-
-
---------------- 1963 - Math - Fibonacci’s sequence
-
- You would not think that raising rabbits would lead to a historical mathematical theory, but, the ideas did.
-
- In 1202, Leonardo Pisano, also known as “ Fibonacci” defined this very problem. You start out with a pair of rabbits. You know what the reputation is for rabbits and their proliferation.
-
- ;How many pairs of rabbits will be produced in one year? Assume each pair is male and female giving birth to make one male and one female offspring once a month, 2 months after their birth.
-
- The monthly total of rabbits becomes:
-
-------MONTH------------- 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12
-
-----RABBITS------------- 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 , 89 , 144
-
- This population of rabbits is known as the Fibonacci Sequence.
-
- Each number in the sequence is the sum of the previous two numbers.
-
- If there are 8 pairs of rabbits in month 6 how many in month 12, at the end of the year?
-
- Leonardo has 144 rabbits at the end of the 1st year.
-
- The number of rabbit pairs in a generation is equal to the number of rabbit pairs in the previous generation plus all the newborn pairs that are at least 2 months old.
-
- What would happen if rabbits mated after 1 month instead of every 2 months?
-
- -----MONTH---- 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12
-
-----RABBITS---- 1 , 2 , 4 , 8 , 16 , 32 , 64 , 128 , 256 , 512 , 1024 , 2048
-
- The number of pairs doubles each month. At the start of the next year there are 4096 rabbit pairs, 8,192 rabbits. Oh my gosh, we need to import some foxes.
-
- Ok, what if rabbit reproduction was not as prolific? What if rabbits were 3 months old before they started reproducing?
-
- -----MONTH---- 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12
-
-----RABBITS---- 1 , 1 , 1 , 2 , 3 , 4 , 6 , 9 , 13 , 19 , 28 , 41
---------------------------------------------------------------------------------------
-
- The sequence?
-
- Each number is equal to the sum of the previous number and the number 3 months back in the sequence.
-
----------- 1 + 3 = 4 , 2 + 4 = , 6, 3 + 6 = 9, …………… 28 + 13 = 41
-
- We would have 41 rabbit pairs in first year.
-
- Ok, last question. How many pairs of rabbits after 12 months if each pair spawned a new pair after 1 month, a second pair in the second month and they lost interest in reproducing?
-
- The sequence:
-
- - -----MONTH---- 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12
-
-----RABBITS---- 1 , 2 , 4 , 7 , 12 , 20 , 33 , 54 , 88 , 143 , 232 , 376
-
- Each number in the sequence is one more than the sum of the previous two numbers.
-
- 1 + 2 + 1 = 4, 2 + 4 + 1 = 7, 7 + 12 + 1 = 20, ……….. 143 + 232 +1 = 376
-
- You have 376 pairs and 752 rabbits to feed. You really ought to write these sequences down if you are going to get in the rabbit breeding business. The Easter Bunny is just around the corner.
-
- Even more amazing mathematically speaking. If you divide a Fibonacci Number by the previous one you get the Golden Ratio
-
- Fibonacci Sequence:
-
- 1 , 1 , 2 , 3 , 5 , 8 , …………………
-
- 5 / 3 = 1.6666 , 8 / 5 = 1.625 ………………….. 1.61803399 …………
-
- The Golden Ratio is 1.618. This Golden Ratio appears in the Leonardo da Vinci paintings in the Parthenon. It appears in the Frank Lloyd Wright architecture. It appears in sea shells. In plant growth. In the 5 x 3, 6 x 4, 8 x 5 inch index cards.
-
-5 / 3 = 1.6666 , 6 x 4 = 1.5 , 8 / 5 = 1.625 …….. 1.61803399 …………
-
- If we made other index cards they would be:
-
- 3 x 2 , 5 x 3, 8 x 5 , 13 x8 , 21 x 13 …………………….
-
-----------------------------------------------------------------------------------
-
- Note (1): Request any of the Reviews by number to learn more.
-
- #853 - The Golden Ratio
-
- #1952 - Transcendental numbers “e” and “pi”
-
- #1953 - Math was invented to solve problems.
-
- #1953 this review list 27 more Reviews all about the wonders of math.
-
- ------------------------------------------ --------------------------------------------
---- Comments appreciated and Pass it on to whomever is interested. ----
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
-- email feedback, corrections, request for copies or Index of all reviews
- to: ------- jamesdetrick@comcast.net ------ “Jim Detrick” -----------
- https://plus.google.com/u/0/ -- www.facebook.com -- www.twitter.com
----- 707-536-3272 ---------------- Saturday, April 1, 2017 -----
------------------------------------------------------------------------------------------
No comments:
Post a Comment