Teach Practical Geometry — Please

Today, one of our math teachers had to leave early, so I found myself teaching a math class — for the second time in a day. Earlier in the day, a number of students were building Venn diagrams for science class. Since they were in a Design Lab study hall, I figured, why not show the practical geometry structure for creating such a diagram? They do have an underlying geometry, you know?

I’d been thinking about this page design issue since I came across a website called The Secret Law of Page Harmony, and began designing page layouts in accord with this system. From there, it was a brief insight this afternoon when I kept hearing the words, Venn diagrams, Venn diagrams muttered all through study hall.

So I showed this system for generating a beautiful — beautiful! — Venn diagram, based on the secret canon of the medieval scribes. How could one go wrong?

Teens.

Look, just because we tell them to build a Venn diagram doesn’t mean they’re going to understand the two thousand years of previous history behind two overlapping circles. Nor do they learn anything about page layout, or page design, or beauty. It’s just a “simple homework assignment”, right? No need to get fancy…

And yet, underlying that “simple” assignment are a whole sheaf of assumptions about beauty, and order, and natural pattern recognition. In other words, the stuff of page layout and graphic design. And underlying that, is all the beauty and order and glory of geometry, the recognition that there is a mindfulness in harmonious composition.

And that means teaching geometry as more than just another type of math, with a textbook as thick as a concrete block and a whole scale of proofs that have no relationship at all to the world of made things.

Yet there is an underlying order. And if the assignment had included the requirement for a “correct” Venn diagram, and there was a video somewhere showing how to put a Venn diagram “correctly” on a page such that it expressed the relationship of written work to the the diagram, and the diagram and textblock were proportional to the page… why, you might reinvent education.

But no… let’s just keep getting kids to draw sloppy, hand-drawn circles, and not help them understand that under the slightly-less sloppy circles of a good compass, there’s a mathematical idea of beauty, in which two distinct ideas share a seed of beauty between them.

Update: Incidentally, I’ve experimented a little with the secret page canons, and here’s a little TextExperiment — a 1949 rant from Jack Parsons, American rocketry scientist, from his less-orthodox work as the occasional leader of a magical order, laid out in the secret page layout that was the method of the medieval scribes.  I think Jack would have been pleased.

Via Flickr:
So, here with the completed Venn Diagram, is the full practical steps necessary to achieve this result.

1) Using a T-square or other long ruler, draw the diagonals from corner to corner of the page (or from margin to margin, if you want to leave a blank edge of the document).
2) The crossing point of the two lines is the centerpoint (O).
3) use the centerpoint O to construct the vertical division and horizontal division of the page.
4) Draw the two diagonals from the vertical half-line to the opposite corners.
5) use the crossing of the full-diagonals and half-diagonals to draw vertical divisions. Where these division lines cross the horizontal center-line, are the centerpoints of your two Venn diagram circles.

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