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Wall-Sun-Sun Prime


In mathematics, a Wall-Sun-Sun prime is a certain kind of prime number. A prime ''p'' > 5 is called a Wall-Sun-Sun prime if ''p''² divides :''F''(''p'' − (''p''|5)), where ''F''(''n'') is the ''n''-th Fibonacci number and (''a''|''b'') is the Legendre symbol of ''a'' and ''b''. Wall-Sun-Sun primes are named after D. D. Wall, Zhi Hong Sun and Zhi Wei Sun; Z. H. Sun and Z. W. Sun showed in 1992 that if the first case of Fermat's last theorem was false for a certain prime ''p'', then ''p'' would have to be a Wall-Sun-Sun prime. As a result, prior to Andrew Wiles' proof of Fermat's last theorem, the search for Wall-Sun-Sun primes was also the search for a counterexample to this century-old conjecture. No Wall-Sun-Sun primes are known to date; if any exist, they must be > 1014. It has been conjectured that there are infinitely many Wall-Sun-Sun primes, but the conjecture remains unproven.

Also see

  • Wieferich prime
  • Wilson prime
  • Wolstenholme prime

  • http://primes.utm.edu/glossary/page.php?sort=WallSunSunPrime The Prime Glossary: Wall-Sun-Sun prime
  • http://www.loria.fr/~zimmerma/records/Wieferich.status Status of the search for Wall-Sun-Sun primes Category:Number theory de:Wall-Sun-Sun-Primzahl fr:Nombre de Wall-Sun-Sun

    Hi-Hat


    A Hi-hat or hihat is a type of cymbal and stand used as a typical part of a drum kit by percussionists in jazz, rock and roll, and other forms of contemporary popular music. It consists of two cymbals mounted on a metal stand, with a pedal-and-spring mechanism designed such that the cymbals can either be brought together by pressing the pedal, or raised to a predetermined (but adjustable before playing) distance by releasing the pedal. The hi-hat can be played by striking it with a drumstick or brush with the cymbals brought together ("closed"), or apart ("open"), or by using the pedal to forcefully bring the cymbal together. When struck closed or played with the pedal, the hi-hat gives a short, muted percussive sound. Adjusting the gap between the cymbals can alter the sound of the open hi-hat from a "shimmering", sustained tone to something similar to a ride cymbal. When struck with a drumstick, the cymbals make either a short, snappy sound or a longer sustaining sandy sound depending on the position of the pedal. It can be also played just by lifting and lowering the foot to clash the cymbals together, a style commonly used to accent beats 2 and 4 in jazz music. In rock music, the hihats are commonly struck every beat or on beats 1 and 3, while the cymbals are held together. The drummer can control the sound by foot pressure. Less pressure allows the cymbals to rub together more freely, giving both greater sustain and greater volume for accent or crescendo. In shuffle time, a rhythm known as "cooking" is often employed. To produce this the cymbals are stuck twice in rapid succession, being held closed on the first stroke and allowed to open just before the second, then allowed to ring before being closed with a "chick" to complete the pattern (the cymbals may or not be struck on the "chick"). A right-handed drummer will normally play the hi-hat pedal with their left foot, and may additionally use either or both drumsticks. The traditional

    Six Thinking Hats


    ''Six Thinking Hats'' is the title and subject of a book by Edward De Bono, published in 1985. In it De Bono describes a process of deliberately adopting a particular approach to a problem as an aid to lateral thinking. Six different approaches are described, and each is symbolised by the act of putting on a coloured hat, either actually or imaginatively. This he suggests can be done either by individuals working alone or in groups. De Bono's six hats are:
  • White hat (Blank sheet): Information & reports (''objective'')
  • Red hat (Fire): Opinion & emotion (''subjective'')
  • Yellow hat (Sun): Praise, positive aspects, (''objective'')
  • Black hat (Judge's robe): Criticism, negative aspects, modus tollens (''objective'')
  • Green hat (Plant): Intuition, new approaches & 'everything goes' (''speculative'')
  • Blue hat (Sky): "Big Picture," "Meta hat," overall process (''overview'') Category:1985 books Category:Books by title Category:Self help books

    Hat


    For the H.A.T. TLAs, see HAT. ---- A hat is an item of clothing which is worn on the head – a kind of headgear. Hats are differentiated from caps by being more elaborate; hats have a high crown, a brim, or both and are larger than caps. A hat may be either placed on the head or, in the case of some women's hats, secured with hat-pins (which are pushed through the hat and the hair). Many hats are intended only for men or for women, while other hats are fashionable on both sexes. Purveyors of men's hats are called hatters and purveyors of ladies' hats are called milliners. While in common usage a hat can refer to nearly anything placed on ones head, this article deals only with headgear with brims or that could not be considered any other form of headgear.

    Physical attributes

    Hats are made from a variety of materials, including wool and fur felt, twill, canvas, leather and straw. Fabric, leather and straw hats are specially constructed to be a certain shape. Most felt, straw, and some fabric hats differ only by cosmetics, determined by how the hat is ''blocked'', or shaped by a mold or by hand. Blocking the hat shapes the crown by applying steam to the material to soften the fabric and, once finished and dried, fix the shape of the hat. If the hat's material is strong enough, it often can be reblocked to another shape. Felt hats also vary by stiffness, depending on how much shellac is applied to the felt. Additionally, many soft wool felt hats are ''crushable'' or ''packable'', meaning that the material can return to and hold its original shape even after being folded and put in a suitcase. Hats that are not explicitly advertized as such should never be folded as they may be permanantly damaged. Some straw hats can also rolled up to fit in a tube. Such a rolling practice was done for unblocked Panama hats, resulting in a distinctive crown with an narrow outward lengthwise crease. Due to the round stiff nature of most hats, special hat

    Hats


    :'': list of hats and headgear'' A hat is an item of clothing which is worn on the head – a kind of headgear. Hats often have a brim, and may be either placed on the head, or in the case of some women's hats, secured with hat-pins (which are pushed through the hat and the hair). Category:Headgear


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