Monday, January 21, 2013
I was having trouble thinking of something to blog about today. Then I saw the word “triangles” written in a children’s book open on the table. Ok, then. There’s the challenge: blog about triangles, the simplest of all polygons.
There are some very important (or, perhaps, infamous) triangles in the world. Love triangles and the Bermuda triangle come to mind. There are equilateral triangles, isosceles triangles, and the ever-popular scalene triangles. There is the percussion instrument of the same name, which even I have a chance of mastering. Let’s not forget the all-important tripod, whose feet make a triangle upon the ground. For the mathematically inclined there is Pascal’s Triangle. How about the Sierpinski Triangle (yeah, I had to look it up too)?
In fact, we can thank the triangle (via Pythagoras) for giving us a entire branch of mathematics – trigonometry. I know many of you will be deeply grateful to Pythagoras. I know how many of you longed to hear the next episode of trigonometry’s story. Remember that night, the night after you learned about sines and cosines? How you longed to hear about tangents the next day! Hypotenuse, adjacent, opposite – pure poetry.
Of course, the triangle’s claim to fame is really due to its famous cousin, the circle. Those of you who have followed this blog for a while will have come across circles before. What do those sharp, pointy things (triangles) have to do with those smooth round things (circles)? Angles. The concept of an angle only makes sense in the context of the circle. Degrees – we are talking fractions of a circle. π (as in The Life of...), radians – these building blocks of trigonometry are so very circular.
I am not a mathematician, and I know that the sight of numbers, let alone Xs and Ys (how very triangular), sends some people into anaphylactic shock. Nevertheless, mathematics is beautiful and astonishing. It never ceases to amaze me how these concepts hold together. They are like conceptual snowflakes.