Tim Johson, curator of the University of Minnesota Cuneiform page johns976@tc.umn.edu Leslie Welser of Univ. of Nevada, Reno with her Star Teach site lwelser@physics.unr.edu %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% David J. Jeffery Department of Physics University of Nevada, Las Vegas 2003 August 19 Dear Dr. Johnson: I would like permission to use one of your cuneiform table images http://special.lib.umn.edu/rare/cuneiform/images/large/um5obv.jpg in set of web notes I am preparing to teach in the 2003/2004 semesters. I'm just using it as a good example of the appearance of cuneiform writing. The image will be shown with credit and link to your exhibit page http://special.lib.umn.edu/rare/cuneiform/index.html Thank you for your consideration. Sincerely David J. Jeffery (They replied by hardmail with a bunch of verbage. All this for just showing a picture of a clay tablet. In my view, it is hard to claim copyright on a mere image of document that was never copyrighted. But everyone is so hyper about getting credit and controling their images. Oh, well, so be it.) David J. Jeffery Department of Physics University of Nevada, Las Vegas 2003 August 19 Dear Dr. Johnson: Re: my request to reproduce the image of your cuneiform tablet UM 5 of 2003 August 19. Your terms are acceptable to me. Thank you for your consideration. Sincerely David J. Jeffery %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% David J. Jeffery Department of Physics University of Nevada, Las Vegas 2003 August 19 Dear Ms. Welser: I would like permission to use the image of the Venus tablet that you show on your Mesopotamian astronomy page http://www.physics.unr.edu/grad/welser/astro/mesopotamian.html and I wonder if you could provide me with the proper credit information for this image. Thank you for your consideration. Sincerely David J. Jeffery From: "Leslie Welser" To: "David Jeffery" References: <20030819222320.3FE7C57D25@hal.physics.unlv.edu> Subject: picture Date: Tue, 19 Aug 2003 15:47:30 -0700 Dr. Jeffery, No problem. The photo is from Anthony Aveni's great book, Stairways to the Stars. There is a copy of this book in the UNR library. The reference for the book is at the bottom of the page you mentioned. Leslie Welser ---------------------------------------------------------------------------- -------------------- Leslie Welser Department of Physics / 220 University of Nevada, Reno Reno, NV 89557 775-787-8454 Visit StarTeach Astronomy Education at http://www.physics.unr.edu/grad/welser/astro ! David J. Jeffery Department of Physics University of Nevada, Las Vegas 2003 August 19 Dear Ms. Welser: Thank you very much. By the I liked your Star Teach site, though I've not explored it much. Sincerely David J. Jeffery %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Date: Sun, 05 Oct 2003 12:43:29 -0700 To: jeffery@physics.unlv.edu From: John Halloran Subject: Mesopotamian 360-degree division of sky circle Dr. David Jeffery, I was thinking about adding a link to your page on Mesopotamian Astronomy from the links page at my web site www.sumerian.org. But first I would like to respond to your statement that "The late Babylonian astronomers divided the circle into 360 degrees. No one knows why." Here is a newsgroup post and my response to it. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Any chosen number base is somewhat arbitrary. I've seen different ideas put forward for why 360 was chosen to divide the circle. One idea is that there are about 30 days in a lunation cycle, about 12 lunation cycles in a year, and 30 x 12 = 360. I don't know if that's really "the reason," but it's interesting that a lunar year is about 354 days, a solar year is about 365 days, and 360 is about halfway between those two numbers. Another idea is that the Babylonians used 60 as a number base for their currency, weights, measurements, etc., the reason being that 60 is a highly divisible number. Of course, there are 60 minutes in a degree, and 60 seconds in a minute. The story goes that the circle was divided into 360 units because 6 x 60 = 360. I think that's only a partial explanation, because it doesn't explain why 360 was chosen instead of some other multiple of 60; for example, it would seem more in keeping with base 60 to use either 60 itself, or perhaps 3600 (60 x 60). But then, 360 is close to the number of days in the year (both the solar year and the lunar year). Another idea I've seen put forward in one of the mathematical newsgroups (and I'm paraphrasing heavily, as I can't remember the way it was stated) is that the Babylonians thought highly of the equilateral triangle, which has angles of 60 degrees, so they chose 360 degrees because it's a multiple of 60. This is really just a variation of the preceding idea, but I think it sounds backwards, because to have angles of 60 degrees in an equilateral triangle, you must first define how large a degree is! But it may be that the angles in an equilateral triangle were set at 60 units first (60 being the Babylonians' number base of choice), and this in turn gave rise to 360 units in a circle. It is true that the Sumerians and after them the Babylonians used 60 as the base of their sexagesimal number system, but the division of time into 360 units probably results instead from the multiplication of 30 units by 12 hours. The following two entries from my Sumerian lexicon show that the use of 12 units and 360 units as a measure for the time of a day's rotation goes back to the Sumerians. danna, dana: road-length measure, 'march' = 30 USH = 21600 cubits = ca. 6.7 miles/10.8 kilometers; double hour (twelfth part of a full day) = the time it takes to march a length of 1 danna (Akkadian etymology from 'place of strength or safety'). USH: a length measure, reading unknown, = 6 ropes = 60 nindan rods. Do you have any questions about the Sumerian measurement terminology? Regards, ------------------------------------------- John Halloran http://www.sumerian.org/ e-mail: jah7@pacbell.net (Do I have any questions? Well not at this time of night.) David J. Jeffery Department of Physics University of Nevada, Las Vegas 2003 October 5 Dear Dr. Halloran: Thanks for your information. I think my Mesopotamian astronomy page is unworthy to be linked to---I should link to yours as indeed I do. I just hacked my page together for my teaching needs when I cover the history of astronomy. It is pretty much an amateur effort. Sincerely David J. Jeffery