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- 1. The Golden RatioThe Golden RatioBy Carlos A. CarleBy Carlos A. Carle
- 2. Golden RatioGolden Ratio A universal proportion found inA universal proportion found innature.nature. The ratio can be found in theThe ratio can be found in thesequence discovered by the Italiansequence discovered by the Italianmathematician Leonardo Fibonacci.mathematician Leonardo Fibonacci.
- 3. Fibonacci SequenceFibonacci Sequence Each element in the sequence is foundEach element in the sequence is foundby 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 13ththelement, dividing an element withelement, dividing an element withthe 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 BDNA are measured and dividedDNA are measured and divided(major and minor groove), they will(major and minor groove), they willapproximate the golden ratio.approximate the golden ratio. 21 angstrom / 13 angstrom = 1.61621 angstrom / 13 angstrom = 1.616
- 6. The Golden Ratio –The Golden Ratio –Human BodyHuman Body The height of the whole body divided byThe height of the whole body divided bythe measure from the head to the middlethe measure from the head to the middleof the Femur bone gives the Goldenof the Femur bone gives the GoldenRatio. This can be repeated with otherRatio. This can be repeated with othermeasures while achieving constantmeasures while achieving constantresults.results.
- 7. The Golden Ratio –The Golden Ratio –Human FaceHuman Face The same concepts can apply to theThe same concepts can apply to theface, which is filled with Golden Ratioface, which is filled with Golden Ratiomeasurementes.measurementes.
- 8. Even our teeth!!
- 9. The Golden Ratio –The Golden Ratio –NatureNature The Golden Ratio can be found inThe Golden Ratio can be found incountless aspects of nature. Forcountless aspects of nature. Forexample, many plants form spirals. Ifexample, many plants form spirals. Ifthese are measured, the Fibonaccithese are measured, the Fibonaccinumbers can be found, meaning that thenumbers can be found, meaning that theGolden Ratio will be present.Golden Ratio will be present.
- 10. The Golden Ratio -The Golden Ratio -NatureNature The same spiral pattern can be found inThe same spiral pattern can be found insea shells. The increasing curve followssea shells. The increasing curve followsthe Fibonacci sequence and thereforethe Fibonacci sequence and thereforethe Golden Ratio.the Golden Ratio.
- 11. The Golden Ratio – OurThe Golden Ratio – OurGalaxyGalaxy The same spiral pattern can be observedThe same spiral pattern can be observedin our Milky Way galaxy.in our Milky Way galaxy.
- 12. ConclusionConclusion This presentation is just a glimpse of howThis presentation is just a glimpse of howthe Golden Ratio or Phi can be foundthe Golden Ratio or Phi can be foundnaturally in the Universe; a merenaturally in the Universe; a meremathematic term with a significantmathematic term with a significantimportance. It can also be understood asimportance. It can also be understood asthe base of life in terms of measurementsthe base of life in terms of measurementsas it forms part of everything thatas it forms part of everything thatconstitutes us and all around us.constitutes us and all around us.

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