Lanj: 2012/3/9

Translated from the original Japanese.

2014/02/07

Note from Nias: This account is ported from an old edition.

2012/3/9.

Seren sat down on the bed in Mel’s room to ask her a question.

“A piece of wire is cut into two in a certain ratio, and a circle and a square are made from the respective pieces. To minimize the sum of their areas, what do you think that ratio should be?”

Seren held in his hands some notes with a vast number of equations written. He had solved the problem with algebra by the book.

Having glanced at the top-right for a moment, she answered, “π : 4”.

Seren was surprised at the sheer speed of the answer. “How did you know!? No matter how you look at it, that’s too fast for mental math. Or maybe it’s somehow simple enough to do in your head?”

“I wasn’t solving it with algebra before doing the mental math.”

“Then, how did you do it?”

“If you inscribe the circle inside the square, then the sum of their areas will be at their minimum. Therefore, π : 4.”

Seren was left absent-minded with his mouth wide open.