Quadratic irrational numbers | Mathematical constants | History of geometry | Golden ratio | Euclidean plane geometry
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 and with , where the Greek letter phi ( or ) denotes the golden ratio. The constant satisfies the quadratic equation and is an irrational number with a value of 1.618033988749.... The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli, and also goes by several other names. Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of —may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural objects and artificial systems such as financial markets, in some cases based on dubious fits to data. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other parts of vegetation. Some 20th-century artists and architects, including Le Corbusier and Salvador Dalí, have proportioned their works to approximate the golden ratio, believing it to be aesthetically pleasing. These uses often appear in the form of a golden rectangle. (Wikipedia).
This video introduces the Golden ratio and provides several examples of where the Golden ratio appears. http:mathispower4u.com
From playlist Mathematics General Interest
Defining and Finding the Value of the Golden Ratio
This video focuses explores the great number Phi, also known as the Golden Ratio. The definition and exact value of the Golden Ratio is explained in this video. This Golden Ratio video series seeks to explore one of the most significant numbers in mathematics. This goal of this video se
From playlist Golden Ratio Series
Demystifying the Golden Ratio (Part 1)
Part 1 of series offering a mathematical explanation of why the Golden Ratio is commonly found in nature. In this video we discuss some basic aspects of the Golden Ratio, and its relationship with the Fibonocci numbers.
From playlist Demystifying the Golden Ratio
Is the beauty of Charlize Theron based on a myth? Does her face really have the golden ratio? Are the aesthetics that we are drawn into far from individual aesthetic understanding? Does the golden ratio compel us to like certain types of beauty? Or have we been led to believe a lie? Let
From playlist Myth or Fact?
The Golden Ratio: Is It Myth or Math?
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From playlist Be Smart - LATEST EPISODES!
Golden Ratio ϕ hidden in Pentagon!
The ratio of a common diagonal and side of regular pentagon is equal to golden ratio. Golden ratio is an irrational constant in mathematics, ϕ = 1.618033... Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regula
From playlist Summer of Math Exposition Youtube Videos
The Patterns and Appearances of the Golden Ratio
#some2 #goldenratio #fibonacci This Video is a collab between me and Justin Golden. We are both fascinated by the golden ratio and decided to make a video about why we see it so often and have come up with a lot of diffrent things but also show how certain properties of the golden ratio c
From playlist Summer of Math Exposition 2 videos
The Golden Ratio, which is one of the most famous irrational numbers that go on forever, appears in nature and some pieces of art from Michelangelo or Leonardo Da Vinci. Some civilizations even used it in architecture throughout history. But is this number, that is also related to the Fibo
From playlist Theory to Reality
The Golden Ratio and the Fibonacci Numbers
This video seeks to explore the connection between the Golden Ratio and the Fibonacci Numbers. That is, this video highlights how the ratio of consecutive Fibonacci Numbers tends to Phi, the Golden Ratio. This video is part of a series on the Golden Ratio. The goal of this video series
From playlist Golden Ratio Series
The Golden Ratio: Nature's Favorite Number
The Golden Ratio: Nature's Favorite Number - https://aperture.gg/goldenratio Get 3 years of protection with AtlasVPN for $1.39 a month: http://atlasv.pn/Aperture Follow me on Instagram: https://www.instagram.com/mcewen/ The golden ratio is everywhere. From the smallest places known to hum
From playlist Science & Technology 🚀
Golden Ratio BURN (Internet Beef) - Numberphile
Seriously? Matt Parker is talking about Fibonacci and Lucas numbers again. Part 2: https://youtu.be/z1THaBtc5RE More links & stuff in full description below ↓↓↓ See part 2 on Numberphile2: https://youtu.be/z1THaBtc5RE The original trilogy of videos where this all started: http://bit.ly/G
From playlist Matt Parker (standupmaths) on Numberphile
The golden ratio | Lecture 3 | Fibonacci Numbers and the Golden Ratio
The classical definition of the golden ratio. Two positive numbers are said to be in the golden ratio if the ratio between the larger number and the smaller number is the same as the ratio between their sum and the larger number. Phi=(1+sqrt(5))/2 approx 1.618. Join me on Coursera: http
From playlist Fibonacci Numbers and the Golden Ratio
2. The Golden Ratio & Fibonacci Numbers: Fact versus Fiction
(October 8, 2012) Professor Keith Devlin dives into the topics of the golden ratio and fibonacci numbers. Originally presented in the Stanford Continuing Studies Program. Stanford University: http://www.stanford.edu/ Stanford Continuing Studies Program: https://continuingstudies.stanfor
From playlist Lecture Collection | Mathematics: Making the Invisible Visible
Ed Pegg - New Substitution Tilings - CoM Apr 2021
A previously unknown substitution tiling can be directly built from powers 0 to 4 of a complex root of x^3 = x^2+1, the supergolden ratio. This talk will discuss new and old tiling systems and the algebraic roots behind them. Ed Pegg Jr is a long time recreational mathematician who worked
From playlist Celebration of Mind 2021
Mathematical Games Hosted by Ed Pegg Jr. [Episode 3: Algebraic Number Magic]
Join Ed Pegg Jr. as he explores a variety of games and puzzles using Wolfram Language. In this episode, he features games and puzzles focusing on algebraic number magic. Follow us on our official social media channels. Twitter: https://twitter.com/WolframResearch/ Facebook: https://www.f
From playlist Mathematical Games Hosted by Ed Pegg Jr.
Demystifying the Golden Ratio (Part 2)
In this second video of the series, we explore the relationship between the Golden Ratio and the equation defining the Fibonocci numbers.
From playlist Demystifying the Golden Ratio