Monthly Archives: March 2018

Geometry: A good triangle

One of the curious details about life in the modern age is how much we get …. I was going to say wrong, but let’s say off, instead… about graphic design.

Consider the basic triangular shape.  Let’s say that you’re designing a logo for a business, and you want to use a triangle.  You go into your basic Vector Shapes tool, you click the triangle button, and Pop! Here’s a triangle.

It probably looks a great deal like the triangle at the left — steep sided, mountainous, a pretty vigorous triangle to all appearances.  Nothing wrong with it, right?

Except that, once you start working with that triangle, something seems not quite right about it, and so you have to fuss and fume about it to get it accurately to the shape you want it to be.  It just doesn’t want to be the shape you want it to be, though.

In frustration, you might wind up turning to a quite different set of tools, or scrap the idea of using a triangle completely.

First by Geometry…

The thing is, you’re not wrong. The triangle is not in fact the correct shape. Adjusting it to the correct shape isn’t going to help, either, because the triangle itself doesn’t have the correct proportions to be pleasing to the human eye. The triangle was coded into the software by a group of programmers who knew the mathematical rules governing triangles, but not what proportions of triangles are pleasing to the human eye.  They knew a triangle was a figure with three sides, and that you generated one by a formula, 1/3 base x height.  And that’s it.  Naturally, you’re going to get an isosceles triangle — with the two rising sides subtly longer than a narrow base.

But if you want an equal-sided triangle, which speaks to and appeals to the human eye in a unique way?

For that, you need a designer — a human designer, with a few years of experience in studying, and explaining, geometry and art history.  In the second diagram, here’s our computer-generated vector graphic of a triangle, with its subtle offness, compared with the same program’s standard vector-graphic circle…. and then two of those standard circles overlaid on one another, to show the relationship between the center and circumference of each circle… And the equilateral triangle that results as the proportion from those two standard circles.

And finally, this “golden triangle” (which isn’t really the Golden Triangle — that’s either a triangle formed from the Golden Mean, or a region in southeast Asia where opium is produced) is overlaid on the original triangle at the original size.

Then, side by side.

Finally, we can compare them side-by-side.   This time, the yellow triangle has been increased in size, but without changing the proportions, to match the initial vector-graphic triangle. The base of the blue triangle is subtly narrower than the yellow one  — the blue triangle has upward force, but no stability.  The yellow triangle, on the other hand, has both upward force and stability.  It has both strength and a desire to rise.  It has a proportion and a grace to it that other triangles can’t manage — and no matter how you turn it, it’s going to turn out stable and in command.

If you look at just the first triangle, the blue one, at the top of this post, there’s a pretty good chance that it looks all right.  Not Bad, as the saying goes.  But now that you’ve seen them together, and now that you know one of them is generated geometrically by someone who knows what they’re doing — you’re going to see evidence of isosceles triangles everywhere you go…. and virtually no equilateral triangles except in objects and diagrams that are more than a century old.

Perhaps an isosceles triangle is an example of lazy, computer-generated design — and an equilateral triangle shows a human touch.