A year ago, I took a math exam for a job application. I passed the exam, made it to the interviews, and actually got qualified for the training. Eventually, I decided not to take that opportunity, and I chose to pursue the job that I have right now. But this article is not about that missed job or any jobs. This is about a particular math problem in the math exam. It was so interesting that I told myself I would write about it. And after 1 year, here it is. The problem went like this: It is 2:00. What time will the hour hand and the minute hand make a straight line together? Before this exam, I had never solved a problem like this. I had no idea where to begin (let alone solve it). I could skip this problem and not give a fuck about this 1 point. But I did not. I wanted to solve it not for the point, but for the sake of solving it. I wanted to prove to myself that my knack for geometry from high school was still sitting behind my brain, awaiting to be tapped. I so began thinking. ...
I woke up early in the morning and sat at my computer. I was about to study Japanese when I suddenly remembered how I made a perfect star in high school. At that time, I had a good grasp of elementary geometry, so I was able to easily make it with a ruler and a protractor. With a ruler to measure length and a protractor to measure angles, it was easy to make a star. A star is a polygon with ten sides. Technically, it is a decagon. But a star can be created by laying out only five lines from its center as its frame. To make a perfect star, all five lines must have the same length and must have equal angles between them. A complete rotation has 360°. To determine the angle from one line to the other, 360° is divided by the number of lines, which is 5. 360° / 5 = 72° From the angle alone, and with a ruler and a protractor, a perfect star can be drawn like so: Draw a line with length x from the center upward. Then, measure 72° from the center to its left and right, and draw the...