The Sexy prime Freudenthal–Tits magic square Lie Algebra
In mathematics, sexy primes are prime numbers that differ from each other by six. For example, the numbers 5 and 11 are both sexy primes, because 11 minus 5 is 6. If p + 2 or p + 4 (where p is the lower prime) is also prime, then the sexy prime is part of a prime triplet.
The term "sexy prime" is a pun stemming from the Latin word for six: sex. In mathematics, the Freudenthal magic square (or Freudenthal–Tits magic square) is a construction relating several Lie algebras (and their associated Lie groups). It is named after Hans Freudenthal and Jacques Tits, who developed the idea independently. It associates a Lie algebra to a pair of division algebras A, B. The resulting Lie algebras have Dynkin diagrams according to the table at right. The "magic" of the Freudenthal magic square is that the constructed Lie algebra is symmetric in A and B, despite the original construction not being symmetric, though Vinberg's symmetric method gives a symmetric construction.
In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10/\100.
In mathematics, the sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit.
In mathematics, the sieve of Sundaram is a simple deterministic algorithm for finding all the prime numbers up to a specified integer. It was discovered by Indian mathematician S. P. Sundaram in 1934.
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair.
In number theory, a prime k-tuple is a finite collection of values representing a repeatable pattern of differences between prime numbers.
In the theory of ordinary differential equations (ODEs), Lyapunov functions are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Named after the Russian mathematician Aleksandr Mikhailovich Lyapunov, Lyapunov functions (also called the Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory. A similar concept appears in the theory of general state space Markov chains, usually under the name Foster–Lyapunov functions.
Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Lyapunov Stability.
How to cut octonions into quaternions without the tears of sedenions... Python code for octonion and sedenion multiplication
The Ulam spiral or prime spiral (in other languages also called the Ulam cloth) is a graphical depiction of the set of prime numbers, devised by mathematician Stanislaw 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 conjecture as to what that asymptotic density should be.
In 1932, more than thirty years prior to Ulam's discovery, the herpetologist Laurence M. 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.
Matrices and Eigenvectors
By Casa Software Ltd.
A group of anagrams of supposed occult significance. A bastard mixture of Latin, French, Hebrew, and Egyptian, Rota Taro Orat Tora Ator reads as follows:
Rota: the wheel, or cycle
Taro: the Tarot, or Book of Thoth
Orat: speaks or teaches (verb)
Tora: the Torah, or Law
Ator: Hathor, the goddess of love.
The Sator Square (or Rotas Square) is a word square containing a five-word Latin palindrome
Cryptography or cryptology (from Ancient Greek: κρυπτός, translit. kryptós "hidden, secret"; and γράφειν graphein, "to write", or -λογία -logia, "study", respectively) is the practice and study of techniques for secure communication in the presence of third parties called adversaries.
Christian symbolism is the use of symbols, including archetypes, acts, artwork or events, by Christianity. It invests objects or actions with an inner meaning expressing Christian ideas.
Some people are more flexible with ideas than others.
Agile learning: how to build a brain like a gymnast
By Aytekin Tank
Jacques Tits developed the idea independently, associates a Lie algebra to a pair of division algebras A, B. The resulting Lie algebras have Dynkin diagrams.
A ḍākinī (Tibetan: མཁའ་འགྲོ་མ་, Wylie: mkha' 'gro ma, THL: Khandroma; Mongolian: хандарма; Chinese: 空行母; pinyin: Kōngxíng Mǔ; alternatively Chinese: 荼枳尼; pinyin: Túzhǐní) is a type of spirit in Vajrayana Buddhism. The Sanskrit term is likely related to the term for drumming, while the Tibetan term means "skygoer" and may have originated in the Sanskrit khecara, a term from the Cakrasaṃvara Tantra. Dakinis are often represented as consorts in Yab-Yum representations. The masculine form of the word is ḍāka, which is usually translated into Tibetan as pawo "hero" (Wylie: dpa' bo).
The End of Theoretical Physics As We Know It
By Sabine Hossenfelder
And the good shepherd with all the giraffe of Africa, all the dolphin of the world's ocean... being all high and mighty, taking case by case...
2 Corinthians 3:4-6 New King James Version (NKJV)
The Spirit, Not the Letter
4 And we have such trust through Christ toward God. 5 Not that we are sufficient of ourselves to think of anything as being from ourselves, but our sufficiency is from God, 6 who also made us sufficient as ministers of the new covenant, not of the letter but of the [a]Spirit; for the letter kills, but the Spirit gives life.
The book of Numbers to the Sri Yantra power of a Mayan Mersenne
In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be an immediate consequence of the postulates of special relativity.
A NEW ANGLE
A universal way to solve problems, from a mathematical genius
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Some suggest, if you put a letter 'c' in words like "mediation", you get words like 'medication', however add a letter 't' and you get the word 'meditation'. Perhaps an optometrist may remedy such human errors for Saint Lucy sake.
How Claude Shannon and the Bell Labs Mathematics Department founded the digital age.
The Beatitudes are eight blessings recounted by Jesus in the Sermon on the Mount in the Gospel of Matthew. Each is a proverb-like proclamation, without narrative. Four of the blessings also appear in the Sermon on the Plain in the Gospel of Luke, followed by four woes which mirror the blessings. In the Vulgate, each of these blessings begins with the word beati, which translates to "happy", "rich", or "blessed" (plural adjective). The corresponding word in the original Greek is μακάριοι (makarioi), with the same meanings. Thus "Blessed are the poor in spirit" appears in Latin as beati pauperes spiritu. The Latin noun beātitūdō was coined by Cicero to describe a state of blessedness, and was later incorporated within the chapter headings written for Matthew 5 in various printed versions of the Vulgate. Subsequently, the word was anglicized to beatytudes in the Great Bible of 1540, and has, over time, taken on a preferred spelling of beatitudes.
"Some dudes have attitudes" the girl suggested as a distinct possibility, in theology class. Or some other memory of Catholic grade school lessons with lessons from books, quoting, “It doesn’t matter what you say you believe - it only matters what you do.” ― Robert Fulghum, All I Really Need to Know I Learned in Kindergarten
Thanks Reading Rainbow and PBS for all the help along the way. I really enjoyed the PBS, 1970's Hey You Guys, 'Electric Company' as a child. The new version has it's own flavor and is fun for many too.
calculateprimes
James M. McCanney, M.S. Physics
The letter of the law versus the spirit of the law is an idiomatic antithesis. When one obeys the letter of the law but not the spirit, one is obeying the literal interpretation of the words (the "letter") of the law, but not necessarily the intent of those who wrote the law. Conversely, when one obeys the spirit of the law but not the letter, one is doing what the authors of the law intended, though not necessarily adhering to the literal wording.
Riemann Sphere and Möbius Transformation
Hubert Shutrick
Researchers achieve first ever acceleration of electrons in a proton-driven plasma wave
August 29, 2018 by Achintya Rao
The Most Important Skill For Interacting With People
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Idiom (or expression): "put words in someone's mouth." to say that someone means one thing when the person really meant something else: I never said you should leave – don't put words in my mouth.
National karma of Texas as a state of friendship
what is suggestive speech? The definition of suggestive is something hinted at or recommended. An example of suggestive is a very flirtatious comment; a suggestive comment. An example of suggestive is someone saying they might be interested in going out dancing; a suggestive idea.
"Law" originally referred to legislative statute, but in the idiom may refer to any kind of rule. Intentionally following the letter of the law but not the spirit may be accomplished through exploiting technicalities, loopholes, and ambiguous language.
chasm K clique number v. schism clan complex network
Sigmund Freud emphasized the importance of the unconscious mind, and a primary assumption of Freudian theory is that the unconscious mind governs behavior to a greater degree than people suspect. Indeed, the goal of psychoanalysis is to make the unconscious conscious.
Totem, Taboo and the Concept of Law:
Myth in Hart and Freud
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Serenity Sells
Debye toroidal moment of surface plasmons as SBIR ESCO model