## Friday, August 25, 2017

### Babylonian "trig"

"Plimpton 322 predates Hipparchus by more than 1000 years," says Dr Wildberger. "It opens up new possibilities not just for modern mathematics research, but also for mathematics education. With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own."

When I read "However unlike today’s trigonometry, Babylonian mathematics used a base 60, or sexagesimal system, rather than the 10 which is used today. Because 60 is far easier to divide by three, experts studying the tablet, found that the calculations are far more accurate." I surmised that Sarah Knapton (Science Editor for the Telegraph) probably wouldn't know a sine if it hung blinking above the highway.

And it turns out the good Dr. Wildberger has a book to hawk. Said book is supposedly going to revolutionize the teaching of trig, apparently by using rational numbers and limits. (Don't reporters do any background checking anymore?)

Want a different view of the Plimpton tablet? It looks like a table of Pythagorean triples. Pythagorean triples are a fun topic that mathematicians have been working on for several thousand years now. I've played with them myself. The simplest one is the (3, 4, 5) triangle. The next is (5, 12, 13). There are an infinite number of them, and if it amused you (and apparently it amuses Dr Wildberger) you can get arbitrarily close to the shape of any right triangle with a Pythagorean triple triangle.

The traditional approach to trig links neatly with complex numbers and turns up smoothly in various branches of math. His scheme avoids some ambiguities with orientation, just as he claims, but also misses out on the connections. Poor choice.

In India, 1400 years ago, sine and cosine were approximated with parabolas, and I vaguely remember the idea being considerably older than that; so I'm not saying the Babylonians didn't do any trig. But this is not it.