Title: Survival time of Princess Kaguya in an air-tight bamboo chamber,
Abstract: Princess Kaguya is a heroine of a famous folk tale, as every Japanese knows.
She was assumed to be confined in a bamboo cavity with cylindrical shape, and
then fortuitously discovered by an elderly man in the forest. Here, we pose a
question as to how long she could have survived in an enclosed space such as
the bamboo chamber, which had no external oxygen supply at all. We demonstrate
that the survival time should be determined by three geometric quantities: the
inner volume of the bamboo chamber, the volumetric size of her body, and her
body's total surface area that governs the rate of oxygen consumption in the
body. We also emphasize that this geometric problem shed light on an
interesting scaling relation between biological quantities for living
organisms.