Fixed points (mathematics) | Mathematical constants | Real transcendental numbers
In mathematics, the Dottie number is a constant that is the unique real root of the equation , where the argument of is in radians. The decimal expansion of the Dottie number is . Since is decreasing and its derivative is non-zero at , it only crosses zero at one point. This implies that the equation has only one real solution. It is the single real-valued fixed point of the cosine function and is a nontrivial example of a universal attracting fixed point. It is also a transcendental number because of the Lindemann-Weierstrass theorem. The generalised case for a complex variable has infinitely many roots, but unlike the Dottie number, they are not attracting fixed points. Using the Taylor series of the inverse of at (or equivalently, the Lagrange inversion theorem), the Dottie number can be expressed as the infinite series where each is a rational number defined for odd n as The name of the constant originates from a professor of French named Dottie who observed the number by repeatedly pressing the cosine button on her calculator. If a calculator is set to take angles in degrees, the sequence of numbers will instead converge to , the root of . (Wikipedia).
This is the third video of a series from the Worldwide Center of Mathematics explaining the basics of vectors. This video explains the precise definition of dot product (also known as scalar product) and shows some examples of calculated dot products. For more math videos, visit our channe
From playlist Basics: Vectors
Introduction to the Dot Product
Introduction to the Dot Product If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Calculus 3
Calculus 3: Vector Calculus in 2D (12 of 39) What is the Dot Product? (Scalar Product)
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is dot product or scalar product of 2 vectors A and B. Then I will give 4 “typical” examples of dot products. Next video in the series can be seen at: https://youtu.be/Q3FVhpsF5aU
From playlist CALCULUS 3 CH 3 VECTOR CALCULUS
Coding Math: Episode 54 - Dot Product
Let's take a look at what "dot product" is - a couple of ways to calculate it, and some uses for it. Support Coding Math: http://patreon.com/codingmath Source Code: http://github.com/bit101/codingmath http://jsbin.com/hutisoq/edit?js,output
From playlist Episodes
What is the formula for the dot product
http://www.freemathvideos.com In this video series I will show you how to apply the dot product of two vectors and use the product to determine if two vectors are orthogonal or not. The dot product does not produce another vector like scalar multiplication but rather produces a scalar tha
From playlist Vectors
Train your logical thinking skills and learn how to deal with complex numbers by trying out Brilliant! =D https://brilliant.org/FlammableMaths Subscribe to @FlammysWood to see your dad working his wood :^D https://youtu.be/9B9ZNyuqwOY Handcrafted products, puzzles and more :0 https://stem
From playlist Taylor Series
We learned how to add and subtract vectors, and we learned how to multiply vectors by scalars, but how can we multiply two vectors together? There are two ways to do this, and one of them is called the dot product. Let's learn how to find the dot product of two vectors now! Watch the whol
From playlist Mathematics (All Of It)
Solving the Listener Crossword no 4,476 by Nebuchadnezzar
Mark solves the Listener puzzle from 10th November - an excellent crossword called His by Nebuchadnezzar
From playlist Listener crossword guides
Solving Integrals is the First sin(sin(sin(sin(sin(...))))) of Madness
Train your logical thinking skills by trying out Brilliant! =D https://brilliant.org/FlammableMaths Handcrafted products, puzzles and more :0 https://stemerch.eu/collections/handmade-by-stemerch-eu A Very Sophisticated Maths Meme Merch! :D https://stemerch.eu/collections/a-very-sophisticat
From playlist Integrals
Impossible Squares - Numberphile
Ben Sparks shows us a simple problem that takes some fascinating twists. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More videos with Ben Sparks: http://bit.ly/Sparks_Playlist Catch
From playlist Ben Sparks on Numberphile
Multivariable Calculus | The dot product.
We present the definition of the dot product as well as a geometric interpretation and some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Vectors for Multivariable Calculus
Inheritance (Crime Documentary) | Real Stories
A serious yet quirky exploration into the mystery of a treacherous mother and daughter act who trick lonely old men into appointing them as beneficiaries in their wills. The story unearths a legacy of crime dating back over forty years. Want to watch more full-length Documentaries? Click
From playlist Crime Documentaries
Live CEOing Ep 135: Formal Symbols Font Design in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Formal Symbols Font Design in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Multivariable Calculus | Some applications of the dot product.
We present some applications of the dot product, including finding orthogonal vectors and angle measures. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Vectors for Multivariable Calculus
Marcello Porta - Correlation energy of a weakly interacting Fermi gas
Marcello Porta (SISSA) Correlation energy of a weakly interacting Fermi gas. In this talk I will discuss the ground state properties of homogeneous, interacting Fermi gases, in the mean-field regime. In this regime, Hartree-Fock theory provides a good approximation for the ground state e
From playlist Large-scale limits of interacting particle systems
8.01x - Module 12.02 - Multiplication of vectors,
Multiplication of vectors, Dot products and vector products. Scalars and vectors
From playlist 8.01x - MIT Help Sessions
What is the dot product of two vectors? How is it useful? Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/2SGI5Kvpk9
From playlist Introduction to Vectors