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.



Building a MakerSpace

Let’s say you’re part of an institution — a church, a library, a school — that’s decided to start a MakerSpace. You’ve read all the books, skimmed numerous articles, watched all the videos, and gotten the go-ahead from your stakeholders. You hired a contracting company, and the workmen are going to be ripping out walls and installing new electrical wiring any week now. You are completely confident in your plan, and you are sure that you have thought of everything. 

But what if you haven’t?

There are at least seventeen major errors that we are aware of, that most schools and libraries have failed to think about. Many of them have to do with the curious blind spots these organizations have with regard to planning for maker spaces and maker programs.  And unfortunately, the more money the organization is throwing us for your Mischel launch of their maker space, the more likely it is that they will make a greater number of these serious mistakes. Shortsighted thinking in favor of “building is now “can lead to costly and painful decision making later on. It can hamper the growth of the maker space program, and it can block it from becoming fully integrated into the institution’s existing program.

email us, or give us a phone call. Guide you through our checklist of common problems, risks , and opportunities.  For our low introductory consulting fee, we’ll guide you through the shoals where you are navigating blind. 

New Article on MakerSpaces in Schools and Libraries

Andrew Watt, our Creative, just wrote this 4,000 word article on MakerSpaces in schools and libraries, following up on his appearance at EdCampSWCT yesterday.

It’s available here.

The big reminder is at the end:

F. Buckminster Fuller was assigned the task of writing the history of America’s technological innovation to reach the Moon. It was expected to be a celebration of American technological advances, and a series of biographies of great American inventors whose engineering accomplishments resulted in humanity’s march to the stars.  Yet in the first chapter of that book, Critical Path, Fuller admits that it was less a case of American ingenuity that sent the Apollo 11 astronauts to the Moon’s surface, but rather the ingenuity of humanity — ceramic parts for the Saturn 5 rocket had been made that used porcelain recipes that were six thousand years old; bronze-alloy couplings that relied on four thousand year old metallurgy helped the rocket’s various stages separate from one another when the bronze melted away under intense heat.

I invite you, readers, to think of yourselves like that — that your task as MakerSpace teachers and librarians and archivists, is to be oriented on what humanity has already done, technologically, and to help students understand the old technologies so that they can borrow from them to develop new solutions to problems.

And a Shout Out…

If you or your school would like assistance in putting these principles into action in your school, please be in touch.  I am available for consulting services; or to run workshops on sewing, bookbinding, or basic carpentry for teachers and MakerSpaces; or for ongoing coaching services for new MakerSpace atelierists.

What is a MakerSpace?

A big article on what a MakerSpace is, and how it relates to other types of work areas for artists, designers, and Makers.

So, that’s the way I see these things — MakerSpaces revel in the sheer joy of creativity; DesignSpaces build things with a purpose; ArtistSpaces explore creativity without necessarily giving it purpose; and TinkerSpaces are for sticking things together until you get ideas… but won’t necessarily help you build anything real.

Where does your space sit in the definitions?  Are you really operating a DesignStudio when you think you’re running a MakerSpace?  Is your school’s MakerSpace really a TinkerLab?

Read the full article; it’s worth it.


Hello world!

Welcome to the Watermountain Studios.

You can find us on Etsy at

The primary purpose and philosophy of the Watermountain Studios is three-fold:

  • Make things out of natural materials and sell them to people who want to make things;
  • Make tools, books, furniture and other things in traditional ways that help reveal how things are made;
  • Provide teaching and consulting services to others on how to make things in traditional ways.

We do this in a number of ways:

  1. We make things out of wood, cloth, and paper;
  2. We sell them on Etsy and through other outlets;
  3. We offer consulting services to schools, MakerSpaces, and libraries (as well as individuals and other institutions) through the Thinkery.
  4. We build things and explain how they got built and why, on