Geometry Doc2

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10/6/2009

Golden Ratio in HumanDevelopment and Heartbeat And in Fractals and Murals.

NATIONAL INSTITUTE OF FASHION TECHNOLOGY, GANDHINAGAR

SUBMITTED BY : Mehak Jain

DEPARTMENT : Fashion Programme Technology

SEMESTER : 1 ROLL NO. 7

SUBMITTED TO: Mr. Piyush Goghari


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CONTENTS

1 SAC G2 H G L N A AN B NACC

SERIES

3. H W IS THE G L EN RATIORELATED TO FIBONACCI SERIES?

4.

IS THERE A COMMO N FACTOR IN

FIBONACCI SEQUENCE?

5. FIBONACCI NUM BERS DEFINE KEYPOINTS IN HUM AN AGEING

6. THE HUM AN HEARTBEAT7. GOLDEN RATIO IN BODY

TEMPERATURE

8. GOLDEN RATIO IN FRACTALS9. MASONIC MUR AL BASED ON

GOLDEN PROPORTIO N

10 . CONCLUSION

11 . BIBLIOGRAPHY


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SACRED GEOMETRY

Sacred means something that is symbolic of a transcendent truth, and worthyof study, contemplation, and veneration. When referred to Sacred Geometry , itis about geometry that is derived from or directly related to the structure of nature. Structural forms seen at the microscopic level are repeated at otherscales, and the laws of fractional symmetry appear to apply throughout. So,geometry that refers to the structural unity of nature is a powerful metaphorfor the mystery of life, and thus sacred. One of the best examples of SacredGeometry are forms based on the Golden Ratio .

THE GOLDEN RATIO

Knowledge of the Golden Section, ratio, or proportion has been known for avery long time. The Egyptians knew about it and the Greeks learned about itfrom them. It is called phi, , in honor of Phideas, the architect of theParthenon, and is approximated by the irrational fraction 0.618034 ... Shamans,priests, and artists throughout the world and across history have understood

and applied to ritual, architecture, art, and the crafting of musicalinstruments and everyday objects.


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F IBONACCI SERIESFibonacci Numbers are directly and intricately related to another very specialmath formula that is found all throughout life and the physical universe. This is

the Golden Ratio or Phi ( as i t i s more commonly known). It is an irrationalnumber who s decimal place is never-ending, non-repeating and goes onforever and it looks like this:

1.6 18033988 749894848 20 4586834365638 117720 30917 98 057 to infinity

Although, for the most part scientists and academics alike have ro unded it off to five decimal places. So, for all intensive purposes the Golden Ratio (or Phi) is1.6 1803.

Th Fibon i s i s :


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HOW IS THE GOLDEN RATIO RELATED TOF IBONACCI NUMBERS?

If we were to divide each consecutive Fibonacci number, instead of adding.We find the results gradually converge on The Golden Ratio.

The line in the chart below, represents the Golden ratio 1.61803 . The dotsrepresent the results of dividing two consecutive Fibonacci numbers. Theresults gradually converge closer and closer to the Golden Ratio. The reasonthe result do not equal the Golden Ratio is because it is an irrational number(decimal goes on forever).


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IS THERE A COMMON F ACTOR IN THE F IBONACCI SEQUENCE?

It was discovered in the 1960 s that the Periodic Table of Elements (bu i ld i ngb locks of everyt hi ng) are numerical structured based on the number 19 . TheGolden Ratio (& Fibonacci Numbers) relates to growth and creation of life andphysical structures in our universe. In other words, the elements are thebuilding blocks of all things and the Golde n Ratio/ Fibonacci Numbers is howthese blocks come together .

Order Fibonacci Numbers DivideBy 19 Results

1 0 0.02 1 0.13 1 0.14 2 0.15 3 0.26 5 0.37 8 0.48 13 0.79 21 1.110 34 1.8

11 55 2.912 89 4.713 144 7.614 233 12.315 377 19.816 610 32.117 987 51.918 1597 84.119 2584 136.020 4181 220.1

21 6765 356.122 10946 576.123 17711 932.224 28657 1508.325 46368 2440.426 75025 3948.727 121393 6389.1


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28 196418 10337.829 317811 16726.930 514229 27064.731 832040 43791.632 1346269 70856.3

33 2178309 114647.834 3524578 185504.135 5702887 300151.936 9227465 485656.137 14930352 785808.038 24157817 1271464.139 39088169 2057272.140 63245986 3328736.141 102334155 5386008.242 165580141 8714744.3

43 267914296 14100752.444 433494437 22815496.745 701408733 36916249.146 1134903170 59731745.847 1836311903 96647994.948 2971215073 156379740.749 4807526976 253027735.650 7778742049 409407476.3

Clearly, 19 was not the Common Denominator of the Fibonacci Seque nce.However, the 19 th Fibonacci Sequence ( 2584 ) was divisible by 19 and the di gits(2+5+8+4 ) also equal 19 .


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F IBONACCI NUMBERS DE F INE KEY POINTS IN HUMAN AGEING AND

DEVELPOPMENT

Fibonacci numbers mark key points in the human aging and developmentprocess, as illustrated in the following table , based on insights provided byNorman S. Rose, Ph.D.

HumanAge DevelopmentStage Key Attributes

0 Gestation Conception

1 Newborn Birth

1 Infant Walking, vocalizing

2 Toddler Talking, expressing, imitating

3 Toddler Self image and control, toilet training

5 Early child Formal education begins

8 Mid child Age of reason, knowing of right and wrong

13 Adolescent Thinking, puberty, sexual maturation and drive

21 Young adult Full physical growth, adult in society, educationcomplete, beginning career, financial responsibility,eligible for voting

34 Mid adult Refinement of adult skills, parenting role

55 Elder adultFulfillment of adult skills, serving, retirement beginswith eligibility for Medicare, Social Security andAARP

89 Completion Insight and wisdom into life


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THE HUMAN HEARTBEAT

A peaceful heartbeat is said by some to beat in a Phirhythm

The prominent parts of an electrocardiogram (ECG) are the P wave, adeflection caused by the current originating in the atrium; the QR S complex,showing the passage of the electrical activity into the ventricles; and the Twave, as the ventricles reset themselves. The electrocardiograms (ECG) of human heartbeats vary considerably depending on a variety of factors.

Heartbeat 2000 seeks to study the relationships between the physical heartand the spiritual heart, that is the soul, of human beings. The views presentedthere suggest that a heartbeat that produces a phi relationship in the T pointof the ECG represents a state of being , that is, one of health, peace andharmony.

While this is an area that still needs research and scientific corroboration, it is

an interesting perspective on another potential appearance of phi in life.


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When looking at an electrocardiogram (ECG), it is said by some that aheartbeat at rest beats in a Golden Ratio rhythm.

ECG's show a resemblance to the Fibonacci Convergence

As explained on the Fibonacci Series page, the ratio of each successive pair of numbers in the Fibonacci series ( 0 , 1, 1 , 2 , 3, 5 , 8 , 13 , 21 , 34 , 55 , 89 , 144 , . . . )converges on phi ( 1 .618 . . .) as you go higher in the series.

The first numbers in the series give an approximation of phi.

For example:

1 / 0 =

1 / 1 = 1

2 / 1 = 2

3 / 2 = 1.5

5 / 3 = 1.666..

8 / 5 = 1.6

13 / 8 = 1.625


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Curiously, if you graph these approximations of phi in the series above you getthe chart below, the first part of which bears a similarity to the ECG pattern of the human heartbeat.

The extraction and identification of ECG (electrocardiogram) signalcharacteristic parameters are the basis of ECG analysis and diagnosis. The fastand precise detection of QR S complexes is very important in ECG signalanalysis, for it is the precondition of the correlative parameters calculation

and diagnosis. The modulus maxima of wavelet transform was applied to theQRS complexes detection of ECG signal firstly. Once misdetections or fail-detections happen, we used the Golden Section Search to adjust thethresholds of maxima determination. The correct detection rate of the QR S complexes is up to 99 .6% .

Golden Section Search calculates simply. It can be used to adjust the detectionthresholds which play a major role in detection different ECG signals, therebyimproving the accuracy rate.


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From the diagram, it is clear that if the function yields f 4a then aminimum lies between x 1 and x 4 and the new triplet of points will be x 1 ,

x 2 , and x 4 . However, if the function yields the value f 4b then a minimum lies

between x 2 and x 3 , and the new triplet of points will be x 2 , x 4 , and x 3.Thus, in either case, we can construct a new narrower search intervalthat is guaranteed to contain the function's minimum.

When applied the golden section search, the continuity and differentiability of the function are not required. And it isn't necessary to write the analyticalexpression of the function. We only need to find the corresponding functionvalues of the chosen insertion points. The golden section search has a broadscope to be applied in.

Fig 2 : Decomposition of ECG signal at different scales


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GOLDEN RATIO IN BODY TEMPERATURES

B ody temperatures and sterilization points fall near the phi (Golden Ratio)

points between freezing and boiling.

B ody temperatures vary, even within humans. The body temperatures of mammals range from around 97 to over 103 Fahrenheit. B irds have averagetemperatures of around 105 Fahrenheit.

The phi (Golden Ratio) point between the freezing temperature ( 32 F) and theboiling temperature ( 212 F) of water is 100 .8 F, or 38 .2 Centigrade.

Take the phi (Golden Ratio) point from the other end of the scale of

temperature and you arrive at 143 , which is about the temperature requiredto kill bacteria. (Generally rounded and stated as 140 in most literature.)

If you take the phi (Golden Ratio) point of 37 degrees centigrade, which is theaverage human body temperature, you get 23 degrees centi grade or 73 degrees Fahrenheit, a "room" temperature that many would consider to be

just about perfect for indoor comfort and outdoor enjoyment.

Water has a very unusual property in that it reaches maximum density in theliquid state at 4 C, instead of in the solid state. This allows ice to float, which is

vital to sustaining life beneath its surface in cold climates. If this criticaltemperature is regarded instead of 0 C, we find that the phi (Golden Ratio)point is 105 .2 F, and this defines the uppe r end of body temperatures. Thuseven key temperatures for body heat and comfort reflect the phi (GoldenRatio)


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MASONIC MURAL IN CALIF ORNIA GRAND

LODGE BASED ON GOLDEN PROPORTION


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CONCLUSION

The world to many seems to be a world of chaos, disorder, confusion, and above all,randomness. Indeed, the world has seemed this way for hundreds of thousands of years, the

apparent randomness causing a catalyst for mankind to improve on what it was given. From

naturally-growing wood we constructed houses, from stone we constructed forts, from

petroleum we made plastic.

All of evolution, all of history, can be summarized as an attempt by mankind to insulate

itself from the harsh randomness of the outside world, an attempt to ensure the survival of the

species by improvisation using our minds. What a comfort then it must have been to

Leonardo Pisano, Sir Isaac Newton, and other brilliant mathematicians to discover the

underlying order in the universe, the one thing that bonds all random events together, from

weather to erosion to growth and even life itself. As Dr. Stephen Marquardt so wisely stated,

"All life is biology. All biology is physiology. All physiology is chemistry. All chemistry is

physics. All physics is math."(Marquardt, 2001) Math is indeed the underlying order of the

universe, and the Fibonacci sequence and Phi are indeed some of the most fascinating

discoveries made in the mathematical world since the time of Archimedes.


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BIBLIOGRAPHY

www.d osto .co gol de nnu b er. ne t pe op le. hw s.ed u www.m iq e l.com

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