Transcript A Very Special Sequence

MATH
Math text books and math note books on your
desks, please.
 Sharpened pencils
 Calculators if you have one


Brain starter: Add up all the numbers from 1 to
10 in you head.
TODAY’S LESSON
Fibonacci Numbers
A little history
 A little sequence
 A little biology
 A little poetry, architecture & art
 How to eat Fibonacci Numbers

OBJECTIVE OF LESSON

You will understand what the Fibonacci
Numbers are and how to generate them.

You will know who Fibonacci was.

You will eat some Fibonacci Numbers
LEONARDO FIBONACCI
Leonardo Pisano
 Leonardo of Pisa
 Filius Bonacci (Son of Bonaccio)

 1170
to 1250
“Son” in French is “fils”
In Italian it is “figlio” (the “g” is silent)
In Latin it is “filius”
LEANING TOWER OF PISA
• Started construction the
year of Fibonacci’s birth
(1170)
• Finished about 1514
• About 56 m high (184
feet)
What did Fibonacci give us?
FIBONACCI’S CONTRIBUTION TO MATH

In1202, published “Book of Calculation”
(Fibonacci was Italian, but wrote his book in
Latin)

Fibonacci gave us mathematical terms
 Factor
 Multiple
(1, 2, 5, 10)
(10, 20, 30, 40, 50, …)
NUMBER SYSTEMS
XXIII
+ IV
XXVII
23
+4
27
XXIII
x IV
XCII
23
x4
92
Roman Numerals
Additive system
Hindu / Arabic
Positional system
THE FIBONACCI SEQUENCE
1)
2)
3)
4)
5)
6)
7)
8)
1
1
2
3
5
8
13
21
9)
10)
11)
12)
13)
14)
15)
16)
34
55
89
144
233
377
610
987
Why are Fibonacci numbers
interesting?
Fibonacci
numbers are
EVERYWHERE!
THE FIBONACCI SEQUENCE
1)
2)
3)
4)
5)
6)
7)
8)
1
1
2
3
5
8
13
21
9)
10)
11)
12)
13)
14)
15)
16)
34
55
89
144
233
377
610
987
Did I say that
Fibonacci
numbers are
EVERYWHERE?
WHICH SHAPE DO YOU LIKE BETTER?
A
B
C
FIBONACCI IN ARCHITECTURE
FIBONACCI IN ART
FIBONACCI IN NATURE
FIBONACCI & POETRY
Di dum di di dum di di dum,
Di dum di di dum di di dum,
Di dum di di dum,
Di dum di di dum,
Di dum di di dum di di dum.
ANALYSIS
Syllables
8
8
5
5
8
Total: 34
Di’s and Dum’s
5, 3
5, 3
3, 2
3, 2
5, 3
Total: 21, 13
I think Fibonacci is fun:
We start with a 1 and a 1
Then 2, 3, 5, 8
But don’t stop there, mate!
The fun has just barely begun.
The End