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Bridging the Gap Between Theory and Practice: Astronomical Instruments - Teaching a Course in Ancient Mathematical Astronomy

Toke Knudsen (State University of New York at Oneonta)

Teaching a Course in Ancient Mathematical Astronomy

The course was offered for the first time in Fall 2010. At that time, the course ran as a special-topics course due to a delay in final approval over uncertainty over how to handle a potential student fee for the materials used to construct the instruments. Soon after the special-topics course started, the course received full approval as a permanent course at SUNY Oneonta. Four years later, in Fall 2014, the course was offered again. As such, the course has been offered twice at SUNY Oneonta. The present article details my experiences from teaching Ancient Mathematical Astronomy these two times.

Both times it was offered, the course had an excellent enrollment for an elective in the Department of Mathematics, Computer Science, and Statistics at SUNY Oneonta. The following table shows the enrollment in Fall 2010 and Fall 2014, including the majors of the students enrolled. The data for Fall 2010 includes an auditor, an Adolescence Education: Mathematics major, who, while not required to do any of the coursework and unable to receive a final grade, participated fully in the course.

Major   Fall 2010 Fall 2014
Mathematics    5  3
Adolescence Education: Mathematics    5  2
Physics    1  5
Adolescence Education: Physics    1  1
Chemistry    2  0
Art    1  0
Total   15 11

In Fall 2010, the course attracted a more diverse range of majors than expected, whereas in Fall 2014, the range of majors was limited to precisely those majors that I originally had in mind for the course.

Required course work

Ancient Mathematical Astronomy has no sit-in tests. Instead it is required for the students to hand in five assignments, an instrument paper, and a final research paper. In addition, homework problems and readings are assigned on a regular basis, and students are required to make presentations before the class.

The idea of the instrument paper is to familiarize the students with the instrument that they are undertaking to design. In addition to the history of the instrument, the instrument paper must include a theoretical section on how the instrument works, as well as notes on the design of the instrument. Ideally, the students should also include sketches of their design. More often than not, however, the papers did not include useful sketches. One reason for this is that it is hard to produce the sketches before understanding the theory behind the instrument, an understanding that the instrument paper is meant to bring about.

For the part of the course dealing with design of instruments (including working on the instrument paper), the students are divided into groups of two or three, who in consultation with me agree on an instrument to work on. In Fall 2010, each student wrote an individual instrument paper, whereas in Fall 2014 each group handed in one paper for all the members. I felt that requiring individual papers was unnecessary given that the students work so closely together on researching and designing the instrument. After receiving feedback from me on the instrument papers, the groups began actively designing the instrument. During this phase, the students worked closely with Anderson, who advised on what is feasible and offered feedback on the ideas of the students. Anderson would later construct the parts required by the students' designs.

The final research paper is an open and flexible paper meant to allow each student to dive into a topic that they find especially interesting. The final research paper can be focused on the history of astronomy, formulae and derivations from mathematical astronomy, or philosophical questions relevant to the development of astronomy. Among the topics chosen by students are the computation of square roots in the ancient world, archeoastronomy, Ptolemy's Almagest, and the use of sine tables in the ancient world.

Planetarium and Observatory visits

SUNY Oneonta has a planetarium with a digital projector system that can provide views of the stars, planets, luminaries, and constellations, as well as 3D movies. The system is based on Evans & Sutherland Digistar 4 software. The Planetarium is available for class visits by appointment.

The college also has an observatory. The observatory has a large number of telescopes, both mounted and mobile. In particular, the SUNY Oneonta Observatory owns a 1-meter JMI NTT-40 mobile telescope, the largest optical telescope in the state of New York. The Observatory hosts open nights, and is also available for class visits by appointment.

I naturally sought to make use of these two excellent resources in Ancient Mathematical Astronomy. In Fall 2010, the class visited both the Planetarium and the Observatory. At the Planetarium, the class saw a presentation by a SUNY Oneonta student on astronomical coordinate systems. The visit to the Observatory, guided by former Planetarium and Observatory Director and astronomy professor Dr. Quinn Minor, focused on observing the moon by telescope.

In Fall 2014, the class made two visits to the Planetarium. A planned visit to the Observatory had to be canceled due to bad weather, and it was not possible to find another date that worked for all the students. The first visit to the Planetarium featured a presentation on astronomical coordinate systems. At the second visit, the class watched the 3D documentary Stars of the Pharaohs from 2004, produced by Evans & Sutherland. Both presentations at the Planetarium were given by Planetarium and Observatory Director and astronomy professor Dr. Joshua Nollenberg, who was also scheduled to guide the Observatory visit that was canceled.

Course fee

It was originally unclear how expensive the construction of the instruments would be, and I expected that there would be a small course fee per student, perhaps $20 or so. However, it turned out that the cost of constructing the instruments was low enough that the Science Technician's budget covered most of it. Students paid for minor things here and there (mirrors for the sextants, for example), but the costs of most of the materials were covered by the Science Technician.

Toke Knudsen (State University of New York at Oneonta), "Bridging the Gap Between Theory and Practice: Astronomical Instruments - Teaching a Course in Ancient Mathematical Astronomy," Convergence (May 2015)