Leonardo Fibonacci
July 24, 1204
Dearest Frederick,
I hope you are
doing well. I know the Roman Empire is a
bit chaotic these days, mostly fighting on the outskirts of Turkey. Yet, I know
you possess the skills to bring peace to a realm renowned for its advancement
in technology, education, and organized government. My friend Abdul just told
me of your most recent experiment. How did you decide to lock ten convicts in a
room so small they suffocated, and then open the door to see if their souls
came out? You have always been so creative, my dearest Frederick. I know the
life of an emperor is most very busy, but I have written to you to share a new
discovery. I last saw you at court in Florence in about 1203, where we were
involved in a competition of algebraic equations, which I quickly won. I have
continued to develop my mathematic theories ever since. As you know I wrote the
book, Liber Abaci, two years ago.
However, I do not think you have read this particular problem, which I have
begun to dissect and answer completely.
“A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair, which from the second month on becomes productive?”
The sequence is
1, 1, 2, 3, 5, 8, 13, 21,
34, 55…
After much study and deliberation of the rabbits, I now
know that each group of rabbits’ born is the sum of the two preceding groups of
rabbits’ born. I find this sequence very interesting, and have begun to apply
it to nature. For example, did you know that most daisies have 34, 55, or 89
petals? I’m sure you quickly realized that 34+55 is 89. I plan to do much work
exploring this sequence, and will share my thoughts with you as soon as
possible. However, dearest Freddy, I knew you would appreciate an update from
your closest math scholar.
Please
send my regards to your beloved wife Penelope and two children. Henry and Jack
were always so athletic and skilled at archery; what fine boys they must be by
now. I would also love it if you would make a few copies of the text Liber Abaci, and deliver it around the
empire. Many mathematicians across the empire are sending me requests of
shipment at least once a fortnight. Within this letter, I have enclosed a
painting of me, since you have always wished for one to hang in the section of
your library, which houses the math texts. Hope all is well.
Many Thanks.
Sincerely,
Fibonacci
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What an incredible friendship you have with Frederick! Your connection with the Roman Empire through the emperor, is so kind spirited, and I find it great that you have kept in touch for so many years. He seems like an interesting man, and I was so delighted to hear about your number sequence. Perhaps you have worked with Abdul to create this theory. I admire greatly that you are discovering math and its real life applications, for this has been my professional goal since I was in college. For me, I use geometry in my tessellations and produce them onto wood, or other mediums of my preference. I can't wait to get my hands on your book, Liber Abaci, and perhaps you could send me a copy. You have described in your letter the number of petals on daisies, and I was wondering if you were investigating other flowers or plants that connect to your sequence? I would find it truly incredible if you found even more uses to your numbers that are found in the natural world. I would also love to see if your number sequence correlates to any of my art, because that would be so fascinating!
ReplyDeleteI wish you the best of luck with continuing this sequence,
M.C. Escher
Leonardo,
ReplyDeleteI am happy to hear that you can stay in touch with your home. And who better to connect you with Europe than an avid math lover and fellow mathematician! The problem you mentioned is very interesting, and the number sequence you discovered is even more intriguing! I am very interested in how this series applies to the world at large and how you can apply this knowledge. I am astounded that the petals follow the pattern dictated in your sequence. I understand that you are trying very hard to meet the demand for your book, but if it isn't too much trouble I'd love a copy, even just to borrow and look over. I do wonder how this sequence manifests itself as the numbers get larger, and if those numbers correspond with more things in the real world. My favorite part of this whole sequence though is its simplicity to form. The rules which govern this set are simple and vacuously true. There is no need for clarity in the rules that govern it, because it is so simple!
Best,
David Hilbert