ebook img

Another Hanukkah Miracle: The Gaps Between Consecutive Christmas-in-Hanukkah Years is ALWAYS a Fibonacci Number! PDF

0.04 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Another Hanukkah Miracle: The Gaps Between Consecutive Christmas-in-Hanukkah Years is ALWAYS a Fibonacci Number!

Another Hanukkah Miracle: The Gaps Between Consecutive Christmas-in-Hanukkah Years is ALWAYS a Fibonacci Number! By Shalosh B. EKHAD In fond memory of Marvin Isadore Knopp (1933-2011) z”l, who left us this Christmas Eve, the fifth candle of Hanukkah 5772, who did not like computers (even for Email), but was nevertheless one of the kindest and warmest neshamot (souls) on this planet. 2 1 0 Jane Legrange, the beloved wife of my beloved master, commented this last Christmas Eve that it 2 is so nice to be able to light a menorah (or chanukiah) at the same time as the (Christian) goyim n sitting next to their Christmas trees, and sheasked her husband,whoasked me, how special is that a J coincidence? Using the Maple package 3 http://www.math.rutgers.edu/~zeilberg/tokhniot/LUACH ] O H written by Zeilberger a few years ago, and updated and upgraded recently in order to answer this . question, I figured out that in this, third, millenium, it happens 270 times, so %27 of the time. h t In the next two millenia after that it would happen 266 times in each. In the sixth millenium a m (i.e. between 5001 and 6000), it would only happen 263 times, while in the seventh millenium (i.e. [ between6001and7000), itwouldonlyhappen258times. Ifwearestillaliveintheeighthmillenium 1 (i.e. between 7001 and 8000), it would only happen 134 times, and in the ninth millenium, only v 15 times! After that it will never happen for many many years, certainly not until 20000 AD. The 8 5 last year is 8473, where we would light the first candle on Christmas Eve. After that Hanukkah 5 will always be way after Christmas. 0 . 1 But cheer up! Eventually we can, every few years, sit in a Sukkah during Christmas Eve! The first 0 2 time this would happen is 16103, when Christmas would be on the 20th day of Tishrei, and we can 1 put the Christmas tree inside the Sukkah. During the 17th millenium (between 16001 and 17000) : v we would only have 68 Sukkah Christmases, but during the 18th (between 17001 and 18000) we i X wouldhave207ofthem,duringthe19thwewouldhave239butonly235duringthe20thmillenium. r a While doing these calculations, I noticed something really amazing! Between the Gregorian years of1801 and7390 (whenChristmas-in-Hanukkhaisstartingtoget rarerandrareruntilitdisappears completely) the gap between consecutive such lucky years is always a Fibonacci number, in fact, it is always a member of the set {2,3,5,8}. It would be interesting to have a conceptual proof, in addition to my computational proof. Andguess what! Once Christmas-in-Sukkotbecomes not toorare, and thatwould happenin 17064 A.D., we have the same phenomenon, the gaps between consecutive Christmas-in-Sukkot years is also always a member of the set {2,3,5,8}, at any rate, until 20000 A.D. Of course, eventually Christmas will say good-bye to Sukkot also, and start visiting Rosh Hashana (but not that often since the latter is only two-days long), then Shavuot, and then Pesach. Readers are welcome to experiment with the Maple package LUACH to continue these preliminary investigations. 1 For a list of all the Christmas-in-Hanukkah years (between 1801 and 20000 (of course it ends in 8478)) see, http://www.math.rutgers.edu/~zeilberg/tokhniot/oLUACHs1 and for a list of all the Christmas-in-Sukkot years (also between 1801 (of course it only starts in 16103) and 20000), see http://www.math.rutgers.edu/~zeilberg/tokhniot/oLUACHs2 . ShaloshB.Ekhad,c/oD.Zeilberger,DepartmentofMathematics,RutgersUniversity(NewBrunswick), Hill Center-Busch Campus, 110 Frelinghuysen Rd., Piscataway, NJ 08854-8019, USA. Email: c/o zeilberg at math dot rutgers dot edu , Written: Jan. 2, 2012 . 2

See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.