This is the presentation I made for a competition that the Science Team of my school participated in. Check out the video here: http://youtu.be/bI3tTrdpRPU

1. The Golden RatioThe Golden Ratio
By Carlos A. CarleBy Carlos A. Carle

2. Golden RatioGolden Ratio
 A universal proportion found inA universal proportion found in
nature.nature.
 The ratio can be found in theThe ratio can be found in the
sequence discovered by the Italiansequence discovered by the Italian
mathematician Leonardo Fibonacci.mathematician Leonardo Fibonacci.

3. Fibonacci SequenceFibonacci Sequence
 Each element in the sequence is foundEach element in the sequence is found
by adding the previous two numbers…by adding the previous two numbers…
 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

4. Fibonacci SequenceFibonacci Sequence
 After the 13After the 13thth
element, dividing an element withelement, dividing an element with
the previous one will give you a constant result:the previous one will give you a constant result:
1.61803398875 or Φ (phi)1.61803398875 or Φ (phi)
 21/13=1.61521/13=1.615
 34/21=1.61934/21=1.619
 55/34=1.61855/34=1.618
 89/55=1.61889/55=1.618
 And so on…And so on…

5. The Golden Ratio -The Golden Ratio -
DNADNA
 If the two grooves of the spiral of BIf the two grooves of the spiral of B
DNA are measured and dividedDNA are measured and divided
(major and minor groove), they will(major and minor groove), they will
approximate the golden ratio.approximate the golden ratio.
 21 angstrom / 13 angstrom = 1.61621 angstrom / 13 angstrom = 1.616

7. The Golden Ratio –The Golden Ratio –
Human BodyHuman Body
 The height of the whole body divided byThe height of the whole body divided by
the measure from the head to the middlethe measure from the head to the middle
of the Femur bone gives the Goldenof the Femur bone gives the Golden
Ratio. This can be repeated with otherRatio. This can be repeated with other
measures while achieving constantmeasures while achieving constant
results.results.

9. The Golden Ratio –The Golden Ratio –
Human FaceHuman Face
 The same concepts can apply to theThe same concepts can apply to the
face, which is filled with Golden Ratioface, which is filled with Golden Ratio
measurementes.measurementes.

10. Even our teeth!!

11. The Golden Ratio –The Golden Ratio –
NatureNature
 The Golden Ratio can be found inThe Golden Ratio can be found in
countless aspects of nature. Forcountless aspects of nature. For
example, many plants form spirals. Ifexample, many plants form spirals. If
these are measured, the Fibonaccithese are measured, the Fibonacci
numbers can be found, meaning that thenumbers can be found, meaning that the
Golden Ratio will be present.Golden Ratio will be present.

13. The Golden Ratio -The Golden Ratio -
NatureNature
 The same spiral pattern can be found inThe same spiral pattern can be found in
sea shells. The increasing curve followssea shells. The increasing curve follows
the Fibonacci sequence and thereforethe Fibonacci sequence and therefore
the Golden Ratio.the Golden Ratio.

15. The Golden Ratio – OurThe Golden Ratio – Our
GalaxyGalaxy
 The same spiral pattern can be observedThe same spiral pattern can be observed
in our Milky Way galaxy.in our Milky Way galaxy.

17. ConclusionConclusion
 This presentation is just a glimpse of howThis presentation is just a glimpse of how
the Golden Ratio or Phi can be foundthe Golden Ratio or Phi can be found
naturally in the Universe; a merenaturally in the Universe; a mere
mathematic term with a significantmathematic term with a significant
importance. It can also be understood asimportance. It can also be understood as
the base of life in terms of measurementsthe base of life in terms of measurements
as it forms part of everything thatas it forms part of everything that
constitutes us and all around us.constitutes us and all around us.