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The World’s Wit and Humor: An Encyclopedia in 15 Volumes. 1906.

Enrico Castelnuovo (1839–1915)

The Pythagorean Problem

From “Smiles and Tears”

“THE PYTHAGOREAN Problem!” said Professor Roveni, in a tone of mild sarcasm, as he unfolded a paper which I had extracted, very gingerly, from an urn standing on his desk. Then he showed it to the government inspector who stood beside him, and whispered something into his ear. Finally he handed me the document, so that I might read the question with my own eyes.

“Go up to the blackboard,” added the professor, rubbing his hands.

The candidate who had preceded me in the arduous trial, and had got out of it as best he could, had left the school-room on tiptoe, and in opening the door let in a long streak of sunshine, which flickered on wall and floor, and in which I had the satisfaction of seeing my shadow. The door closed again, and the room was once more plunged into twilight. It was a stifling day in August, and the great sun-blinds of blue canvas were a slight defense against the heat, so that the Venetian shutters had been closed as well. The little light which remained was concentrated on the master’s desk and the blackboard, and was, at any rate, sufficient to illuminate my defeat.

“Go to the blackboard and draw the figure,” repeated Professor Roveni, perceiving my hesitation.

Tracing the figure was the only thing I knew how to do; so I took a piece of chalk and conscientiously went to work. I was in no hurry; the more time I took up in this graphic part, the less remained for oral explanation.

But the professor was not the man to lend himself to my innocent artifice.

“Make haste,” he said. “You are not going to draw one of Raphael’s Madonnas.”

I had to come to an end.

“Put in the letters now. Quick! You are not giving specimens of handwriting. Why did you erase that G?”

“Because it is too much like the C which I have made already. I was going to put an H instead of it.”

“What a subtle idea!” observed Roveni, with his usual irony. “Have you finished?”

“Yes, sir,” said I; adding under my breath, “more’s the pity!”

“Come, why are you standing there moonstruck? Enunciate the theorem!”

Then began my sorrows. The terms of the question had escaped my memory.

“In a triangle—” I stammered.

“Go on.”

I took courage and said all I knew.

“In a triangle—the square of the hypotenuse is equal to the squares of the other two sides.”

“In any triangle?”

“No, no!” suggested a compassionate soul behind me.

“No, sir!” said I.

“Explain yourself. In what sort of triangle?”

“A right-angled triangle,” whispered the prompting voice.

“A right-angled triangle,” I repeated, like a parrot.

“Silence behind there!” shouted the professor, and then continued, turning to me, “Then, according to you, the big square is equal to each of the smaller ones?”

Good gracious! the thing was absurd! But I had a happy inspiration.

“No, sir; to both of them added together.”

“To the sum, then—say to the sum. And you should say equivalent, not equal. Now demonstrate.”

I was in a cold perspiration—icy cold, despite the tropical temperature. I looked stupidly at the right-angled triangle, the square of the hypotenuse, and its two subsidiary squares; I passed the chalk from one hand to the other and back again, and said nothing, for the very good reason that I had nothing to say.

No one prompted me any more. It was so still you might have heard a pin drop. The professor fixed his gray eyes on me, sparkling with a malignant joy; the government inspector was making notes on a piece of paper. Suddenly the latter respectable personage cleared his throat, and Professor Roveni said in his most insinuating manner, “Well?”

I did not reply.

Instead of at once sending me about my business, the professor tried to imitate the cat which plays with the mouse before tearing it to pieces.

“Perhaps,” he sneered, “you are seeking a new solution. I do not say that such may not be found, but we shall be quite satisfied with one of the old ones. Go on. Have you forgotten that you ought to produce the two sides, DE, MF, till they meet? Produce them—go on!”

I obeyed mechanically. The figure seemed to attain a gigantic size, and weighed on my chest like a block of stone.

“Put a letter at the point where they meet—an N. So. And now?”

I remained silent.

“Don’t you think it necessary to draw a line down from N through A to the base of the square, BHIC?”

I thought nothing of the kind; however, I obeyed.

“Now you will have to produce the two sides, BH and IC.”

Ouf! I could endure it no more.

“Now,” the professor went on, “a child of two could do the demonstration. Have you nothing to observe with reference to the two triangles, BAC and NAE?”

As silence only prolonged my torture, I replied laconically, “Nothing.”

“In other words, you know nothing at all?”

“I think you ought to have seen that some time ago,” I replied, with a calm worthy of Socrates.

“Very good! Very good! Is that the tone you take? And don’t you even know that the Pythagorean Problem is also called the Asses’ Bridge, because it is just the asses who cannot get over it? You can go. I hope you understand that you have not passed in this examination. That will teach you to read Don Quixote and draw cats during my lessons!”

The government inspector took a pinch of snuff. I laid down the chalk and the duster, and walked majestically out of the hall, amid the stifled laughter of my schoolfellows.

Three or four of my comrades who had already gone through the ordeal with no very brilliant result were waiting for me outside.

“So you have failed, eh?”

“Yes, I’ve failed!” I replied, throwing myself into an attitude of heroic defiance, adding presently, “I always said that mathematics were only made for fools.”

“Of course!” exclaimed one of my young friends.

“What question did you have?” asked another.

“The Pythagorean Problem. What can it matter to me whether the square of the hypotenuse is or is not equal to the sum of the squares of the two sides?”

“Of course it can’t matter to you—nor to me—nor to any one in the world!” chimed in a third with all the petulant ignorance of fourteen. “If it is equal, why do they want to have it repeated so often? And if it is not, why do they bother us with it?”

“Believe me, you fellows,” said I, ending the discussion with the air of a person of long experience, “you may be quite certain of it, our whole system of education is wrong.”