Wheel Rug, Revisited


Shaker “Wheel” rug.  http://www.willishenry.com/auctions/05/DougTowleCatalog/DougTowleCatalog.htm

Christine here.  In the July 2014 issue of the newsletter, I wrote an article on the “Wheel Rug,” which is a large central circle (or rarely, oval or square) surrounded by a lot of smaller circles. No, I didn’t give it that name; it was a name given to similar rugs in the early 1900’s, when the style was popular and common in both crocheted and braided rugs.

Since the next issue of the newsletter (if I can ever get it finished) is about flower rugs, I was thinking about wheel rugs, which are kind of flower-like, right?  So I decided that I wanted to make a large wheel rug.  Then I wanted to figure out how big a given number of braided rounds would need to be in order to fit neatly around a larger center circle.  I didn’t want to do this by trial and error.  I wanted to know ahead of time just what I was in for, and not have to add or subtract from a central circle in order to get everything to fit properly.

Another Shaker Wheel Rug -- from http://www.willishenry.com/auctions/05/DougTowleCatalog/DougTowleCatalog.htm

Another Shaker Wheel Rug from the Doug Towle Catalog

I took my usual course whenever I have a math question:  I went to my Math Professor husband and said, “Please figure this out for me so that I get a formula.”  He looked at my example of a large circle surrounded by 18 smaller ones drawn out on the back of an envelope and frowned.  “I’m grading quizzes,” he said, hedging.  “Whenever you can get to it,” I said.

He returned 2 days later with a formula that involved the radius of the center circle, and the cosign of something else… and a theta symbol… and my eyes crossed.  But he was proud of himself for figuring it out, so I sat there and listened to his (long) explanation of different approaches he had taken and how he finally figured out how to solve the problem and generate a formula for me.  I thanked him for all of his hard work, patted him on the back in congratulation, and promptly buried his formula calculations in a stack of papers that I will surreptitiously throw out.

I like math, I really do, but my last course in trigonometry was 39 years ago.  The cosigns and the theta in the formula creeped me out.  I’m good with algebra, but prefer to leave trig alone.

So, I did what I should have done to begin with:  I googled it. “Size of circles around a center sphere,” and this wonderful website came up:  https://rechneronline.de/kreise/circles.php.  It has blanks for you to fill in the size of the center circle, the number of small circles you want to place around it, and it will do all the math for you and spit out the exact size of the smaller circles that you need.

Screen Shot 2018-05-24 at 9.22.16 AM

This is the sort of image you get when you pick your sizes and colors from the rechneronline.de/kreise/circles.php website

Now, the only problem – and it’s a minor one – is that we’re used to thinking of our braided circles in terms of diameter.  The website requires you to enter the radius of the center circle, and it gives you an answer for the size of the outer circles with their radius also.  So you just have to remember that the diameter that you want is two times the radius.

Example:  I have a 72” (6 feet) diameter circle, so I enter the following:

Radius center circle:  36
Number of outer circles:  20
Gap between outer circles:  0
Click on “calculate and plot” and you see:  Radius outer circles:  6.6”.
So, the diameter of the outer circles is 2 times the radius or 13.2” to place 20 of them around a 6 foot center round braided rug.

And look!  You escape trigonometry.  Wonderful!