A Problem in Trigonometry

An excerpt from “Education made Agreeable: or, The Diversions of a Professor,” chapter six of Moonbeams From the Larger Lunacy by Stephen Leacock (1915). The text is in the public domain.

A few days ago during a pause in one of my college lectures (my class being asleep) I sat reading Draper’s Intellectual Development of Europe. Quite suddenly I came upon the following sentence:

“Eratosthenes cast everything he wished to teach into poetry. By this means he made it attractive, and he was able to spread his system all over Asia Minor.”

This came to me with a shock of an intellectual discovery. I saw at once how I could spread my system, or parts of it, all over the United States and Canada. To make education attractive! There it is! To call in the help of poetry, of music, of grand opera, if need be, to aid in the teaching of the dry subjects of the college class room.

I set to work at once on the project and already I have enough results to revolutionize education.

In the first place I have compounded a blend of modern poetry and mathematics, which retains all the romance of the latter and loses none of the dry accuracy of the former. Here is an example:

The poem of
LORD ULLIN’S DAUGHTER
expressed as
A PROBLEM IN TRIGONOMETRY

Introduction. A party of three persons, a Scotch nobleman, a young lady and an elderly boatman stand on the banks of a river (R), which, for private reasons, they desire to cross. Their only means of transport is a boat, of which the boatman, if squared, is able to row at a rate proportional to the square of the distance. The boat, however, has a leak (S), through which a quantity of water passes sufficient to sink it after traversing an indeterminate distance (D). Given the square of the boatman and the mean situation of all concerned, to find whether the boat will pass the river safely or sink.

A chieftain to the Highlands bound
   Cried “Boatman do not tarry!
And I’ll give you a silver pound
   To row me o’er the ferry.”
Before them raged the angry tide
X2 + Y from side to side.

Outspake the hardy Highland wight,
   “I’ll go, my chief, I’m ready;
It is not for your silver bright,
   But for your winsome lady.”
And yet he seemed to manifest
   A certain hesitation;
His head was sunk upon his breast
   In puzzled calculation.

“Suppose the river X + Y
And call the distance Q
Then dare we thus the gods defy
I think we dare, don’t you?
   Our floating power expressed in words
   Is X + 47/3”

“Oh, haste thee, haste,” the lady cries,
“Though tempests round us gather
I’ll face the raging of the skies
But please cut out the Algebra.”

The boat has left the stormy shore (S)
A stormy C before her
C1 C2 C3 C4
The tempest gathers o’er her
   The thunder rolls, the lightning smites ’em
   And the rain falls ad infinitum.

In vain the aged boatman strains,
His heaving sides reveal his pains;
The angry water gains apace
Both of his sides and half his base,
   Till, as he sits, he seems to lose
   The square of his hypotenuse.

The boat advanced to X + 2,
Lord Ullin reached the fixed point Q,
   Then the boat sank from human eye,
OY, OY2, OGY.

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