# ✎✎✎ Golden Ratio Research Paper

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The Golden Ratio vs. The Rule of Thirds

Across the globe, an estimated 19 million pregnant women and million children suffer from the condition. The good news, however, is that dietary supplementation of vitamin A can eliminate VAD. One way that holds particular promise is the administration via GR, which had been engineered to produce large amounts of vitamin A. A study by Tang et al. Unfortunately, public misconceptions about genetically modified GM organisms have prevented GR from being available to the countries most affected by VAD. An official blessing of the church, therefore, could do a great deal to build support, allowing the Philippines to serve as a model for many of its neighbors on the potential health impacts of widespread availability and consumption of the golden grain.

Regrettably, the church did not provide an official endorsement. It turns out that there is quite a distinction between the pope's personal blessing and an official statement of support from the Vatican. At the time of the blessing, Ingo, a member of the Pontifical Academy of Sciences, had been attending a meeting at the Vatican on the interaction of nutrition and brain development. At the end of the meeting, he was able to meet Pope Francis and took the opportunity to share a packet of GR. In response, the pope offered his personal blessing. From Ingo's perspective, the pope is concerned that genetic modification technology primarily benefits big business and not the poor.

The most immediate hurdle to the usage of GR, according to Ingo, is the impending deregulation by the Philippine Department of Agriculture. Although no damage has been reported from the recent typhoon Haiyan that struck this part of the world, the fields had already been harvested. Philippine officials have been following GR development and field trials for several years, and Ingo believes that the government will ultimately give "the green light. Only after the study will farmers be allowed to plant GR, said Ingo. GR distribution will be carried out by existing small-scale operations. Further, it will be sold at the same price as conventional cultivars. It is believed that this will help to facilitate adoption.

In addition to vitamin A production, Ingo believes that other agronomic improvements, such as increased pest resistance and yield, will further increase the attractiveness of GR to farmers. While not a full-throated endorsement of GR or GM, the pope's blessing is a step in the right direction. It is also an important indicator of slowly shifting global attitudes regarding the role that GM foods will play in the world's long-term food security.

Dietary micronutrient deficiencies, such as the lack of vitamin A, iodine, iron or zinc, are a major source of morbidity increased susceptibility to disease and mortality worldwide. These deficiencies affect particularly children, impairing their immune system and normal development, causing disease and ultimately death. The best way to avoid micronutrient deficiencies is by way of a varied diet, rich in vegetables, fruits and animal products.

The second best approach, especially for those who cannot afford a balanced diet, is by way of nutrient-dense staple crops. Sweet potatoes, for example, are available as varieties that are either rich or poor in provitamin A. In this case, what needs to be done is to introduce the biofortified varieties to people used to the white-fleshed varieties, as is happening at present in southern Africa by introducing South American varieties of orange-fleshed sweetpotatoes. Unfortunately, there are no natural provitamin A-containing rice varieties. The outer coat of the dehusked grains—the so-called aleurone layer—contains a number of valuable nutrients, e.

These nutrients are lost with the bran fraction in the process of milling and polishing. While it would be desirable to keep those nutrients with the grain, the fatty components are affected by oxidative processes that make the grain turn rancid when exposed to air. Thus, unprocessed rice—also known as brown rice—is not apt for long-term storage. Even though all required genes to produce provitamin A are present in the grain, some of them are turned off during development.

They figured out how to turn on this complex pathway again with a minor intervention. The shocking fact is that, far from reaching the envisaged Millenium Development Goals, more than 10 million children under the age of five are still dying every year. A high proportion of those children die victims of common diseases that could be prevented through a better nutrition. It is unfortunate that the world is not embracing more readily a number of approaches wih the potential to substantially reduce the number of deaths. It has been calculated that the life of 25 percent of those children could be spared by providing them with diets that included crops biofortified with provitamin A beta-carotene and zinc.

Golden Rice is such a biofortified crop. Those involved in the project are hopeful that in a near future Golden Rice will be growing in farmers' fields and helping to improve the diets of millions of people. Golden Rice grains are easily recognisable by their yellow to orange colour. While a yellow rice is still unfamiliar to most of us, it is hoped that the pleasant colour will help promote its adoption. Would you believe that once upon a time carrots were white or purple? Orange-coloured carrots are the product of a mutation selected by a Dutch horticulturist a few hundred years ago, because it was the colour of the Dutch Royal House of Orange-Nassau! J Exp Bot Both genes are naturally involved in carotene biosynthesis.

The difference here is that the reconstructed pathway is not subject to downregulation, as usually happens in the grain. Our goal is to make sure that people living in rice-based societies get a full complement of provitamin A from their traditional diets. This would apply to countries such as India, Vietnam, Bangladesh. Golden Rice could still be a valuable complement to children's diets in many countries by contributing to the reduction of clinical and sub-clinical vitamin A deficiency-related diseases. Many people are aware that vitamin A has something to do with vision, especially at night. But many are not aware of the central role it plays in maintaining the integrity of the immune system. According to the World Health Organization, dietary vitamin A deficiency VAD compromises the immune systems of approximately 40 percent of children under the age of five in the developing world, greatly increasing the risk of severe illnesses from common childhood infections, thus causing hundreds of thousands of unnecessary deaths among them.

In remote rural areas Golden Rice could constitute a major contribution towards sustainable vitamin A delivery. To achieve this goal a strong, concerted, and interdisciplinary effort is needed. This effort must include scientists, breeders, farmers, regulators, policy-makers, and extensionists. The latter will play a central role in educating farmers and consumers as to their available options. While the most desirable option woud be a varied and adequate diet, this goal is not always achievable, at least not in the short term. The reasons are manifold, ranging from tradition to geographical and economical limitations. Golden Rice is a step in the right direction in that it does not create new dependencies or displace traditional foodstuff.

From the beginning Golden Rice was conceived as a public-good project under the guidance of the Golden Rice Humanitarian Board. From to the project dealt mainly with breeding the novel trait into locally adapted rice varieties. Several companies have provided free access to their patented technologies necessary to generate Golden Rice. PhilRice is preparing a submission to the regulatory authority of the Philippines in , which could lead to initial releases to farmers in And the work doesn't stop there.

If the first hurdles are taken successfully, then Golden Rice will be heading towards China, India, Bangladesh, Indonesia, and Vietnam. In those countries national programs are already involved in laying out the necessary groundwork. Helen Keller International Helen Keller International HKI has been working to address vitamin A deficiency VAD for well over 30 years and continues to work with local partners to deliver vitamin A to those in need through implementation of complementary interventions including vitamin A supplementation, promotion of optimal breastfeeding, dietary diversification and food fortification.

HKI considers that Golden Rice may have the potential to be another complementary vehicle to combat vitamin A deficiency, particularly among those who are not reached by other mechanisms. Hence, HKI is working on determining the efficacy of Golden Rice to improve the vitamin A status in deficient individuals. According to HKI million pre-school children and 19 million pregnant women are currently vitamin A deficient. Each year, an estimated , children will die from VAD, and , will go blind.

In the Philippines, approximately 1. In Bangladesh, one in every five of pre-school aged children are estimated to have VAD. In these, as almost in all developing countries, effective distribution systems for vitamin A supplementation are not in place to reach all people in need adequately and consistently. Supplementation programs incur high logistic costs that not every region can afford. Those most in need of this new seed-based technology are those who can least afford buying an adequate diet, rich in essential nutrients.

This has been taken into consideration by the creators of Golden Rice , Profs Peter Beyer and Ingo Portrykus, and the crop protection company Syngenta, who have worked together to make the latest, improved version of Golden Rice available for humanitarian use in developing countries, free of charge. The Golden Rice Humanitarian Board encourages further research to determine how the technology may play a part in the ongoing global effort to fight Vitamin A Deficiency in poor countries. While Golden Rice is an exciting development, it is important to keep in mind that malnutrition is to a great extent rooted in political, economic and cultural issues that will not be solved by a technical fix.

Yet Golden Rice offers people in developing countries a valuable and affordable choice in the fight against the scourge of malnutrition. This site is maintained by the Golden Rice Humanitarian Board for the purpose of providing information on the background and progress of the Golden Rice Humanitarian Project. Eat orange! A motto promoted by HarvestPlus. Richard J Roberts, Nobel Prize Winner in Physiology or Medicine, on behalf of the Nobel Prize winners and 13, co-signers supporting GMOs, have expressed their delight with the recent announcement of the move by the Philippine Department of Agriculture to authorize the direct use of Golden Rice as food and feed or for Processing.

Visit Support Precision Agriculture. Dr Ariel Wilner is an Argentinian biologist and artist who has created an audiovisual art piece with the title "Lack of Light". In his piece, Ariel has connected Golden Rice to the challenges of millions of children affected by malnutrition and fighting for survival in this world. Regulatory status Check updates on regulatory status in the Regulatory section. Golden Rice vs White Rice A study carried out by IRRI, PRRI and the Danforth Center scientists and published in June shows that the only noticeable differences between Golden Rice and its non-transgenic counterpart are the elevated levels of beta-carotene and related carotenes.

For more detail continue reading here. The main cause appears to be failure to immunise enough children. Many children in countries where VAD is endemic are not immunised. Tuberculosis is a neglected disease, according to a newly published report in the Lancet, a medical journal. That is ambitious, even by the lofty measure of such proclamations. In tuberculosis killed 1. The plan calls for new drugs, vaccines and diagnostic tests, as well as doubling annual spending. Treating those who fall ill is crucial to preventing its spread. Yet currently more than a third of them go untreated. And nearly half a million new cases are resistant to several tuberculosis drugs.

August The paper, with data based on a registered clinal trial, has been published by the American Journal of Clinical Nutrition. And there is good reason to conduct these studies in China, considering the low vitamin A status of a great proportion of Chinese children see Nutrition and Health Status Report. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned.

Le Corbusier explicitly used the golden ratio in his Modulor system for the scale of architectural proportion. He saw this system as a continuation of the long tradition of Vitruvius , Leonardo da Vinci's " Vitruvian Man ", the work of Leon Battista Alberti , and others who used the proportions of the human body to improve the appearance and function of architecture.

In addition to the golden ratio, Le Corbusier based the system on human measurements , Fibonacci numbers , and the double unit. He took suggestion of the golden ratio in human proportions to an extreme: he sectioned his model human body's height at the navel with the two sections in golden ratio, then subdivided those sections in golden ratio at the knees and throat; he used these golden ratio proportions in the Modulor system. The villa's rectangular ground plan, elevation, and inner structure closely approximate golden rectangles. Another Swiss architect, Mario Botta , bases many of his designs on geometric figures. Several private houses he designed in Switzerland are composed of squares and circles, cubes and cylinders. In a house he designed in Origlio , the golden ratio is the proportion between the central section and the side sections of the house.

Divina proportione Divine proportion , a three-volume work by Luca Pacioli , was published in Pacioli, a Franciscan friar , was known mostly as a mathematician, but he was also trained and keenly interested in art. Divina proportione explored the mathematics of the golden ratio. Though it is often said that Pacioli advocated the golden ratio's application to yield pleasing, harmonious proportions, Livio points out that the interpretation has been traced to an error in , and that Pacioli actually advocated the Vitruvian system of rational proportions.

Leonardo da Vinci 's illustrations of polyhedra in Divina proportione [46] have led some to speculate that he incorporated the golden ratio in his paintings. But the suggestion that his Mona Lisa , for example, employs golden ratio proportions, is not supported by Leonardo's own writings. The dimensions of the canvas are a golden rectangle. A huge dodecahedron, in perspective so that edges appear in golden ratio to one another, is suspended above and behind Jesus and dominates the composition. A statistical study on works of art of different great painters, performed in , found that these artists had not used the golden ratio in the size of their canvases. The study concluded that the average ratio of the two sides of the paintings studied is 1.

Many books produced between and show these proportions exactly, to within half a millimeter. According to some sources, the golden ratio is used in everyday design, for example in the proportions of playing cards, postcards, posters, light switch plates, and widescreen televisions. The golden ratio is also apparent in the organization of the sections in the music of Debussy 's Reflets dans l'eau Reflections in Water , from Images 1st series, , in which "the sequence of keys is marked out by the intervals 34, 21, 13 and 8, and the main climax sits at the phi position".

The musicologist Roy Howat has observed that the formal boundaries of Debussy's La Mer correspond exactly to the golden section. Though Heinz Bohlen proposed the non-octave-repeating cents scale based on combination tones , the tuning features relations based on the golden ratio. As a musical interval the ratio 1. Johannes Kepler wrote that "the image of man and woman stems from the divine proportion. In my opinion, the propagation of plants and the progenitive acts of animals are in the same ratio". The psychologist Adolf Zeising noted that the golden ratio appeared in phyllotaxis and argued from these patterns in nature that the golden ratio was a universal law. However, some have argued that many apparent manifestations of the golden ratio in nature, especially in regard to animal dimensions, are fictitious.

The golden ratio is a critical element to golden-section search. The golden ratio is an irrational number. Below are two short proofs of irrationality:. Another short proof — perhaps more commonly known — of the irrationality of the golden ratio makes use of the closure of rational numbers under addition and multiplication. The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. The absolute value of this quantity 0. The vertices of a regular icosahedron are those of three mutually orthogonal golden rectangles.

There is no known general algorithm to arrange a given number of nodes evenly on a sphere, for any of several definitions of even distribution see, for example, Thomson problem or Tammes problem. However, a useful approximation results from dividing the sphere into parallel bands of equal surface area and placing one node in each band at longitudes spaced by a golden section of the circle, i. Application examples you can see in the articles Pentagon with a given side length , Decagon with given circumcircle and Decagon with a given side length. Both of the above displayed different algorithms produce geometric constructions that determine two aligned line segments where the ratio of the longer one to the shorter one is the golden ratio.

In a regular pentagon the ratio of a diagonal to a side is the golden ratio, while intersecting diagonals section each other in the golden ratio. This result is a straightforward consequence of the intersecting chords theorem and can be used to construct a regular pentagon, a construction that attracted the attention of the noted Canadian geometer H. Coxeter who published it in Odom's name as a diagram in the American Mathematical Monthly accompanied by the single word "Behold! The golden ratio plays an important role in the geometry of pentagrams.

Each intersection of edges sections other edges in the golden ratio. The pentagram includes ten isosceles triangles : five acute and five obtuse isosceles triangles. The obtuse isosceles triangles are golden gnomons. The golden ratio properties of a regular pentagon can be confirmed by applying Ptolemy's theorem to the quadrilateral formed by removing one of its vertices. A golden rhombus is a rhombus whose diagonals are in the golden ratio. The rhombic triacontahedron is a convex polytope that has a very special property: all of its faces are golden rhombi. The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected. The Fibonacci sequence is:.

A closed-form expression for the Fibonacci sequence involves the golden ratio:. The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence or any Fibonacci-like sequence , as shown by Kepler : [79]. For example:. The golden ratio has the simplest expression and slowest convergence as a continued fraction expansion of any irrational number see Alternate forms above. It is, for that reason, one of the worst cases of Lagrange's approximation theorem and it is an extremal case of the Hurwitz inequality for Diophantine approximations. This may be why angles close to the golden ratio often show up in phyllotaxis the growth of plants.

The multiple and the constant are always adjacent Fibonacci numbers. The golden ratio appears in the theory of modular functions as well. This gives an iteration that converges to the golden ratio itself,. These iterations all converge quadratically ; that is, each step roughly doubles the number of correct digits. The golden ratio is therefore relatively easy to compute with arbitrary precision. An easily programmed alternative using only integer arithmetic is to calculate two large consecutive Fibonacci numbers and divide them.

Both Egyptian pyramids and the regular square pyramids that resemble them can be analyzed with respect to the golden ratio and other ratios. The isosceles triangle that is the face of such a pyramid can be constructed from the two halves of a diagonally split golden rectangle of size semi-base by apothem , joining the medium-length edges to make the apothem. The Rhind papyrus has another pyramid problem as well, again with rational slope expressed as run over rise.

Egyptian pyramids very close in proportion to these mathematical pyramids are known. He did not apply the golden ratio to the Great Pyramid of Giza, but instead agreed with John Shae Perring that its side-to-height ratio is 8 : 5. In , the pyramidologist John Taylor misinterpreted Herodotus c. Similarly, Howard Vyse reported the great pyramid height Michael Rice [95] asserts that principal authorities on the history of Egyptian architecture have argued that the Egyptians were well acquainted with the golden ratio and that it is part of the mathematics of the pyramids, citing Giedon For example, Keith Devlin says, "Certainly, the oft repeated assertion that the Parthenon in Athens is based on the golden ratio is not supported by actual measurements.

In fact, the entire story about the Greeks and golden ratio seems to be without foundation. From measurements of 15 temples, 18 monumental tombs, 8 sarcophagi, and 58 grave stelae from the fifth century BC to the second century AD, one researcher concluded that the golden ratio was totally absent from Greek architecture of the classical fifth century BC, and almost absent during the following six centuries. The Section d'Or 'Golden Section' was a collective of painters , sculptors, poets and critics associated with Cubism and Orphism. The starting point notwithstanding, the subsequent number is always the sum of the two numbers before it.

The sequence of these numbers can be defined by what is termed the Recurrence Relation. The Fibonacci spiral has its origin in Indian mathematics and also associated with Sanskrit prosody. Be that as it may, the clearest of all the expositions regarding the Fibonacci spiral and its sequences can be found in the findings conducted by Virahanka c. The sequence also got a mention from Hemachandra in c. The Fibonacci spiral equally has popularity outside India. Fibonacci spiral is based on the Fibonacci sequence and each quarter in the spiral is as big as the last two quarters.

The Fibonacci spiral equally crates the golden ratio, which is used for formatting purposes and applications by many smartphones and televisions. Research has shown that the faces of many of the celebrities out there today have a strong match to the ratio. The golden phi or number is 1. This simply means that each of the curves on the Fibonacci spiral will end up being 1. The golden ratio represents the ratio of all the sides that make up a rectangle. If a square with sides represented by the smaller sides of the rectangle is removed from the rectangle, the rectangle remaining will still have sides having the same ratio.

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