The poet Longfellow, in his novel Kavanagh, introduced several clever mathematical problems from an ancient Sanskrit work. I have
used several of them in my Problems of the Week / Month. Below is an excerpt in which the problems appear.
Excerpts from Kavanagh by Henry Wadsworth Longfellow
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"One-third of a collection of beautiful water-
lilies is offered to Mahadev, one-fifth to Huri,
one-sixth to the Sun, one-fourth to Devi, and six
which remain are presented to the spiritual teach-
er. Required the whole number of water-lilies."
"That is very pretty,"said the wife,"and
would put it into the boys' heads to bring you
pond-lilies."
"Here is a prettier one still. One-fifth of a
hive of bees flew to the Kadamba flower; one-
third flew to the Silandhara; three times the dif-
ference of these two numbers flew to an arbor;
and one bee continued flying about, attracted on
each side by the fragrant Ketaki and the Malati.
What was the number of the bees?"
"I am sure I should never be able to tell."
"Ten times the square root of a flock of
geese"
Here Mrs. Churchill laughed aloud; but he
continued very gravely,
Ten times the square root of a flock of
geese, seeing the clouds collect, flew to the
Manus lake; one-eighth of the whole flew from
the edge of the water amongst a multitude of
water-lilies; and three couple were observed
playing in the water. Tell me, my young girl
with beautiful locks, what was the whole number
of geese?"
"Well, what was it?"
"What should you think?"
"About twenty."
"No, one hundred and forty-four. Now try
another. The square root of half a number of
bees, and also eight-ninths of the whole, alighted
on the jasmines, and a female bee buzzed respon-
sive to the hum of the male inclosed at night in a
water-lily. O, beautiful damsel, tell me the num-
ber of bees."
"That is not there. You made it."
"No, indeed I did not. I wish I had made it.
Look and see."
He showed her the book, and she read it her-
self. He then proposed some of the geometrical
questions.
"In a lake the bud of a water-lily was ob-
served, one span above the water, and when
moved by the gentle breeze, it sunk in the water
at two cubits' distance. Required the depth of
the water."
"That is charming, but must be very difficult.
I could not answer it."
"A tree one hundred cubits high is distant
from a well two hundred cubits; from this tree
one monkey descends and goes to the well; an-
other monkey takes a leap upwards, and then de-
scends by the hypotenuse; and both pass over
an equal space. Required the height of the
leap."
"I do not believe you can answer that ques-
tion yourself, without looking into the book,"said
the laughing wife, laying her hand over the solu-
tion."Try it."
"With great pleasure, my dear child,"cried
the confident school-master, taking a pencil and
paper. After making a few figures and calcula-
tions, he answered,
"There, my young girl with beautiful locks,
there is the answer, forty cubits."
His wife removed her hand from the book, and
then, clapping both in triumph, she exclaimed,
"No, you are wrong, you are wrong, my
beautiful youth with a bee in your bonnet. It
is fifty cubits!"
"Then I must have made some mistake."
"Of course you did. Your monkey did not
jump high enough."
She signalized his mortifying defeat as if it had
been a victory, by showering kisses, like roses,
upon his forehead and cheeks, as he passed be-
neath the triumphal arch- way of her arms, trying
in vain to articulate,
"My dearest Lilawati, what is the whole
number of the geese?"