The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later. It is constructed by writing the positive integers in a square spiral and specially marking the prime numbers. Ulam and Gardner emphasized the striking appearance in the spiral of prominent diagonal, horizontal, and vertical lines containing large numbers of primes. Both Ulam and Gardner noted that the existence of such prominent lines is not unexpected, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial x2 − x + 41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with major unsolved problems in number theory such as Landau's problems. In particular, no quadratic polynomial has ever been proved to generate infinitely many primes, much less to have a high asymptotic density of them, although there is a well-supported as to what that asymptotic density should be. In 1932, 31 years prior to Ulam's discovery, the herpetologist Laurence Klauber constructed a triangular, non-spiral array containing vertical and diagonal lines exhibiting a similar concentration of prime numbers. Like Ulam, Klauber noted the connection with prime-generating polynomials, such as Euler's. (Wikipedia).
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
Simplicity making complexity. In one word: Emergence. Ulam Spiral is when you mark the integers on a grid, in a square spiral pattern, and then retain only prime numbers. For this variation, I retained multiples of 1, then multiples of 2, etc. I was inspired by https://www.youtube.com/watc
From playlist Artsy things
Why do prime numbers show up as diagonals in a spiral? In this video, I create a visualization in JavaScript (p5.js) of the Ulam Spiral (aka Prime Spiral) named for Polish Mathematician Stanislav Ulan. https://thecodingtrain.com/CodingChallenges/167-prime-spiral.html p5.js Web Editor Sket
From playlist Recent uploads
41 and more Ulam's Spiral - Numberphile
More on prime numbers and Ulam's Spiral - this time focusing on 41 and Arthur C. Clarke. More links & stuff in full description below ↓↓↓ This video features Dr James Clewett. More Clewett videos at: http://bit.ly/JamesClewett See our other Ulam Spiral video at: http://youtu.be/iFuR97YcS
From playlist Numberphile Videos
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
Prime numbers, Ulam Spirals and other cool numbery stuff with Dr James Grime. More links & stuff in full description below ↓↓↓ James Clewett on spirals at: http://youtu.be/3K-12i0jclM And more to come soon... * subscribing to numberphile does not really change your physical appearance!
From playlist James Grime on Numberphile
#Mandala MANDALA LOVERS ALERT- Mandala (Sanskrit: मण्डल, lit, circle) is a spiritual and ritual symbol in Indian religions, representing the universe-check out more videos about mandala below-. * check out my Blog Post for details on Mandala supplies- https://www.theartgeekblog.com/post/mu
From playlist Bag
Johnathan Bush (7/8/2020): Borsuk–Ulam theorems for maps into higher-dimensional codomains
Title: Borsuk–Ulam theorems for maps into higher-dimensional codomains Abstract: I will describe Borsuk-Ulam theorems for maps of spheres into higher-dimensional codomains. Given a continuous map from a sphere to Euclidean space, we say the map is odd if it respects the standard antipodal
From playlist AATRN 2020
Dimitri Zvonkine - On two ELSV formulas
The ELSV formula (discovered by Ekedahl, Lando, Shapiro and Vainshtein) is an equality between two numbers. The first one is a Hurwitz number that can be defined as the number of factorizations of a given permutation into transpositions. The second is the integral of a characteristic class
From playlist 4th Itzykson Colloquium - Moduli Spaces and Quantum Curves
Doodling in Math: Sick Number Games
I don't even know if this makes sense. Boo cold. Try playing with this: http://www.khanacademy.org/cs/pascals-triangle/803149756 http://en.wikipedia.org/wiki/Ulam_spiral My personal website, which you might like: http://vihart.com
From playlist Doodling in Math and more | Math for fun and glory | Khan Academy
The fundamental theorem of arithmetic | Computer Science | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/the-fundamental-theorem-of-arithmetic-1 Independent realization from an ancestor's perspective Watch the next l
From playlist Journey into cryptography | Computer Science | Khan Academy
Stephan Garcia - LatMath 2022 - IPAM's Latinx in the Mathematical Sciences Conference
Recorded 09 July 2022. Stephan Garcia presents at IPAM's Latinx in the Mathematical Sciences Conference. Learn more online at: http://www.ipam.ucla.edu/programs/special-events-and-conferences/latinx-in-the-mathematical-sciences-conference-2022/
From playlist LatMath 2022 - IPAM's Latinx in the Mathematical Sciences Conference
Three-dimensional mushroom spiral in Oregonator
Produced with Ready: http://code.google.com/p/reaction-diffusion/
From playlist Ready
Why do prime numbers make these spirals? | Dirichlet’s theorem, pi approximations, and more
A curious pattern, approximations for pi, and prime distributions. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/spiral-thanks Based on this Math
From playlist Neat proofs/perspectives