Arco capaz… is there an English word?

Hm… I should start this story from the beginning, as Alice once was told. I make a living from teaching college maths in Madrid, but half of the time I do it in English. (No, no randomness involved, though). I asked my calculus students to solve this problem:

“A soccer player runs with the ball perpendicularly to the goal line, but a little bit to the right of it. Forgetting about the opponent players, when should he shoot?”

My idea was just an optimization problem, but, alas, some of my boys and girls are really smart… and one of them asked me: “Javi, how do you say ‘arco capaz’ in English?” Oh, embarrassment! I didn’t know the word!

Ehm… let’s go by parts, as Jack the Ripper said. For those of you not fluent in the language of Cervantes, arco capaz is the geometrical locus of the points in the plane from which a given segment is seen under a certain angle. It must be an arc, as you can see from the pic:

Okey dokey, so the boy was right, you can solve it using this construction. All you need is… well,  won’t say, just give your proposals :)

Anyway, the interesting part comes now. OMG, I felt so bad that there was a technical word I couldn’t say in English… so I run to wikipedia (all praise be given to her), clicked arco capaz in Spanish, clicked the English button et… voilà? No! It took me to a concept which is completely unrelated!

Hm… how could wikipedia (APBGTH) fail me???? Then I found this link in wordreference (also all praise… whatever) in which… the hypothesis was advanced that there was no word in English for that concept! They even cited a webpage where Patrick Morandi, head of dept of maths in the New Mexico state university, used the Spanish term…

After that I found few entries with the French term “arc capable”, but the term in Spanish is really common!! All first year students in science and engineering have heard about it! So, perhaps this is the second word (first in science) that goes from Spanish to English. The first one was mosquito

But why is the concept not lexicalized in English? I can give no citations, but I heard (my grandpa, long back) that it was born in navigation science. Using it, you can find out where you are on the map very easily as soon as you have three landmarks that you can recognize… Did sailors use a different technique in other countries? Maybe they used it but they didn’t give a name to it? I can imagine: “Captain Haddock, please draw the two… ehm… yes, draw the two circles and see where do they intersect”, “Which circles?”, “Yes, the circles from which the two given segments are seen under the correct angles…” Messy.

Yes, giving names to the correct things can save a lot of work. Or give a lot of work, if you do it wrong…