Saturday, January 23, 2010

Golden Ratio

This is something related to my FYP :p My FYP title is - Biped Walking Robot. Aiyoo, i think it is possible, but but...haha :p Right now, me and my partner still not buying the component. Aigoo~how many month left already, u think i can make it? (-___-) Ok2, enough2, here is something about golden ratio.

Golden Ratio
In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to (=) the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.6180339887. Other names frequently used for the golden ratio are the golden section (Latin: sectio aurea) and golden mean. Other terms encountered include extreme and mean ratio, medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, golden number, and mean of Phidias. The golden ratio is often denoted by the Greek letter phi, usually lower case (φ).

Equivalent definition

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.
Mario Livio , The Golden Ratio: The Story of Phi, The World's Most Astonishing Number

Leonardo Da Vinci's 'The Vitruvian Man' approves the Golden Ratio. This drawing also called Canon of Proportions.

Fibonacci sequence approve the golden ratio.

Golden Ration in Nature and Architecture
At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing.

Human Hand

Golden Ration in Mathematics


And lastly this is how Golden Ratio is related to my FYP, it is said that, human body balance is based on this calculation. Even how short or tall you is, every measurement on your body is based on Golden Ratio. Betapa Maha Hebat nya Dia - Subhanallah (^_^) With this measurement, we will apply the calculation to our robot and this will make sure that the robot is balance in term of standing and walking. InshaALLAH.

Human Body
The measurement

The Divine Proportion in the Body

  • The white line is the body's height.
  • The blue line, a golden section of the white line, defines the distance from the head to the finger tips.
  • The yellow line, a golden section of the blue line, defines the distance from the head to the navel and the elbows.
  • The green line, a golden section of the yellow line, defines the distance from the head to the pectorals and inside top of the arms, the width of the shoulders, the length of the forearm and the shin bone.
  • The magenta line, a golden section of the green line, defines the distance from the head to the base of the skull and the width of the abdomen. The sectioned portions of the magenta line determine the position of the nose and the hairline.
  • Although not shown, the golden section of the magenta line (also the short section of the green line) defines the width of the head and half the width of the chest and the hips.
P/S : Help Help Help FYP! Uhuhu (>_<)

Source : Mathworld, Wikipedia, Mathforum, Artofraz, Emptyeasel, Freemason, Golden Number


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Zer0 said...

just want to add.. there is also golden ratio for face. it is said that whomever face exhibit the golden ratio, he/she have a beautiful face..for the record, only one person have this golden ratio face..

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