The document discusses the golden ratio. It defines the golden ratio mathematically as two quantities where the ratio of the sum to the larger quantity equals the ratio of the larger to the smaller quantity. This value is approximately 1.618. The golden ratio has appeared throughout history in art and architecture believed to be aesthetically pleasing. It also appears in nature. Mathematicians have further explored its properties. The use of the golden ratio can be traced back to ancient Egyptians and Greeks and it continued to be used and studied by many famous mathematicians and artists throughout history.
In this presentation, we see that how golden ratio and Fibonacci series are calculated or working? and What is the problem faced by Fibonacci in Fibonacci series.
Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.
It is the ratio of a line segment cut into two pieces of different lengths such that the ratio of the whole segment to that of the longer segment is equal to the ratio of the longer segment to the shorter segment.
In this presentation, we see that how golden ratio and Fibonacci series are calculated or working? and What is the problem faced by Fibonacci in Fibonacci series.
Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.
It is the ratio of a line segment cut into two pieces of different lengths such that the ratio of the whole segment to that of the longer segment is equal to the ratio of the longer segment to the shorter segment.
Fibonacci Sequence .
The Fibonacci Sequence is a definite pattern that can begin with either 0, 1 or 1, 1. The sequence is generated by adding the previous terms, so that 0 +1 equals 1, 1+1 equals 2, 2 + 1 equals 3, 2 + 3 equals 5, 5 + 3 equals 8, 8 + 5 equals 13, 13 + 8 equals 21, 21 + 13 equals 34, 34 + 21 equals 55, and so on. Fibonacci can be found in in every domain such as nature, art, infrastructure ,humans etc. .
The golden ratio is about 1.618, and represented by the Greek letter phi.
The golden ratio is sometimes called the "divine proportion," because of its frequency in the natural world.
The fibonacci sequence and the golden ratio #Scichallenge2017Miléna Szabó
#SciChallenge2017
In this presentation I would like to show how important mathematics is. It is shows up in everyday life through nature.
"In order to understand the Universe you must know the language which it is written and that is Mathematics." /Galileo Galilei/
Grid Systems in Graphic Design by ADMEC Multimedia InstituteRavi Bhadauria
ADMEC Multimedia Institute is growing institute that is providing industry oriented training to the world at large. Being a multimedia institute we offer training for creating or designing content for information technology mainly.
Fibonacci Sequence .
The Fibonacci Sequence is a definite pattern that can begin with either 0, 1 or 1, 1. The sequence is generated by adding the previous terms, so that 0 +1 equals 1, 1+1 equals 2, 2 + 1 equals 3, 2 + 3 equals 5, 5 + 3 equals 8, 8 + 5 equals 13, 13 + 8 equals 21, 21 + 13 equals 34, 34 + 21 equals 55, and so on. Fibonacci can be found in in every domain such as nature, art, infrastructure ,humans etc. .
The golden ratio is about 1.618, and represented by the Greek letter phi.
The golden ratio is sometimes called the "divine proportion," because of its frequency in the natural world.
The fibonacci sequence and the golden ratio #Scichallenge2017Miléna Szabó
#SciChallenge2017
In this presentation I would like to show how important mathematics is. It is shows up in everyday life through nature.
"In order to understand the Universe you must know the language which it is written and that is Mathematics." /Galileo Galilei/
Grid Systems in Graphic Design by ADMEC Multimedia InstituteRavi Bhadauria
ADMEC Multimedia Institute is growing institute that is providing industry oriented training to the world at large. Being a multimedia institute we offer training for creating or designing content for information technology mainly.
Describe how golden ratio is used in making of finest structures. It present three paradigmatic case studies where Golden Mean rectangles allegedly apply in architecture: (i) The Parthenon in Athens; (ii) The United Nations Secretariat Building in New York City; and (iii) The Great Pyramid of Giza.
This presentation is about GATE which is a Natural Language Processing Platform That supports many Languages. It also mentions Mimir which is an Indexing server for GATE that enables its users to search in a corpus of documents
A VizMath presentation featuring videos by Neil Currie on the golden ratio and by Rostom Kouyoumdjian on drawing with one point perspective. Illustrations of the use of math in art through the ages.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2. WHAT IS GOLDEN RATIO ?
DIVYANSH
• In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of
their sum to the larger of the two quantities. Expressed algebraically, for
quantities a and b with a > b,
• where the Greek letter phi ( ) represents the golden ratio. Its value is
• :
• The golden ratio is also called the golden section (Latin: section aurea) or golden
mean. Other names include extreme and mean ratio,medial section, divine proportion, divine
section (Latin: section divina), golden proportion, golden cut, and golden number.
3. • 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 (see Applications and observations
below). Mathematicians since Euclid have studied the properties of the golden
ratio, including its appearance in the dimensions of a regular pentagon and in
a golden rectangle, which can be cut into a square and a smaller rectangle
with the same aspect ratio. The golden ratio has also been used to analyze
the proportions of natural objects as well as man-made systems such
as financial markets, in some cases based on dubious fits to data.
• At least 1,000,000,000,000 decimal digits are known
4. CALCULATION
•
•
•
Two quantities a and b are said to be in golden ratio if
A+b/a = a/b =φ
One method for finding the value of φ is to start with the left fraction. Through
simplifying the fraction and substituting in b/a = 1/φ,
• A+b/a=1+b/a= 1+1/φ
• By definition, it is shown that
• 1+1/φ =φ
• Multiplying by φ gives
Φ + 1= φ . Φ
which can be rearranged to
5. Φ . Φ – Φ-1 =0
Using the quadratic formula, two solutions are obtained:
Φ = 1+root5 / 2 = 1.61803…………
And
Φ = 1 – root5/2 =.61803……………..
Because φ is the ratio between positive quantities φ is necessarily positive
Φ = 1+root5 / 2 = 1.61803…………
6. Uses in architecture date to the ancient
Egyptians and Greeks
• It appears that the Egyptians may have used both pi and phi in the design of
the Great Pyramids. The Greeks are thought by some to have based the design
of the Parthenon on this proportion, but this is subject to some conjecture.
• Phidias (500 BC – 432 BC), a Greek sculptor and mathematician, studied phi
and applied it to the design of sculptures for the Parthenon.
• Plato (circa 428 BC – 347 BC), in his views on natural science and cosmology
presented in his “Timaeus,” considered the golden section to be the most binding of
all mathematical relationships and the key to the physics of the cosmos.
7. • Euclid (365 BC – 300 BC), in “Elements,” referred to dividing a line at the
0.6180399… point as “dividing a line in the extreme and mean ratio.” This later
gave rise to the use of the term mean in the golden mean. He also linked this
number to the construction of a pentagram.
pentagram
8. The Fibonacci Series was discovered around 1200
AD
• Leonardo Fibonacci, an Italian born in 1175 AD (2) discovered the
unusual properties of the numerical series that now bears his name, but
it’s not certain that he even realized its connection to phi and the Golden
Mean. His most notable contribution to mathematics was a work known as
Liber Abaci, which became a pivotal influence in adoption by the
Europeans of the Arabic decimal system of counting over Roman
numerals. (3)
9. Golden proportion was first called the “Divine
Proportion” in the 1500 ′ s
• Da Vinci provided illustrations for a dissertation published by Luca Pacioli in
1509 entitled “De Divina Proportione” (1), perhaps the earliest reference in
literature to another of its names, the “Divine Proportion.” This book contains
drawings made by Leonardo da Vinci of the five Platonic solids. It was probably
da Vinci who first called it the “sectio aurea,” which is Latin for golden section.
section
• The Renaissance artists used the Golden Mean extensively in their paintings and
sculptures to achieve balance and beauty. Leonardo Da Vinci, for instance, used it
to define all the fundamental proportions of his painting of “The Last Supper,”
from the dimensions of the table at which Christ and the disciples sat to the
proportions of the walls and windows in the background.
10. • Johannes Kepler (1571-1630), discoverer of the elliptical nature of
the orbits of the planets around the sun, also made mention of the “Divine
Proportion,” saying this about it:
• “Geometry has two great treasures: one is the theorem of Pythagoras; the
other, the division of a line into extreme and mean ratio. The first we may
compare to a measure of gold; the second we may name a precious jewel.”
11. The term “Phi” was not used until the 1900 ′ s
• It wasn’t until the 1900′s that American mathematician Mark Barr used the
Greek letter phi (Φ) to designate this proportion. By this time this ubiquitous
proportion was known as the golden mean, golden section and golden ratio as well
as the Divine proportion. Phi is the first letter of Phidias (1), who used the
golden ratio in his sculptures, as well as the Greek equivalent to the letter “F,”
the first letter of Fibonacci. Phi is also the 21st letter of the Greek
alphabet, and 21 is one of numbers in the Fibonacci series. The character for
phi also has some interesting theological implications.
12. Recent appearances of Phi in math and physics
• Phi continues to open new doors in our understanding of life and the
universe. It appeared in Roger Penrose’s discovery in the 1970 ′s of
“Penrose Tiles,” which first allowed surfaces to be tiled in five-fold
symmetry. It appeared again in the 1980′s in quasi-crystals, a newly
discovered form of matter.
matter
13. MATERIAL CONTRIBUTED BY OTHER GROUP
MATES
AND FOR SOME OF YOU WHO DID NOT WATCH
THE PPT , THE PPT WAS