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Transcript
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. (There’s an easier way) 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. 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” What did Fibonacci give us? Mathematical Terms • Factor • Multiple Turn to page 452 in your math text. 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! Fibonacci’s Rabbits • Group activity • Page 38 of your math text book 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? Fibonacci (& the Golden Ratio) 1 2 3 4 5 6 7 8 1 1 2 3 5 8 13 21 b/a 1 2 1.5 1.666 1.6 1.625 1.615 9 10 11 12 13 14 15 16 34 55 89 144 233 377 610 987 1.619 1.6176 1.6181 1.6179 1.61805 1.61802 1.61803 1.61803 The Di Dum Poem 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.