Spirals | Circle packing

Doyle spiral

In the mathematics of circle packing, a Doyle spiral is a pattern of non-crossing circles in the plane in which each circle is surrounded by a ring of six tangent circles. These patterns contain spiral arms formed by circles linked through opposite points of tangency, with their centers on logarithmic spirals of three different shapes. Doyle spirals are named after mathematician Peter G. Doyle, who made an important contribution to their mathematical construction in the late 1980s or early 1990s. However, their study in phyllotaxis (the mathematics of plant growth) dates back to the early 20th century. (Wikipedia).

Doyle spiral
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A variation on an Ulam Spiral: a Sacks Spiral

Simplicity making complexity. In one word: Emergence. Using the same process as my Ulam Spiral video, https://youtu.be/JjBnLz0SF3A but this time in a Sacks Spiral, https://youtu.be/iFuR97YcSLM?t=6m3s Enjoy. Animation made with FMS Logo.

From playlist Artsy things

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What is... an elliptic curve?

In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were

From playlist An Introduction to the Arithmetic of Elliptic Curves

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Rigidity of the hexagonal triangulation of the plane and its applications - Feng Luo

Feng Luo, Rutgers October 5, 2015 http://www.math.ias.edu/wgso3m/agenda 015-2016 Monday, October 5, 2015 - 08:00 to Friday, October 9, 2015 - 12:00 This workshop is part of the topical program "Geometric Structures on 3-Manifolds" which will take place during the 2015-2016 academic year

From playlist Workshop on Geometric Structures on 3-Manifolds

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Instrument for drafting spiral 1

The orange nut-wheel, by revolving about the fixed central point, describes a spiral by moving along the screw threaded axle either way, and transmits the same to drawing paper on which transfer paper is laid with colored side downward. The obtained spiral is not an Archimedean one.

From playlist Mechanisms

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The Riemann Hypothesis - Picturing The Zeta Function

in this chapter i will show how to visualize the zeta and eta functions in the proper way meaning that everything on those two functions is made out of spirals all over the grid and the emphasis in this chapter will be on the center points of the spirals mainly the divergent spirals 0:00

From playlist Summer of Math Exposition Youtube Videos

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What is the curl?

Free ebook http://tinyurl.com/EngMathYT A basic introduction to the curl of a vector field - one of the basic operations of vector calculus. I show how to calculate the curl and discuss its relationship with rotation and circulation density. Many examples are presented.

From playlist Engineering Mathematics

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To construct a PENTAGON with ruler (straightedge) and compass

Geometrical construction of a pentagon with Euclidean Tools Follow me: http://www.twitter.com/dantecardoso

From playlist Math

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Curves from Antiquity | Algebraic Calculus One | Wild Egg

We begin a discussion of curves, which are central objects in calculus. There are different kinds of curves, coming from geometric constructions as well as physical or mechanical motions. In this video we look at classical curves that go back to antiquity, such as prominently the conic sec

From playlist Algebraic Calculus One from Wild Egg

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Cycloid

#Cycloid: A curve traced by a point on a circle rolling in a straight line. (A preview of this Sunday's video.)

From playlist Miscellaneous

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Algebraic geometry 44: Survey of curves

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives an informal survey of complex curves of small genus.

From playlist Algebraic geometry I: Varieties

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Student Exemplar: 'The Sign of Four'

Buy my revision guides in paperback on Amazon*: Mr Bruff’s Guide to GCSE English Language https://amzn.to/2GvPrTV Mr Bruff’s Guide to GCSE English Literature https://amzn.to/2POt3V7 AQA English Language Paper 1 Practice Papers https://amzn.to/2XJR4lD Mr Bruff’s Guide to ‘Macbeth’ htt

From playlist 'The Sign of Four' by Arthur Conan Doyle - Analysis

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Three-dimensional mushroom spiral in Oregonator

Produced with Ready: http://code.google.com/p/reaction-diffusion/

From playlist Ready

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The Hound of the Baskervilles by Sir Arthur Conan Doyle - So You Haven't Read

Enjoyed our breakdown of The Hound of the Baskervilles? Then why not support the show and get early access to all our shows plus Wallpapers, music, and more! Just click the link to sign up http://bit.ly/EHPatreon So you haven't read The Hound of the Baskervilles? Then have a seat as we

From playlist So You Haven't Read (ALL EPISODES)

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1950 Baseballs and Bullets at The Polo Grounds

The History Guy remembers an extraordinary night when there were bullets falling at the Dodgers/Giants MLB game at The Polo Grounds, New York City, in 1950. It is history that deserves to be remembered. Facebook: https://www.facebook.com/TheHistoryGuyYT/ Patreon: https://www.patreon.com/T

From playlist History without War

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Q&A 103: How Many Stars Have Zero Planets? And More...

In this week's questions show, I explain why we'll never know which stars have no planets. How we could prevent a catastrophe to Earth, and why aliens might still be a threat to us. Check out more of Dustin Gibson's photographs at: https://www.instagram.com/gibsonpics/ 00:48 How many sta

From playlist Questions and Answers with Fraser Cain

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Structure Analysis: 'The Sign of Four' (plus my dog barking)

Buy my revision guides in paperback on Amazon*: Mr Bruff’s Guide to GCSE English Language https://amzn.to/2GvPrTV Mr Bruff’s Guide to GCSE English Literature https://amzn.to/2POt3V7 AQA English Language Paper 1 Practice Papers https://amzn.to/2XJR4lD Mr Bruff’s Guide to ‘Macbeth’ htt

From playlist 'The Sign of Four' by Arthur Conan Doyle - Analysis

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Who IS Sherlock Holmes - Neil McCaw

View full lesson: http://ed.ted.com/lessons/who-is-sherlock-holmes-neil-mccaw More than a century after first emerging into the fogbound, gaslit streets of Victorian London, Sherlock Holmes is universally recognizable. And yet many of his most recognizable features don't appear in Arthur

From playlist New TED-Ed Originals

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The search for extraterrestrial intelligence | Computer Science | Khan Academy

Can information theory help us talk to aliens? Watch the next lesson: https://www.khanacademy.org/computing/computer-science/internet-intro/internet-works-intro/v/the-internet-wires-cables-and-wifi?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Missed the previous lesson? htt

From playlist Journey into information theory | Computer Science | Khan Academy

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Funhouse spiral staircase

I found this strange spiral staircase at Chris Hughes' and Alexa Meade's infinitely tall Funhouse. @AlexaMeadeArt http://funhouse.house The raw footage we used to make this video is at https://youtu.be/HT9HbMS-ZvE

From playlist Spherical video

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Anton Arnold: Modal based hypocoercivity methods on the torus and the real line with application...

CIRM VIRTUAL EVENT Recorded during the meeting "Kinetic Equations: from Modeling, Computation to Analysis" the March 22, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide m

From playlist Virtual Conference

Related pages

Fibonacci number | Schwarzian derivative | Circle packing theorem | Conformal map | Algebraic number | Circle packing | Point at infinity | Exponential function | Golden ratio | Cone | Logarithmic spiral | Hyperbolic space | Coxeter's loxodromic sequence of tangent circles | Fermat's spiral | Kleinian group | Natural number | Tangent circles | Golden angle | Similarity (geometry) | Möbius transformation | Spiral galaxy | Cylinder