The Golden RatioThe Golden Ratio

By Carlos A. CarleBy Carlos A. Carle

Golden RatioGolden Ratio

A universal proportion found in A universal proportion found in nature.nature.

The ratio can be found in the The ratio can be found in the sequence discovered by the Italian sequence discovered by the Italian mathematician Leonardo Fibonacci.mathematician Leonardo Fibonacci.

Fibonacci SequenceFibonacci Sequence

Each element in the sequence is found Each 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…

Fibonacci SequenceFibonacci Sequence

After the 13After the 13thth element, dividing an element with element, 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=1.618 89/55=1.618 And so on…And so on…

The Golden Ratio - DNAThe Golden Ratio - DNA

If the two grooves of the spiral of B If the two grooves of the spiral of B DNA are measured and divided DNA 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

The Golden Ratio – The Golden Ratio – Human BodyHuman Body

The height of the whole body divided by The height of the whole body divided by the measure from the head to the middle the measure from the head to the middle of the Femur bone gives the Golden of the Femur bone gives the Golden Ratio. This can be repeated with other Ratio. This can be repeated with other measures while achieving constant measures while achieving constant results.results.

The Golden Ratio – The Golden Ratio – Human FaceHuman Face

The same concepts can apply to the The same concepts can apply to the face, which is filled with Golden Ratio face, which is filled with Golden Ratio measurementes.measurementes.

Even our teeth!!

The Golden Ratio – The Golden Ratio – NatureNature

The Golden Ratio can be found in The Golden Ratio can be found in countless aspects of nature. For countless aspects of nature. For example, many plants form spirals. If example, many plants form spirals. If these are measured, the Fibonacci these are measured, the Fibonacci numbers can be found, meaning that the numbers can be found, meaning that the Golden Ratio will be present. Golden Ratio will be present.

The Golden Ratio - NatureThe Golden Ratio - Nature

The same spiral pattern can be found in The same spiral pattern can be found in sea shells. The increasing curve follows sea shells. The increasing curve follows the Fibonacci sequence and therefore the Fibonacci sequence and therefore the Golden Ratio.the Golden Ratio.

The Golden Ratio – Our The Golden Ratio – Our GalaxyGalaxy

The same spiral pattern can be observed The same spiral pattern can be observed in our Milky Way galaxy.in our Milky Way galaxy.

ConclusionConclusion

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