The Mathematical Ninja takes a square root
“So,” said the Mathematical Ninja, “we meet again.”
“In fairness,” said the student, “this is our regularly-scheduled appointment.”
The Mathematical Ninja was unable to deny this. Instead, it was time for a demand: “Tell me the square root of 22.”
“Gosh,” said the student. “Between four-and-a-half and five, definitely. 4.7 or so?”
The Mathematical Ninja nodded. “Four and seven tenths is an excellent initial approximation. Allow me to demonstrate a better one.”
The student allowed.
“You have correctly - I presume - made your initial estimate by noting that 22 is 3 smaller than
“Of course, sensei,” said the student, who had done nothing of the sort. He had interpolated quickly.
“A better second estimate is
“Thirty… over 100 + 3. Wai… wah!”
“
The student was unlikely to forget that now. “So, I could apply the same process again to get a correction of…” (pause for thought) “
The Mathematical Ninja nodded again. “You could continue the process for as long as you felt the need - each iteration gets you a slightly better estimate.
The student felt that there was little need to make it any more accurate than that - although he’d never tell the Mathematical Ninja that. He had developed a little sense.