Golden spiral fibonacci


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Golden spiral fibonacci

  1. 1. This presentation has been made for you byFRANCISCO GUIJARRO BELDA From Isaac Albéniz Secondary School Leganés. Madrid. Spain.
  2. 2. THE FIBONACCI SERIESFibonacci was a mathematician who wondered himself about the fashion rabbitsbred. He studied an ideal situation and was able to determine a compelling seriesof numbers out of this uncommon survey: 1, 1, 2, 3, 5, 8, 13, 21…Can you figure out how the series works?Any number from the series is the outcome of adding up the two previousnumbers. For instance, If you added up the two first, you would get 1+1=2. Again, ifyou added up the second and the third ones you would get 1+2=3 and so on.Besides, If you divided any component of the series by its precedent number, youwould get always the same ratio: 1,618 (with the exception of the first ones).
  3. 3. LET S APPLY THIS IDEA TO A SERIES OF SQUARES1) We are going to draw two squares that are equal. Their side has 1 cm length . Weput them together. 1 1
  4. 4. 2) Upon the largest side of the rectangle you got from the two original squares, wedraw a new one whose side will be, obviously 2 cm side. 1 2 1
  5. 5. 3) Again, we draw a new square on the bottom side of the rectangle brought aboutby the square 2 and one of the original squares as you can see in the picture. 1 2 1 3
  6. 6. 4) You can keep working the same way as many times as you want. 1 2 1 5 3
  7. 7. 5) Next step will be to draw an arc with the compass. You will put the point of it onthe middle of the two 1 cm side squares and take a radius of the same length. 2 5 3
  8. 8. 6) Once you have drawn the semicircle,You must join points P and Q with the you will keep drawing another arc on compass square number 2. Take center on point B and radius the side of the square (2 Q cm) 2P B 5 3
  9. 9. 7) Keep going the same way with the other squares and you will have accomplishedthe drawing of a beautiful golden spiral. I marked points C and D on the picture tomake you know where are the centers of the new arcs. I guess you can determinewhat is the length of the correspondent radius. D C 5
  10. 10. 7) And here we go. It is needless to say that we could have developed the spiralendlessly. Unfortunately we are hampered by our drawing sheet limits.