3 minute read
Fibonacci Fun For Math Patterning
0,1, 1, 2, 3, 5, 8, 13, 21, 34...
Leonardo Fibonacci made brilliant discoveries about the number patterns in life. The code to many elements in nature like flowers, pineappples, seashells, tree branches and countless other natural phenomena demonstrate patterns that are true to the Fibonacci sequence.
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It is the pattern of sums that begins with 0 and then 1 and adds itself to the preceeding number. 1 + 0 = 1 thus the first numbers of the sequence are 0,1, 1 then 1 + 1 = 2, thus 1,1,2 then 2+1=3, thus 1,1,2,3 then 3+2=5, thus 1,1,2,3,5 and so on.
Fibonacci in Biology
Bees’ family trees reflect a Fibonacci number sequence - but only if the bee is male.
Fact Queen Bees are born from the mating of a Queen with a male.
Fact Male bees are born from a Queen without mating with a male. See below for a male bee’s family tree:
Male bee
1
Queen bee
1
Queen bee
Male bee
1
2
Queen bee + Male bee
Queen bee
1
2
3
Queen bee + Male bee | Queen bee
Queen bee + Male bee
1
2
3
4
5
Queen bee + Male bee | Queen bee | Queen bee + Male bee | Queen bee+ Male bee | Queen bee
1
2
3
4
5
6
7
8
1male bee has 1parent, 2 grandparents, 3 great-grandparents, 5 great-great-grandparents, and 8 great-great-great grandparents. nature is pretty amazing isn’t it? Try a family tree for a Queen bee’s family. does her tree also exhibit fibonacci numbers?
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Fibonacci in Language
“Numbers,” says mathemagician Arther Benjamin, “are poetry in motion.” And to demonstrate how true this is, let’s look at a limerick’s rhythm or meter.
LIMERICK DI DUM SYLLABLES
There once was a princess named Jinx, Who was asked what she thought of the Sphinx, She said with a smile, “That fraud by the Nile? I really do think that it stinks!”
di-dum di-di- dum di-di dum
5
3
8
di-dum di-di- dum di-di dum
5
3
8
di-dum di-di dum
3
2
5
di-dum di-di dum
3
2
5
di-dum di-di- dum di-di dum
5
3
8
TOTAL 21 13 34
Fibonacci in Play
5
3
2
1
1
}
8
}
}
19 20
1816 17
13 14 15
11 12
8 9 10
5 6 7
}} }
3 4
2
1
Using the Fibonacci numbers 1, 1, 2, 3, 5, and 8, here is a hopscotch to try out. Note that the last 8 squares are broken up into 3, 2, 1, and 2 to make the game easier to play.
What you need
• Bare pavement approximately 4 x 2 metres in area
• Sidewalk chalk in two colours
• An easy-to-throw object that will not bounce or roll: a puck, hacky-sack, or safety-pin chain will each work well.
Rules Throw a hacky sack, puck or chain of safety pins onto the board beginning at square 1. Pick up your object and, carrying it with you, complete the board: Hopping on one foot to start, jump from 1 to 2. You are allowed to land on two feet on squares 3 and 4, 5 and 7, 8 and 10, 11 and 12, 13 and 15, 16 and 17, 19 and 20. You must hop on one foot on all the other squares in order. Note that you cannot hop on the square where your object is sitting – you must hop over it once you have retrieved the object. Then return to the start of the board, throw you object on square to and start again. This is a great game to develop balance, agility, strength and hand-eye coordination. You can play it on your own or with friends.
brainspace SUMMER 2018 15
