Math Open Reference


About the Author

Like many things here in Silicon Valley, Math Open Reference did not start from some grand plan. I was volunteering at my son's school on its technology committee, and being a software engineer, I was quickly struck by the absurdity of his backpack. It weighed 20lb (half his body weight at the time) and contained mostly data. It was a jarring thought that here in the valley, he is carrying data encoded as black marks on slices of dried wood pulp that would easily fit on a flash drive.

I have always loved designing and building things, so I set to thinking about what a modern digital textbook would be like. Obviously not just a copy of the text on a screen. It seemed clear that it should be interactive in some way to engage the student more, and to reveal truths about the subject you could not show in static text. Also, it seemed that teachers with a projector would find it useful to demonstrate concepts to a class in the same way. The trick, I thought, was to really use the power of the computer, not just mimic paper.

When you design software, you are a kind of artist. Your medium is computer code, but the main part of the job is knowing what to paint. This has always fascinated me, because it is really a study of people, not computers. How do people learn to use a new design? How do they want to use it once they understand it? What message or idea are you really trying to convey? It has everything to do with how we perceive things and build mental models of our world.

So the first test page was for the isosceles triangle. It's easy enough to explain that it is a triangle with two congruent sides, but so what? It occurred to me to try the idea of "feature invariance". I had a triangle where you could drag any vertex about. But what I added was code that moved other points as needed to ensure that it stayed isosceles. You could not drag any point and make a triangle that was not isosceles. I hoped that the student would

  • Have fun with it, and
  • Learn what it was that was always true about the figure.

In the classroom, I visualized a teacher wiggling it about (or better let a student wiggle it about) and ask the class what was always true about the shape. The discussion would hopefully lead to its "isosceles-ness" in a way that made them really think hard about it.

I did a few pages like that and put them on the web. The reactions were very positive, as judged by emails and that fact that the pages shot up the Google page ranking system very fast. I have been adding to it ever since.

Looking back

I have been working on computers pretty much since there were computers. Out of school in England I worked at LEO who made one of the first commercial computers in Europe. By modern standards a big lumbering beast. But amazingly, it could multi-task, running 3 or 4 jobs concurrently in 128k of magnetic core memory.

My next stop was at Hewlett-Packard, who were just entering the computer business. I wound up in Cupertino California (also the home of Apple) building database management systems for mini-computers

Three of us eventually left HP to start a software company in response the the Apple II personal computer and later the IBM PC. We managed to squeeze an office software suite (pfs) into a 48k 8 bit micro computer with no hard drive. That company (Software Publishing Corp) was actually the first ever software company to go public. Before Microsoft even!

So the above and other projects left me free to do what I love to do - which is build things. Building this resource has been incredibly rewarding. And it's not done yet! Where is it going next? What do you think?

Write to me

John Page