Calculus Student
Franklin & Marshall College
Lancaster, PA 17604
Dear Calculus Student:
First of all, I would like to thank you on behalf of the entire SILU staff for your efforts in finding us an appropriate pair of formulas for  and e . I am so very sad to say that all the work that you and our many other scientists have done amounts to naught because of problems beyond your control.
Due to the inclement weather our state endures, our telescope domes have been subjected to a lot of strain lately. The wear and tear on them has caused certain portions of the domes to work loose ever so slightly. The ensuing vibrations, as they affected our receivers, more than account for the strange signals that (we thought) we were receiving.
You can understand, I think, what a blow this has been to us. The star Tau Ceti was a very reasonable candidate for such a search, due to the fact that it is the nearest non-binary solar-type star, and the fact that it has some dust around it probably revealing the aftermath of planet formation (see for example Backman and Gillett, 1986 COSPAR Proceedings. Backman is a professor at your own college).
We are not the first to be deluded by mechanical problems (if you ask your professor, I am sure she can tell you about other instances where mechanical disturbances were prematurely interpreted as astronomical phenomena), but this hardly cheers us.
"Your pneumonia does not make my cold feel better," my grandmother used to say,
and she was right.
It is partly this disappointment and partly the interest you essayed in our studies that makes us so bold as to ask another favor of you. We are anxious to repair the damages to our telescope domes so as to get on with our research, and we think that you can help us with this.
We actually have two telescope domes. In fact, they were both built by an F&M alum by the name of John Smith. Smith was a brilliant, albeit eccentric, architect, who was devoted to his alma mater. Plagued by an intellectual genius coupled with a common-place name, Smith grew more and more demented as he aged. The domes he designed for us are exact replicas of George and Martha, the water towers that sit on Buchanan Park right next to your campus. (By "exact", I mean outwardly. Of course they are very much different inside, and of course, the roof of each is hinged so that the telescopes can see out). He claimed that these domes reminded him of the campus he loved so dearly.
By the time Smith died, he was just about as incoherent as the mathematicians we mentioned in our first letter. (We live fairly close to the Eco-Sludge factory in Well Well, PU). By his wishes, and much to our horror, the designs for our domes were cremated with him, leaving us with no blueprints for our buildings. Our engineers believe that they can reconstruct much of the small details of the plans, but they are having trouble with the larger aspects. This, of course, is where you fit in. We would like you to come up with two equations (one for each tower) describing the height of each tower at each point. By this we mean: if we stood on the ground floor with a long pole that could reach the ceiling (somehow passing through the other floors and equipment), how tall would that pole be as we moved around the floor?
Although it is not necessary by any means, we would also be grateful if you could come up with an equation describing the spiral staircase that curls around Martha. This would be a nice "extra" for our engineers to mull over.
You may wonder why we are asking you to do this rather than do it ourselves. There are several reasons, the first two of which are petty. Firstly, you are young and energetic, which few of us are. Secondly, you are now learning mathematics that we have long forgotten. More importantly, however, our domes are perched on the tops of mountains, which makes sighting difficult, whereas your water tanks are on relatively flat ground, making surveying somewhat easier. Fourthly, being at F&M, you have access to protractors (through the Steve Sylvester of the Geosciences Department), and we don't.
We are turning to you in both desperation and hope. If and when you do get the answer we are searching for, please send it to me rather than to Director Bourbaki, as he is busy with the scientific aspects of our data and has handed all mechanical aspects to me. If possible, we would like an answer by March 12, 1993.
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