As I mentioned in the previous post I am considering a new book in geometry. I’ve recently been thinking about what got me into geometry (and mathematics) more generally. One early memory of the weird world of mathematics comes from Doctor Who. When I was about 10 my older brother borrowed the Making of Doctor Who from his school’s library. I already had a copy of the 1976 revised edition which featured Tom Baker on the cover but this was the original book from 1972. My recollection was that the original had some strange parts that were omitted in the revised edition. One of them was about geometry and how on a sphere you can make a triangle in which all three angles are 90 degrees and hence their sum is not 180 degrees as you would expect. Was my memory correct? To find out I ordered a copy from the second hand online bookstore Abebooks. And it arrived this week. I scanned the cover as you can see below.
I quickly flicked through the book and was surprised to find that the text was rather sparse. It wasn’t the book dense with information that I remembered. But the triangle made of right angles was there, almost exactly as I remembered, the only difference was that it does not have the right angle symbols of my memory. (If you download the scan, then you can read the actual text.)
The book contains a mixture of information about making Doctor Who and fictional reports from the program, for example the Doctor’s trial by the Time Lords. It also contains a short chapter by a reverend on God and science fiction which I have no recollection of. What I did recall correctly was that the Time Lords all had names made of mathematical symbols. These symbols had intrigued me at the age of ten. I wanted to know what they meant. I felt that there was a hidden world of mathematics out there which I wanted to find. Unfortunately what they taught me at school was pretty much along the lines of “Here is a quadratic equation. This is how you solve it. This a simultaneous equation. This is how you solve it.”
The interesting stuff such as the triangle with three right angles was never explained. In fact, a couple of years after I read the Making of Doctor Who I showed my science teacher the idea. I even got a small bouncy ball and drew on it with a felt tip to prove to her that it could be done. She just kept telling me that it wasn’t a triangle because it was on a sphere. She didn’t get the point that if the ball was big enough, say the size of a planet such as the Earth, then we would see the lines as straight and the angles as right angles.
Anyhow, it wasn’t until I started doing A level Mathematics that I found that hidden world of mathematics. I was amazed at the idea of differentiation. It was such a great, simple idea that I was kicking myself for not having invented it. And then we did the square root of -1! That was fantastic. Finally we were in the hidden world that I had hoped to find when I read the Making of Doctor Who at the age of ten.
