When the positive integers are arrayed along the Ulam spiral, prime numbers, represented by dots, tend to collect along diagonal lines.

* Ulam spiral

Ulam spiral of size 200 × 200.

Shortly afterwards, in an early application of computer graphics, Ulam with collaborators Myron Stein and Mark Wells used MANIAC II at Los Alamos Scientific Laboratory to produce pictures of the spiral for numbers up to 65, 000.

In March of the following year, Martin Gardner wrote about the Ulam spiral in his Mathematical Games column ; the Ulam spiral featured on the front cover of the issue of Scientific American in which the column appeared.

Ulam constructed the spiral by writing down a regular rectangular grid of numbers, starting with 1 at the center, and spiraling out:

Small Ulam spiral

In the 200 × 200 Ulam spiral shown above, diagonal lines are clearly visible, confirming the pattern.

Since in the Ulam spiral adjacent diagonals are alternatively odd and even numbers, it is no surprise that all prime numbers lie in alternate diagonals of the Ulam spiral.

Mathematician Stanislaw Ulam developed the Ulam spiral for visualization of prime numbers while doodling during a boring presentation at a mathematics conference.

* Ulam spiral

** The Ulam spiral was discovered by accident.

* Ulam spiral

* Ulam spiral, or prime spiral.

In this passage, Clarke describes the prime spiral, a method of graphing the prime numbers that reveals a pattern, seven years before it was discovered by Stanislaw Ulam.

Legendre's conjecture implies that at least one prime can be found in every revolution of the Ulam spiral.

It embodied the Teller – Ulam design, which Sakharov and other Soviet scientists had worked out independently.

But Fermi also participated in preliminary work on the hydrogen bomb at Los Alamos as a consultant, and along with Stanislaw Ulam, calculated that the amount of tritium needed for Edward Teller's model of a thermonuclear weapon would be prohibitive, and a fusion reaction could not be assured to propagate even with this large quantity of tritium.

The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture ( after Stanisław Ulam ), Kakutani's problem ( after Shizuo Kakutani ), the Thwaites conjecture ( after Sir Bryan Thwaites ), Hasse's algorithm ( after Helmut Hasse ), or the Syracuse problem ; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers, or as wondrous numbers.

The Fermi – Pasta – Ulam problem is credited not only as " the birth of experimental mathematics ", but also as inspiration for the vast field of Nonlinear Science.

Otto Frisch, the discoverer of the possibility of chain reactions from fission, in an article in The Bulletin of the Atomic Scientists describing his first impressions of Los Alamos: I also met Stan Ulam early on, a brilliant Polish topologist with a charming French wife.

They also showed how this behavior explained the puzzling earlier work of Fermi, Pasta and Ulam.

They also made the connection to earlier numerical experiments by Fermi, Pasta, and Ulam by showing that the KdV equation was the continuum limit of the FPU system.

The concept was then improved by von Neumann's friend Stanislaw Ulam, also a mathematician ; Ulam suggested that the machine be built on paper, as a collection of cells on a grid.

The phenomenon is related to the Ulam spiral, which is also implicitly quadratic, and the class number ;

The concept was then improved by von Neumann's friend Stanisław Ulam, also a mathematician ; Ulam suggested that the machine be built on paper, as a collection of cells on a grid.

The concept was then extended by von Neumann's friend Stanislaw Ulam, also a mathematician, who suggested that the machine be built on paper, as a collection of cells on a grid.

As it is also the most efficient design concept for small nuclear weapons, today virtually all the nuclear weapons deployed by the five nuclear-weapon states under the NPT use the Teller – Ulam design.

Morland also interviewed ( often informally ) many former Los Alamos scientists ( including Teller and Ulam, though neither gave him any useful information ), and used a variety of interpersonal strategies to encourage informational responses from them ( i. e., asking questions such as " Do they still use sparkplugs?

It was a multi-stage thermonuclear device which utilized radiation implosion called Sakharovs " Third Idea " in the USSR ( the Teller – Ulam design in the USA ).

If is a successor cardinal, this result is due to Ulam and is easily shown by means of what is called an Ulam matrix.

However, in February 1951, Ulam had a new idea, in which the shock wave from an atomic bomb " primary " stage, through an arrangement he called " hydrodynamic lensing ", would compress a " secondary " stage of deuterium fusion fuel wrapped around a plutonium rod or " spark plug ".

Using the above theorem it is easy to see that the original Borsuk Ulam statement is correct since if we take a map f: S < sup > n </ sup > → ℝ < sup > n </ sup > that does not equalize on any antipodes then we can construct a map g: S < sup > n </ sup > → S < sup > n-1 </ sup > by the formula

( this is equivalent to the Borsuk – Ulam theorem )

Ulam is a major presence in the Scottish Book.

It is often designated as the " Teller – Ulam design ".

This addition is the key element of the Fermi – Pasta – Ulam problem, which is often designated by the abbreviation FPU.

One of these introduced the Fermi – Ulam model, which is an extension of Fermi's theory of the acceleration of cosmic rays.

Georgia O ' Keeffe, on seeing Ulam at a party in Santa Fe, New Mexico: Who is that man?

For the sake of history, I think it is more precise to say that Ulam is the father, because he provided the seed, and Teller is the mother, because he remained with the child.

It is due to Kelly and Ulam.

The Borsuk – Ulam theorem is a result from algebraic topology dealing with such pairs of points.

In some forms of thermonuclear weapons, the energy from this explosion is then used to implode a capsule of fusion fuel before igniting it, causing a fusion reaction ( see Teller – Ulam design ).