Geometry: The Heptagram

A while back, I built myself a VLC. VLC stands for “Very Large Compass” and it’s a very different tool than the typical compass one buys in an art supply store. Most of those compasses can’t draw circles larger than a few inches in radius. I needed one that could draw really big circles. For really big geometry. On foamcore or posterboard.

A compass like this:

My VLC: very large compass
The VLC: very large compass

But of course, it’s hard with this kind of photograph to get a sense of what a VLC can do for your artwork, or your classwork, or for your students in Geometry class. Just seeing a point or pin, and a flexible radius (as indicated by the wooden dowel), isn’t really enough to tell you just what you can do with a Very Large Compass.

You could choose to produce a mandala of geomancy, as I did, and link it to alchemy.

But that doesn’t really give anyone a sense of why a VLC is necessary.  And so it becomes necessary to put the VLC to work on other projects.

Like the Heptagram.

Now, there’s actually more than one Heptagram. There’s a skip-1 heptagram, which isn’t actually a seven-pointed star, but more of a seven-sided regular polygon.  And that can be done fairly easily.

There’s also the skip-2 heptagram.  The skip-2 simply means, start at one corner of a heptagon (or seven-sided regular polygon), and draw a line from one point directly to the vertex after the next vertex.  The result is sort of a thing that your brain almost registers as a six-pointed star, except the angles are wrong.

There’s also the skip-3 heptagram. This time, instead of skipping one vertex and going to the next vertex, one skips two vertices, and goes to the third.  This time, one gets a very sharply angled star with a tiny irregular heptagon in the middle, instead of a big blocky one like the skip-2, or the very regular skip-1.

The three types of heptagons, when laid in a circle and assigned their traditional planetary associations with the points, looks something like this:

the three heptagrams

And I must say, I think it’s beautiful.

It’s also big.  Here, the circle (produced by the Very Large Compass) is perhaps two feet across.  I must admit, this is a heptagram produced by neusis rather than accurately measured angles… but there’s only so much that anyone can really do with just a VLC and a VLSE (Very Large Straight Edge— in this case, a long bit of masonite with a precisely cut and shaved edge).

This is eventually going to be a piece of artwork for my classroom, and maybe an auction item for my school’s annual auction — let me know if you’d like to buy it in May? — but for now it’s a elegant reminder of something I’ve said often:

You can’t think with tools you don’t have and have never used.

If you don’t have a VLC of your own, it’s time to build one.  If you don’t have a VLSE for your geometry class, you need one.  Get yourself some foamcore, and some pencils and sharpie markers, and start dreaming big. Start geometrizing big.  Because there are things that you learn on big paper and big surfaces that you cannot learn any other way — about tiling, about shortcuts, about tessellations, about design — that can’t be achieved with the usual tools.

A kid who never picks up a compass in geometry class hasn’t really learned any geometry at all.


  1. Great post, Andrew 🙂 THANKS. I will admit I had no idea there was a technical term, ‘Very Large Compass’. Or even thought about making one. Years back, I found a second hand one at a swap-meet – old army issue from the 60s. It’s done very nicely. Will link this on a Facebook group where the Heptagram has been mentioned 🙂

    • I don’t know that it’s a technical term, “Very Large Compass,” but it’s not a “VSS” — Very Small Skirret, which is just a string attached between a pin and an pencil.

      I’ve just been in a bit of a debate with a person on Flickr, who has been commenting in a somewhat assertive manner about my geometry postings there. I treat the pentagram and pentagon proofs as sacred secrets, but I feel tried.

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