathsisfun.com/pythagoras.html http://en.wikipedia.org/wiki/Pythagorean_theorem

      • Thank you, e, very much for your reply! I am going to give this potholder another shot with your suggestions…can’t wait to actually get a square… Thanks again for your reply!

  2. Yea… I have a square – thanks so much! Perhaps adding the four extra stitches at the end of each FSC and adjusting the golden loop helped. Thanks!

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