665. The Devil’s Stars

From an album by the sixties folk band Pentangle.

Fundamentalist Christians are not only uncomfortable in the presence of the number 666, they aren’t fond of a five pointed star inside a circle either. I found this out the hard way.

I was teaching a unit on Drawing Through Mathematics back when I was a middle school teacher. The technique consisted of using two concentric circles, with dots marked off mathematically, and connecting the dots between the circles with straight lines. Then the circles and dots were to be erased.

In this manner you can make stars with any number of points and control whether they are fat or skinny. I’ll show you how at the bottom of this post. In one session of my class we had already made six and seven pointed stars without any problem, but when we did five pointed stars I unintentionally caused an explosion. One student completed his star, then suddenly sat back, face white with fear, and threw it across the table shouting, “I’ve made a Devil’s star!”

I took me completely by surprise. I would never had let the number 666 creep into class. In fact, when I made up my own math worksheets, I always made sure no answer would be 666. It wasn’t fear of the school board. It was just that every kid has a right to his own beliefs, whether they make sense to me or not, and I saw no reason to make them uncomfortable.

I also knew that a five pointed star inside a circle, particularly if inverted, was a devil or witch sign during the middle ages. I just didn’t know that piece of knowledge was current in my community. I should have, since you see it in so many horror movies, but I don’t watch horror movies and I try to ignore their adds on TV. Besides I didn’t think of what we were doing as putting stars into circles, but using circles (and then erasing them) to make stars.

I explained all that to the frightened student, also invoking the fact that the symbol for the Army Air Force in WWII was a circle containing a five pointed star, and that the US government was certainly not an instrument of the devil. It took a long time to calm him down and he was still shaken when he left classroom.

I felt terrible. Probably every student I’ve ever taught felt differently about religion than I do, so I’ve always worked hard not to put any one of them on the defensive, but this incident had caught me by surprise.

It’s hard to anticipate every possibility.

*         *         *

During the first two or three years of this blog I sometimes offered classroom insights, but I only have a few left that could interest any of my present readers. This might be one. Teach it to your kids, if you have any, and let them impress their teachers. Just stay away from five pointed stars if you are a fundamentalist Christian. Or embrace them if you are a Wiccan.

A three pointed star is rare except for the Mercedes Benz badge. A two pointed star is really just a skinny diamond. A one pointed star can’t exist. Any number of points, other than one, can be drawn by this method with complete control of how skinny or fat the star will be.

Draw a circle the size you want your star to be. Draw a second circle on the same center point inside the first circle. The smaller the inner circle is (compared to the outer), the skinnier the star points will be, and vice versa.

Decide how many points you want on your star. Divide that number into 360. That is the number of degrees each point will take. Divide that number in half. That is the offset.

Example for an eight pointed star —
360 divided by 8 allows 45 degrees for each point, with a 22.5 degree offset.

Draw a line from the center through both circles. Starting on the point where the line crosses the outer circle, draw eight dots 45 degrees apart around the outer circle.

Where the line crosses the inner circle, offset a dot by 22.5 degrees, then draw eight dots 45 degrees apart around the inner circle.

Connect the dots. Voilà. Then erase the construction lines. I still use the method when designing quilt blocks.

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