Preparing for Fibonacci Day - Fibonacci Cabinets

Fibonacci Spiral.

 

REFERENCES:

https://www.behance.net/gallery/2812519/Fibonacci-Cabinet

http://www.gizmag.com/fibonacci-cabinet-math-furniture/24680/

David

Preparing for Fibonacci Day - Fibonacci Spiral

A tiling with squares whose side lengths are successive Fibonacci numbers.

Fibonacci Spiral

REFERENCES:

http://en.wikipedia.org/wiki/Fibonacci_number

http://en.wikipedia.org/wiki/Golden_spiral



David

Preparing for Fibonacci Day - Fibonacci Lemonade

This post is directly taken from Andrea Hawksley’s blog, but I did not include the directions for making Fibonacci Lemonade.  She has done such a good job on this post I simply can’t add to it.  I wanted to post the pictures to get your attention.  Please visit her website to see some very interesting posts on some artistic mathematical projects.  FIELD TRIP: http://blog.andreahawksley.com/fibonacci-lemonade/

 

Layered Drinks!

REFERENCES:

http://blog.andreahawksley.com/fibonacci-lemonade/

David

Solutions to Fridays Brain-O Quiz

Solutions to Fridays Brain-O Quiz

1.  7 + 7 + 7 – 7 – 7 = 7

2.  47.  Add the previous 2 numbers to get the next.

3.  Because polar bears live in the Arctic, not Antarctica.

4.  Baseball.
5.  There is no money missing.  They paid a total of $30.  The hotel kept $25, the bell boy kept $2, and each man got back $1 each.

David

Preparation for Fibonacci Day - Fibonacci Bees

Male bees come from unfertilized eggs, so they have mothers but no fathers. Females come from fertilized eggs, so they have parents of both sexes. This produces an interesting pattern: The number of males in a given generation equals the number of females in the succeeding generation. And the number of females in a given generation equals the number of females in the succeeding two generations:

Genealogy of a male bee, beginning with his "mom" at the bottom level of the chart above (which is the second generation going backwards).

One male be has 1 parent , 2 grand-parents, 3 great grand-parents, 5 great great grand-parents, 8 great great great grand-parents, 13 great great great great grand-parents, ...

So the total number of bees, male and female, (but not counting siblings) in generation n is the Fibonacci number F(n).

W. Hope-Jones discovered the relationship in 1921; this example is from Thomas Koshy’s “Fibonacci and Lucas Numbers With Applications”, 2001.

Reference:

http://www.futilitycloset.com/2013/11/06/busy-2/

David

Preparation for Fibonacci Day - Fibonacci Rabbits

Leonardo of Pisa (or Leonardo Fibonacci – the term Fibonacci means “son of Bonacci”) was born around 1170 into the Bonacci family in Pisa.  He worked in his family business and spent a lot of time in North Africa trading.  While there he learned from the North African about their number system and methods of performing calculations.  He found their mathematics was much simpler than the mathematics he learned and used in Pisa.

He later wrote a book called “Liber Abaci” that showed how to use these Hindu-Arabic numerals and to perform calculations with them.  (This book is the reason you are not doing math with Roman numerals.)

In his book he described a mathematical problem about a man who was starting a business raising rabbits.

“A man put a pair of rabbits (a male and a female) in a garden that was enclosed. How many pairs of rabbits can be produced from the original pair within 12 months, if it is assumed that every months each pair of rabbits produce another pair (a male and a female) in which they become productive in the second month and no death, no escape of the rabbits and all female rabbits must reproduced during this period (year)?"

So in the first month you get a pair (male and female) of baby rabbits and put them in your enclosed garden.  In the second month you still have 1 pair of rabbits because they are not old enough to reproduce.  In the third month you have the same pair of rabbits, but they have also had a pair of babies – for a total of 2 pairs.  In the 4^th month you have the original pair of rabbits, their first pair of babies, and a second pair of babies from the original pair – for a total of 3 pairs.  The original pair continues to have pairs of babies each month, and as the pairs of babies become two months old they begin to have pairs of babies also.  The diagram below illustrates this process for the first 5 months.

Notice the pattern of numbers produced, counting the numbers of pairs of rabbits, month by month.

Mathematicians became interested in this problem and noticed that there was a pattern for these numbers.  After the first and second months (both showed 1 pair of rabbits), the next number could be obtained by adding the two previous numbers.  The third number would be 1 + 1 = 2.  The fourth number would be 1 + 2 = 3.  And so forth.  These mathematicians called this sequence the Fibonacci sequence (though I think it should have been called the Rabbit Sequence).  They also began to prefer the name “Fibonacci” instead of Leonardo of Pisa”.

It is unfortunate that this man is more remembered for one math problem involving rabbits than for teach us how to us hindu-arabic numbers (the system we use today.  Personally, I don’t think I could have ever learned long division if I had to use Roman numbers.

1, 1, 2, 3, 5, 8, …

Remember the Fibonacci cheer: “Two, three, five, eight, who do we appreciate?  Fibonacci!”

References:

“The Man of Numbers: Fibonacci’s Arithmetic Revolution”, Keith Devlin

“Fibonacci Numbers and Golden Ratio in Mathematics and Science” – T. O. Omotehinwa and S. O. Ramon

http://www-history.mcs.st-and.ac.uk/Mathematicians/Fibonacci.html

David

Calendar Update

Today is the 305th day of the year, 1,401st day of the decade, and 5,054th day of the century/millennium.  

The next mathematical holiday coming up is Fibonacci Day on 11/23/2014 (1, 1, 2, 3, ....) so you still have about 3 weeks to prepare.  Keep an eye on my website for the next couple of weeks for updates on Fibonacci.  Some of the updates may have information you already know about, but I guarantee you that several updates will have information you have not heard of yet.  I'm just trying to give you an opportunity to look real good on Fibonacci day.  "2, 3, 5, 8, Who do we Appreciate!  Fibonacci, Fibonacci, Fibonacci!"

There are 54 days until Newton's birthday, 66 days until Phi Day, 98 days until "e" day, 133 days until Pi day, 239 days until Tau Day, 263 days until Pi Approximation Day, and 355 days until Martin Gardner's birthday.



David