Cosines of small angles - Secrets of the Mathematical Ninja
“Where the hell have you been?” asked the student.
The Mathematical Ninja raised an eyebrow into his well-tanned forehead. That, he didn’t say, would be telling.
The student sighed and sketched out a triangle. “I know that doesn’t look like 2º,” she said, to forestall any criticism.
The Mathematical Ninja nodded: “It’s a sketch. The details don’t matter.”
“The hypotenuse is 100 metres,” she said, “and I want the… adjacent side. Ah, rubbish. I could do it with the opposite - that would be about three metres, right?”
“Three and half or so, yep,” said the Mathematical Ninja. “But you can work out
“Where does that come from?”
“Euler series,” said the Mathematical Ninja. “Alternatively, you can say
“I’ll take your word for it,” she said. “So, to get
“It’s not trivial,” admitted the Mathematical Ninja, “but none of those things are too difficult.”
The student narrowed her eyes. “Right,” she said. “Two degrees is about
The Mathematical Ninja nodded. “Keep going!”
“So, that’s the fourth decimal place, 0.0006.
“Try it!” said the Mathematical Ninja.
“
The Mathematical Ninja smiled.
The student thought the Mathematical Ninja should take more holidays.