| Contributed by
Vijay Fafat
Adolfo Sureda had made a lasting promise to himself: to have a house of unique architecture built for him and his bride, Remedios.
For this, he commissioned a recent graduate of architecture who -- in a flash of inspiration -- decided to build a “triangular house” with isosceles triangles for sides (later allusions imply that the house was pyramidal).
| (quoted from The Triangular House [La Casa Triangular])
“Misfortune,” they both thought, “cannot possibly come into a toy house whose doorway is so different from the ones She usually seeks out.” The beseeching eyes of the triangular windows, raised toward Heaven , pleaded mystically for happiness.
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And wouldn’t you know it! The couple was blessed with triplets in that triangular house!
| (quoted from The Triangular House [La Casa Triangular])
“Now,” he thought finally, facing the consequences, “the three angles of the triangle have been found , and these boys should be given names to fit with the letters ABC which label the triangle. Therefore the first born will be named Augusto, the second Benito, and the third Cosar.”
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As the children grew, so did the unrest in the house and around the once-happy couple. Indeed, the middle son started showing signs of a conical head.
One day, Adolfo found a strange, old man peeping and staring inside the house and was none too happy about it. But as the old man explained:
| (quoted from The Triangular House [La Casa Triangular])
Sir, I am a mathematician a geometer—and your house intrigues me because it poses new problems in geometry and trigonometry. Here are the data for the problem . . .” And the geometer showed Adolfo the paper with his figures (which displayed the half-angle formula for calculating the angles of a triangle given its sides):
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Adolfo was overjoyed at finding a kindred spirit. After an admiration-filled house tour, Adolfo told the mathematician about all his recent problems. The geometer had a ready solution for him, which Adolfo on-boarded enthusiastically:
| (quoted from The Triangular House [La Casa Triangular])
“This is happening to you,” the mathematician replied, “because you are not a geometer. If you grasped the triangular sense of the house you- would be invincible: there is nothing more devoid of problems— or more clean-cut in its arrangement of space—than a triangle. Would you like me to instruct you in these matters? It has been my lifelong study. All we need by way of equipment is a blackboard.”
[…]
Adolfo specialized in triangles, and grew steadily more confident about his triangular house. He was amazed at how the triangle kept being solved, thanks to equations and calculations. There were no corners or wasted spaces in his house; logically, it was superior to all other houses. He and the geometer had even decided to collaborate in writing an essay on “The Triangle: A Study in Depth, or, The Intimate Exegesis of the Living Triangle”
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With these new studies, Adolfo drifted away from Remedios, who started getting bored. And then, he got an anonymous letter informing him that Remedios was having an affair behind his back:
| (quoted from The Triangular House [La Casa Triangular])
"Ah!” exclaimed the geometer. "This must be studied as one more problem: the domestic triangle. I had hoped that it might not happen—but it had to happen . . . and better now than later, after all.”
"Great heavens! Better that it had never happened!” Adolfo answered.
The geometer went to the blackboard and rubbed out what was written there with the decisive movements of a fireman putting out a blaze. Then he set about solving the problem.
"You form a scalene triangle . . . we deduce this, not only because of your unequal qualities but also because the moment your wife—angle A—found someone attuned to her nature, you were the perpendicular angle, angle B. Now, since we know angles A and B, all we need do is to find angle C. The problem is extremely simple because A is, of course, equal to C, which is the unknown . . . Does some Cousin of your wife’s have free access to the house?”
"Yes. Enrique.” "Well, that’s the man.” "Is the proof positive?” "Geometrically! Q.E.D.”
Adolfo went out of the study, found his wife, and accused her: "So! It’s Enrique, isn’t it?”
"How did you know?”
"Trigonometric formulas never fail.”
"Ah!” she finally exclaimed, giving herself away.
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One walks away from this story with a philosophical smile. Perhaps at the impish cleverness of using the geometry of triangles to identify the cousin as the adulterer. Perhaps at the paced evolution of the story, leading one from an architectural idea to the triangles in human interactions. Perhaps at the idiosyncratic natures of both, the happenings in the story as well as the character of the mysterious Geometer.
A Note on the Author:
It is worth reading about this remarkable and prolific author on Wikipedia.
Ramon invented a literary form called “Greguerias”, of which he reportedly wrote tens of thousands over his lifetime. As described, “Greguerías are ingenious, and generally brief, sentences that arise from a casual clash between thought and reality.”. Clearly there is much to explore in Ramon’s work…
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