Image Pythagoreancomma difference A1 m2 .PNG thumb right 400px Pythagoreancomma PC defined in Pythagorean ... direction from to C Music to D Music b . Image Pythagoreancomma on C.png thumb right Pythagoreancomma on C. audio Pythagoreancomma on C.mid Play . The note depicted as lower on the staff B ... tuning , the Pythagoreancomma or ditonic comma ref not to be confused with the syntonic comma ... audio Pythagoreancomma on C.mid Play , or D Music b and C Music . ref Apel, Willi 1969 . Harvard Dictionary ... temperament s often refer to tempering is the Pythagoreancomma. ref Coyne, Richard 2010 . The Tuning ... comma can be also defined as the difference between a Pythagorean apotome and a Pythagorean ... between three Pythagorean ditone s and one octave this is the reason why the Pythagoreancomma is also called ditonic comma . The diminished second , in Pythagorean tuning, is defined as the difference between limma and apotome. It coincides therefore with the opposite of a Pythagoreancomma, and can be viewed as a descending Pythagoreancomma e.g. from C Music to D Music b , equal to about &minus 23.46 cents. Derivation As described in the introduction, the Pythagoreancomma may be derived in multiple ..., such as C and B Music audio Pythagoreancomma on C.mid Play , or D Music b and C Music see Pythagoreancomma Circle of fifths and enharmonic change below . Difference between Pythagorean apotome ... is about 407.8 cents. Size The size of a Pythagoreancomma, measured in Cent music cents , is math hbox ... comma.png thumb right Pythagoreancomma as twelve justly tuned perfect fifths. The Pythagorean ... of fifths , the Pythagoreancomma is visible as the small interval between e.g. F music sharp ... keyboard but the music flat scales are one Pythagoreancomma lower. Disregarding ... by one Pythagoreancomma. Scales with http www.cisdur.de e index.html seven accidentals are seldom used ... each fifth by a twelfth of a Pythagoreancomma approximately 2 cents , thus producing ... more details
File Pythagore chartres.jpg thumb Sculpture of Pythagoras at Chartres , France Pythagorean means of or pertaining to the ancient Ionia n mathematician, philosopher, and music theorist Pythagoras . See Philosophy Pythagoreanism is a term used for the esoteric and metaphysical beliefs purported to have been held by Pythagoras. Neo Pythagoreanism was a school of philosophy reviving Pythagorean doctrines that became prominent in the 1st and 2nd centuries AD. Pythagoreanism Vegetarianism Pythagorean diet was the name for vegetarianism prior to the nineteenth century Mathematics Pythagorean theorem Pythagorean triple Pythagorean prime Pythagorean trigonometric identity Table of Pythagoras, another name for the Multiplication table Music PythagoreancommaPythagorean hammers Pythagorean tuning Drinkware Pythagorean cup Graphics Upsilon Symbolism Pythagorean letter Sports statistics Pythagorean expectation disambig ... more details
Image Virguli a i sedila.svg thumb 180px Appearance of comma upper row and cedilla lower row in the Times New Roman font. Diacritical marks nowrap & x021A & x021B T comma lang ro majuscule , minuscule is a letter which is part of the Romanian alphabet , used to represent the Romanian language sound IPA t s , the voiceless alveolar affricate like ts in bolts . It is written as the letter T with a small Comma punctuation comma below and it has both the lower case U 021B and the upper case variants U 021A . It is also a part of the Gagauz language Latin alphabet Gagauz alphabet and the Livonian language Alphabet Livonian alphabet . The letter was proposed in the Buda Lexicon , a book published in 1825, which included two texts by Petru Maior , Orthographia romana sive Latino valachica ... , available from version 1.1.0, June 1993 is often used in digital texts in Romanian. T Comma punctuation comma was introduced only in Unicode 3.0.0 September 1999 at the request of the Romanian ... the recommendation to migrate from cedilla to comma. Full support of this letter has been available ... of the fonts including the Arial Unicode MS render T cedilla as T comma because T cedilla is not used ... been written using S cedilla and T comma. However, in order to correctly encode and render both S comma and T comma, one has to install the European Union Expansion Font Update. Unfortunately, there is no official ... web browser is able to generate S comma and T comma, even if the characters are missing from the system ... render S comma and T comma, since at least 2005. If these characters are missing from a certain ... the correct keyboard ro comma since at least 2005, selecting this keyboard from the user interface e.g. GNOME Keyboard Properties has only recently been made possible. See also D comma S comma Cedilla ... T with comma below http www.fileformat.info info unicode char 0162 index.htm Latin capital letter ... Keyboard driver for Windows XP with S comma and T comma Latin alphabet T comma Category Specific letter ... more details
Image Virguli a i sedila.svg thumb 180px Appearance of Comma punctuation comma upper row and cedilla lower row in the Times New Roman font. S comma lang ro majuscule , minuscule is a letter which is part of the Romanian alphabet , used to represent the Romanian language sound IPA , the voiceless postalveolar fricative like sh in shoe . This letter however was not part of the early Unicode versions, and not in the predecessors like ISO IEC 8859 2 and Windows 1250 , which is why S cedilla is often used in digital texts in Romanian. S cedilla was introduced for computers for the sake of the Turkish language , and later it was used unchanged also for the Romanian language. It was less of a problem then, since the screens and printouts had less resolution and newspapers and books would use a suitable font anyway. S Comma punctuation comma was introduced only in Unicode 3.0 at the request of the Romanian national standardization body, but most computers today still do not have font s compatible with it computers with Microsoft operating system s older than Windows XP do not have compatible fonts. Windows XP does not support this letter out of the box, but it is possible to install http www.microsoft.com downloads details.aspx?FamilyID 0ec6f335 c3de 44c5 a13d a1e7cea5ddea&DisplayLang ... to comma. The letter is placed in Unicode in the Latin Extended B range, under Additions for Romanian , as the capital letter S with comma U 0218 and small letter s with comma U 0219 . ref Unicode ... Folklorica , No. 5, La scrittura funzioni e ideologie. Apr., 1982 , pp. 75 85. ref Use of the comma with the letter S Diacritical marks nowrap unicode & x0218 &thinsp & x0219 caption S comma Romanian language Romanian The Romanian language Romanian letter lang ro S with comma represents the voiceless ... T comma D comma References reflist Latin alphabet S comma Category Specific letter diacritic combinations S comma Category Romanian language S comma br lizherenn de es fr it nl no pl ... more details
other uses Comma disambiguation Punctuation marks , The comma , is a punctuation mark. It has ... of three or more things. The comma is used in many contexts and languages, principally for separating things. According to the Oxford English Dictionary , the word comma comes directly from the Greek ... . This is the origin of the concept of a comma, although the name came to be used for the mark ..., the comma is used where ambiguity might otherwise arise, to indicate an interpretation of the text such that the words immediately before and after the comma are less closely or exclusively linked in the associated grammar grammatical structure than they might be otherwise. The comma may be used ... similar ways in other languages, particularly European ones, although the rules on comma usage and their rigidity ... a cat, a dog, two rabbits, and six mice. In English, a comma may or may not be used before .... A comma used in such a position is called a serial comma or an Oxford or Harvard comma after the Oxford ... cases, use or omission of such a comma may serve to avoid ambiguity Use of serial comma disambiguating .... must be the boys and Sam and Tom I spoke to more than three people Omission of serial comma disambiguating ..., eggs and chips do not need a comma before the final and , but sometimes it can help the reader he ... academic writing guides, require the serial comma all lists must have a comma before the and prefacing ... to separate clause s. In English, a comma is generally used to separate a dependent clause from ... the comma, this would mean that only those trees over six feet tall were cut down. Some style ... for , and , nor , but , or , yet , so must be separated by a comma placed before the conjunction ... Nancy Tuten url http www.getitwriteonline.com archive 020204WhenCommaBfAnd.htm title When to Use a Comma ..., where the second clause is independent because it can stand alone as a sentence , the comma is considered ... is dependent because it cannot stand alone as a sentence , those guides prescribe that the comma ... more details
center 23.460 align center 0 Audio Pythagoreancomma on C.mid play 12 perfect unison P1 align center 1 1 align center align center 1 1 align center 0.000 align center 0 Audio Unison on C.mid play 0 Pythagoreancomma align center 531441 524288 align center align center align center 23.460 align center 0 Audio Pythagoreancomma on C.mid play 12 minor second m2 Pythagorean limma limma , br diatonic semitone ... comma on C.mid play 12 Notice that the terms ditone and semiditone are specific for Pythagorean ... tuning, and their difference, 531441 524288, is known as the Pythagoreancomma . Contrast ...Lead rewrite date November 2010 Image Perfect fifth on C.png thumb right Pythagorean perfect fifth on C audio Just perfect fifth on C.mid Play C G 3 2 1 1 3 2 . In musical tuning theory, a Pythagorean ... Explorations , p.56. ISBN 9780195144369. The frequency ratio of every Pythagorean interval is a ratio between a power of two and a power of three...confirming the Pythagorean requirements that all ... to 2 sup 2 sup 3 sup 1 sup are Pythagorean intervals. All the intervals between the notes of a scale are Pythagorean if they are tuned using the Pythagorean tuning system. However, some Pythagorean intervals are also used in other tuning systems. For instance, the above mentioned Pythagorean perfect ... center 90.225 align center 100 Audio Pythagorean minor semitone on C.mid play 5 augmented unison A1 Pythagorean apotome apotome , br chromatic semitone, br major semitone align center 2187 2048 align center 3 sup 7 sup 2 sup 11 sup align center align center 113.685 align center 100 Audio Pythagorean ... 2 semiditone m3 Pythagorean minor third align center 32 27 align center 2 sup 5 sup 3 sup 3 sup align center align center 294.135 align center 300 Audio Pythagorean minor third on C.mid play 3 augmented ... 317.595 align center 300 Audio Pythagorean augmented second on C.mid play 9 diminished fourth d4 ... center 400 Audio Pythagorean diminished fourth on C.mid play 8 ditone M3 Pythagorean major third ... more details
and chromatic , and hence by a comma of unique size. The same is true for Pythagorean tuning. align ... C to D is narrower than in Pythagorean tuning see below . audio Enharmonic scale segment on C.mid Play Image Pythagoreancomma difference A1 m2 .PNG thumb center 492 px Pythagoreancomma PC defined in Pythagorean ... to be tuned in just intonation . Notice that the Pythagoreancomma PC and the syntonic comma ... align right 21.51 rowspan 2 align center 81 80 Major Major second tone Minor tone Pythagoreancomma PC Ditonic comma align center Pythagorean apotome A1 Pythagorean limma m2 br in Pythagorean tuning ... the opposite of the above mentioned differences. For instance, the Pythagoreancomma can be computed ... equal to the opposite of a Pythagoreancomma , and in Quarter comma meantone Size of intervals quarter ...Image Syntonic comma on C.png thumb right Syntonic comma on C audio Syntonic comma on C.mid Play . Image Pythagoreancomma on C.png thumb right Pythagoreancomma on C audio Pythagoreancomma on C.mid Play . In music theory , a comma is a minute interval music interval , the difference resulting from ..., eds. Macmillan. ref The word comma used without qualification refers to the syntonic comma , ref ..., for instance, as the difference between an F Music tuned using the D based Pythagorean tuning system, and another F Music tuned using the D based quarter comma meantone system. Even within the same ... comma meantone as difference between semitones br m2 A1 117.1 76.0 41.1 cents , or interval ... than in quarter comma meantone see above . In just intonation , more than two kinds of semitones may ..., the difference between them is a small comma called schisma . A schisma is not audible in many ... between tones which is around six cents . class wikitable rowspan 3 Name of comma rowspan 3 Alternative ... comma meantone temperament meantone align center 1 PC 1 SC 8 perfect fifths br 1 major third 5 octaves ... right 8.11 align center 15625 15552 Small undecimal comma ref Halu ka, J n 2003 . The Mathematical ... more details
7. ref Relationships The syntonic comma is the interval between a just major third 5 4 and a Pythagorean ditone 81 64 . Another way of describing the syntonic comma, as a combination of more commonly ... encountered comma is the Pythagoreancomma . Syntonic comma in the history of music The syntonic comma ...Image Syntonic comma on C.png thumb right Syntonic comma on C audio Syntonic comma on C.mid Play . Image ... Play . The perfect fifth above D A is a syntonic comma higher than the just major sixth A music natural ... tone audio Minor tone on C.mid Play . In music theory , the syntonic comma , also known as the chromatic diesis , the comma of Didymus the Musician Didymus , the Ptolemy Ptolemaic comma , or the diatonic comma ref Johnston B. 2006 . Maximum Clarity and Other Writings on Music, edited by Bob Gilmore. Urbana University of Illinois Press. ISBN 0 252 03098 2. ref is a small Comma music comma type ... of the same note than as different notes. The comma is referred to as a comma of Didymus because it is the amount by which Didymus corrected the Pythagorean interval Pythagorean major third ref ... between these is 21.51 cents 81 80 , a syntonic comma. Equally, it can be described ... when deciding which system of musical tuning to use for an instrument. Pythagorean tuning tunes ... comma meantone , on the other hand, uses exact 5 4s for major thirds, but flattens each of the fifths by a quarter of a syntonic comma. Other systems use different compromises. In just intonation , there are two ..., they have a ratio of 9 8 and 10 9, and the ratio between them is the syntonic comma 81 80 . Also ... in Pythagorean tuning were flattened or sharpened to produce just minor and major thirds. In Pythagorean ... fourth . The Pythagorean major third 81 64 and minor third 32 27 were Consonance and dissonance ... Ages , musicians realized that by slightly tempering the pitch of some notes, the Pythagorean thirds could be made Consonance and dissonance consonant . For instance, if you decrease by a syntonic comma ... more details
Image Septimal comma on C.png thumb Septimal comma on C audio Septimal comma on C.mid Play . Image Major second on C.svg thumb right 3 limit 9 8 major second major tone audio Major tone on C.mid Play . Image Septimal major second on C.png thumb right 7 limit 8 7 septimal whole tone audio Septimal major second on C.mid Play . A septimal comma is a small interval music musical interval in just intonation that contains the number 7 number seven in its prime factorization . There is more than one such interval, so the term septimal comma is ambiguous, but it most commonly refers to the interval 64 63. ref name H F cite web url http www.xs4all.nl huygensf doc intervals.html title List of intervals accessdate 2006 07 29 author Manuel Op de Coul work Stichting Huygens Fokker archiveurl http web.archive.org web 20060704064519 http www.xs4all.nl huygensf doc intervals.html Bot retrieved archive archivedate 2006 07 04 ref ref cite journal last Perrett first Wilfrid year 1932 month April title The Heritage of Greece in Music journal Proceedings of the Musical Association volume 58 pages 85 103 format GIF doi 10.1093 jrma 58.1.85 jstor 09588442 ref Use of septimal commas introduces new intervals .... 106 137. ref Specific commas The 64 63 septimal comma Audio Septimal comma on C.mid play , also known as Archytas Comma , ref name H F is the interval equal to the difference between a major and septimal ... between the 16 9 Pythagorean tuning Pythagorean minor seventh the composition of two 4 3 perfect .... ISBN 0521853877. ref . Its size is 27.264 cent music cents , slightly larger than the Pythagoreancomma . The composition of the septimal comma and the syntonic comma is 36 35, known as the septimal ... between the two septimal tritone s, 7 5 and 10 7, or Erlich s decatonic comma , because it plays ... class wikitable Ratio Size in cents Names 64 63 27.3 Septimal comma, Archytas comma 50 49 35.0 Septimal sixth tone , tritonic diesis, Erlich s decatonic comma 49 48 35.7 Septimal diesis Slendro diesis ... more details
see Pythagoreancomma . Thus, A music b and G music , when brought into the basic octave, will not coincide ... one quarter of a semitone, is known as a Pythagoreancomma . To get around this problem, Pythagorean ... can be also defined as one twelfth of a Pythagoreancomma. Pythagorean intervals Main Pythagorean ... used generically for some other intervals. Notice that the Pythagoreancomma does not coincide with the diminished ... comma meantone 1 4 comma br meantone Full Short 0 colspan 2 commaPythagoreancomma br 524288 ...Image Pythagorean diatonic scale on C.png thumb 330px Pythagorean diatonic scale on C audio Pythagorean ... intonation. Image Pythagorean major chord on C.png thumb Pythagorean tonic major chord on C audio Pythagorean major chord on C.mid Play compare audio C major triad.mid Play equal tempered and audio Just major triad on C.mid Play just . Pythagorean tuning lang el is a system of musical ... consonant . Attributed to Pythagoras sixth century BC , the Pythagorean system would appear to be ideal ... 2011 . The Physics of Music and Color , p.362. ISBN 978 1 4614 0556 6. ref The Pythagorean scale ... of fifths generated above gives seven notes, a diatonic major scale on C in Pythagorean tuning, shown in notation on the top right. Method Pythagorean tuning is based on a stack of intervals called perfect ...&pg PA82&dq pythagorean interval&hl en&ei aNrlTpK7BorWiALk1eyZBg&sa X&oi book result&ct result&resnum 10&ved 0CF0Q6AEwCQ v onepage&q pythagorean 20interval&f false Transactions of the Asiatic ..., as the above table indicates, in Pythagorean tuning they have different ratios with respect to D ... as a wolf interval . In the case of Pythagorean tuning, all the fifths are 701.96 cents wide, in the exact ..., the position of the wolf fifth can be changed. For example, a C based Pythagorean tuning would ... flat the wolf interval. However, there will always be one wolf fifth in Pythagorean tuning, making it impossible ... ratios in D based symmetric Pythagorean tuning powers for large numbers .PNG frame right Frequency ... more details
Wiktionary comma A comma is a type of punctuation mark , . The word comes from the Greek komma , which means something cut off or a short clause . Comma may also refer to Comma music , a type of interval in music theory Comma butterfly, the brush footed butterfly Polygonia c album and related species comma butterflies the genus Polygonia in general Comma journal , the journal of the International Council on Archives Comma rhetoric , a short clause in Ancient Greek rhetoric Comma operator , an operator in C and other related programming languages See also Coma disambiguation Commer commercial vehicle manufacturer Kama Disambig fr Comma id Koma it Comma sv Komma ... more details
Pythagorean tree may refer to Tree of primitive Pythagorean triples Pythagoras tree fractal disambig Short pages monitor This long comment was added to the page to prevent it from being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Long comment. Please do not remove the monitor template without removing the comment as well. ... more details
In algebra, a Pythagorean field is a field mathematics field in which every sum of two squares is a square. A Pythagorean extension of a field F is an extension obtained by adjoining an element mrad 1 &lambda sup 2 sup for some in F . So a Pythagorean field is one closure mathematics closed under taking Pythagorean extensions. For any field there is a minimal Pythagorean field containing it, unique up to isomorphism , called its Pythagorean closure . Pythagorean fields can be used to construct models for some of Hilbert s axioms for geometry harv Ito 1980 loc 163 C . The analytic geometry given by F sup n sup for F a Pythagorean field satisfies many of Hilbert s axioms, such as the incidence axioms, the congruence axioms and the axioms of parallels. However, in general this geometry need not satisfy all Hilbert s axioms unless the field F has extra properties for example, if the field is also ordered then the geometry will satisfy Hilbert s ordering axioms, and if the field is also complete the geometry will satisfy Hilbert s completeness axiom. The Pythagorean closure of a non archimedean ordered field , such as the Pythagorean closure of the field of rational function s Q t in one variable over the rational numbers Q , can be used to construct non archimedean geometries that satisfy many of Hilbert s axioms but not his axiom of completeness harv Ito 1980 loc 163 D . Dehn used such a field to construct a non Legendrian geometry and a semi Euclidean geometry in which there are many lines though a point not intersecting a given line. The Witt group Witt ring of a Pythagorean field is of order 2 if the field is not Formally real field formally real , and torsion free otherwise. See also Euclidean field References Citation last1 Elman first1 Richard last2 Lam first2 T. Y. title Quadratic forms over formally real fields and pythagorean fields jstor 2373568 mr ... year 2005 volume 67 chapter Chapter VIII section 4 Pythagorean fields pages 255 264 citation first1 ... more details
In music theory and musical tuning the Holdrian comma , also called Holder s comma , and sometimes the Arabian comma , ref name Touma Habib Hassan Touma 1996 . The Music of the Arabs , p.23. trans. Laurie Schwartz. Portland, Oregon Amadeus Press. ISBN 0 931340 88 8. ref is a small musical interval of approximately 22.6415 cent music cents , ref name Touma equal to one step of 53 equal temperament , or math sqrt 53 2 math Audio Holdrian comma on C.mid play . The name comma music comma is misleading, since this interval is an irrational number and does not describe the compromise between intervals of any tuning system it assumes this name because it is an approximation of the syntonic comma Audio Syntonic comma on C.mid play , which was widely used as a measurement of tuning in William Holder s time. Mercator s comma is a name often used for a closely related interval because of its association with Nicholas Mercator . One of these intervals was first described by Ching Fang in 45 BCE. ref name Touma Mercator s comma and the Holdrian comma Mercator s comma redirects here Mercator applied logarithms to determine that math sqrt 55 2 math 21.8182 cents was nearly equivalent to a syntonic comma of 21.5063 cents a feature of the prevalent sixth comma meantone temperament tuning system of the time . He also considered that an artificial comma of math sqrt 53 2 math might be useful, because ... the Holdrian comma is named, favored this latter unit because the intervals of 53 equal temperament are closer to just intonation than that of 55. Thus Mercator s comma and the Holdrian comma are two distinct but related intervals. Arabian comma The name Arabian comma may be inaccurate the comma ... Sayan . The name of this comma is Holder komas in Turkish. For instance, the makam rast similar ..., Joe 2005 . http www.tonalsoft.com enc m mercator comma.aspx Mercator s Comma , Tonalsoft . Intervals state expanded DEFAULTSORT Holdrian Comma Category Commas ca Coma de Holder es Coma de Holder ... more details
Refimprove date November 2007 A Pythagorean prime is prime number of the form 4 n 1. These are exactly the primes that can be the hypotenuse of a Pythagorean triangle . The first few Pythagorean primes are 5 number 5 , 13 number 13 , 17 number 17 , 29 number 29 , 37 number 37 , 41 number 41 , 53 number 53 , 61 number 61 , 73 number 73 , 89 number 89 , 97 number 97 , 101 number 101 , 109 number 109 , 113 number 113 , OEIS id A002144 . Fermat s theorem on sums of two squares states that these primes can be represented as sums of two squares uniquely up to order , and that no other primes can be represented this way, aside from 2 1 sup 2 sup 1 sup 2 sup . Thus these primes and 2 occur as norms of Gaussian integers , while other primes do not. The law of quadratic reciprocity says that if p and q are distinct odd primes, at least one of which is Pythagorean, then p is a quadratic residue mod q if and only if q is a quadratic residue mod p by contrast, if neither p nor q is Pythagorean, then p is a quadratic residue mod q if and only if q is not a quadratic residue mod p . &minus 1 is a quadratic residue mod p if and only if p is a Pythagorean prime or 2 . In the field Z p with p a Pythagorean prime, the polynomial x 2 1 has two solutions. Category Classes of prime numbers Prime number classes state collapsed numtheory stub da Pythagor iske primtal es N mero primo pitag rico sl Pitagorejsko pra tevilo zh ... more details
italictitle Taxobox name Eastern Comma image Polygonia comma Kaldari 01.jpg status regnum Animal ia phylum Arthropod a classis Insect a ordo Lepidoptera familia Brush footed Butterflies Nymphalidae tribus Nymphalini genus Polygonia species P. comma binomial Polygonia comma binomial authority Thaddeus William Harris Harris , 1842 range map Polygonia comma range map.JPG Range map showing distribution of the Eastern Comma. synonyms Nymphalis comma The Eastern Comma Polygonia comma is a North American butterfly in the family Nymphalidae , subfamily Nymphalinae . Description Image Eastern comma.jpg thumb left Showing upperside of wings This butterfly is seasonally variable. The upper side of the summer ... of both forms is striped with dark and light brown. There is a silvery comma mark in the middle ... Comma may be spotted in woods near rivers, ponds, marshes, swamps, and other water sources. Nectar Plants ... adults overwinter, some will also migrate south for the winter. Similar Species The dark form of comma ... , but the two can readily be distinguished by the shape of the comma mark on the underside. The pale form is easily confused with the Polygonia satyrus Satyr Comma N. satyrus , which usually occurs north and west of the Eastern Comma s range. They can be distinguished by the upperside colour, which is orange brown in comma and tawny yellowish brown in satyrus by the underside pattern, which tends to be mottled in comma but appears to be more longitudinally streaked in satyrus and by the row ... by dark shading in comma, but are larger and tend to run together into a pale band in satyrus. References http www.cbif.gc.ca spp pages butterflies species EasternComma e.php Eastern Comma , Butterflies ... comma.htm Eastern Comma on the University of Florida UF Institute of Food and Agricultural Sciences IFAS Featured Creatures Web site DEFAULTSORT Polygonia Comma Category Butterflies and moths of North America Category Butterflies of Canada fr Polygone virgule nl Polygonia comma ... more details
In Ancient Greek rhetoric a comma is a short clause , something less than a colon rhetoric colon , originally denoted by Comma punctuation comma marks . It is shaped as a small swipe at the bottom of the line. In antiquity comma was defined as a combination of words that has no more than eight syllables. See also Comma Johanneum disputed text in 1 John 5 7 8 References http humanities.byu.edu rhetoric Figures C comma.htm Part of a http humanities.byu.edu rhetoric glossary of classical rhetorical terms . Bibliography Bruce M. Metzger, Bart D. Ehrman, The Text of the New Testament. Its Transmission, Corruption, and Restoration, New York, Oxford Oxford University Press, 2005, pp. 45 46. Category Rhetoric ling stub ... more details
Taxobox image image caption regnum Animal ia phylum Arthropod a classis Insect a ordo Fly Diptera zoosectio Schizophora zoosubsectio Acalyptratae superfamilia Tephritoidea familia Tephritidae genus Trypeta species T. comma binomial Trypeta comma subdivision ranks Subspecies subdivision Trypeta comma is a species of tephritid or fruit flies in the genus Trypeta of the family Tephritidae . ref http www.itis.gov servlet SingleRpt SingleRpt ref ref http nomen.at Trypeta comma ref ref http data.gbif.org species browse taxon 13143053 ref References Reflist Category Trypeta Trypeta stub ... more details
A Pythagoras Pythagorean quadruple is a tuple of integer s a , b , c and d , such that d 0 and math a 2 b 2 c 2 d 2 math , and is often denoted math a,b,c,d math . Geometrically, a Pythagorean quadruple math a,b,c,d math defines a cuboid with side Norm mathematics Euclidean norm lengths a , b , and c , whose space diagonal has integer length d . Pythagorean quadruples are thus also called Pythagorean Boxes . ref R.A. Beauregard and E. R. Suryanarayan, Pythagorean boxes , Math. Magazine 74 2001 , 222 227. ref Parametrization of primitive quadruples The Set mathematics set of all primitive Pythagorean quadruples, i.e., those for which gcd a , b , c 1, where gcd denotes the greatest common divisor of a , b , and c , is parametrized by, ref R.D. Carmichael, Diophantine Analysis , New York John Wiley & Sons, 1915. ref ref L.E. Dickson, Some relations between the theory of numbers and other branches of mathematics , in Villat Henri , ed., Conf rence g n rale, Comptes rendus du Congr s international des math maticiens, Strasbourg, Toulouse, 1921, pp. 41 56 reprint Nendeln Liechtenstein Kraus Reprint Limited, 1967 Collected Works 2, pp. 579 594. ref ref R. Spira, The diophantine equation math x 2 y 2 z 2 m 2 math , Amer. Math. Monthly 69 1962 , 360 365. ref math a m 2 n 2 p 2 q 2, , math ... negative integer s and gcd m , n , p , q 1 and m n p q 1 mod 2 . Thus, all primitive Pythagorean ... Pythagorean quadruple math a,b,c,d math Parametrization parametrized by math m,n,p,q math corresponds ..., Letter to the Editor , Amer. Math. Monthly 94 1987 , 757 758. ref Pythagorean quadruples with small ... Alternate parametrization All Pythagorean quadruples including non primitives, and with repetition ... a and b as follows ref Wac aw Sierpi ski Sierpi ski, Wac aw , Pythagorean Triangles , Dover, 2003 ... be an even factor of math a 2 b 2 math . No such method exists if both a and b are odd. See also Pythagorean ... title Pythagorean Quadruple MathWorld urlname LebesgueIdentity title Lebesgue s Identity ... more details
original research date January 2009 Image Pythagorean.svg thumb The Pythagorean theorem nowrap a sup 2 sup b sup 2 sup c sup 2 sup File Theorem.gif thumb Animation demonstrating the simplest case of the Pythagorean Triple 3 sup 2 sup 4 sup 2 sup 5 sup 2 sup . A Pythagorean triple ... 3, 4, 5 . If nowrap a , b , c is a Pythagorean triple, then so is ka , kb , kc for any positive integer k . A primitive Pythagorean triple PPT is one in which a , b and c are pairwise coprime . A right triangle whose sides form a Pythagorean triple is called a Pythagorean triangle . The name is derived from the Pythagorean theorem , stating that every right triangle has side lengths satisfying the formula nowrap a sup 2 sup b sup 2 sup c sup 2 sup thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non integer sides do not form Pythagorean ..., but 1, 1, 2 is not a Pythagorean triple because 2 is not an integer. Moreover, 1 and 2 do not have ... of a primitive Pythagorean triple, one in which the terms are relatively prime. Image Pythagorean triple scatterplot2.png thumb A scatter plot of the legs a , b of the Pythagorean triples with c ... clearly. There are 16 primitive Pythagorean triples with nowrap c 100 style margin auto cellspacing ... plot. Additionally these are all the primitive Pythagorean triples with nowrap 100 c 300 style ... Pythagorean triples Image PrimitivePythagoreanTriplesRev08.svg thumb 300px alt Primitive Pythagorean triples shown as triangles on a graph The primitive Pythagorean triples. The odd leg a is plotted ... of constant m n and of constant m n in Euclid s formula. Image Pythagorean Triples from Grapher.png ... Pythagorean triples given an arbitrary pair of positive integers m and n with nowrap m n . The formula states that the integers math a m 2 n 2 , , b 2mn , , c m 2 n 2 math form a Pythagorean ... and n are coprime. ref Mitchell, Douglas W., An alternative characterisation of all primitive Pythagorean ... more details
Pythagorean expectation is a formula invented by Bill James to estimate how many games a baseball team ... s actual and Pythagorean winning percentage can be used to evaluate how lucky that team was by examining ... to the Pythagorean theorem . The basic formula is math mathrm Win frac text runs scored 2 text ... pyth Baseball reference.com What is pythagorean winning percentage? Bot generated title ref The updated ... Prospectus Articles Revisiting the Pythagorean Theorem Bot generated title ref developed by Clay ... Prospectus Articles Revisiting the Pythagorean Theorem Bot generated title ref Less well known but equally ... scored and allowed into the pythagorean formula, one can generate second order wins, the number of wins .... In 2003, Hein Hundal provided an inexact derivation of the formula and showed that the Pythagorean ... of James Pythagorean Formula Long url http groups.google.com group rec.puzzles browse thread thread ... Magazine 20 2007 , no. 1, 40 48 pages 9698 title A Derivation of the Pythagorean Won Loss Formula ... journal first Steven J last Miller title A Derivation of the Pythagorean Won Loss Formula in Baseball .... By comparing the Giants expected wins as calculated by the Pythagorean theory with an exponent of 1.83 ... to adapt James Pythagorean expectation to professional basketball while a researcher at STATS, Inc ... . math Daryl s Modified Pythagorean Theorem was first published in http morey.org pythbook.gif STATS ... James Pythagorean theory to professional basketball. The result was similar. Another noted basketball statistician, John Hollinger , uses a similar Pythagorean formula except with 16.5 as the exponent ... stat website and publisher Football Outsiders , where it is known as Pythagorean projection . The 2011 ... Football League NFL in Pythagorean wins, while only seven were one by the team with the most actual victories. Super Bowl champions that led the league in Pythagorean wins but not actual wins ... participants from 2005 2008, it reasserted itself in 2009 and 2010. Furthermore, t he Pythagorean projection ... more details
Ecphantus or Ecphantos lang grc is a shadowy Greek pre Socratic philosopher. He may not have actually existed. ref Some scholars have argued that Hicetas and Ecphantus, both of Syracuse, were not historical figures at all but rather characters in dialogues written by Heraclides of Pontus . From the Stanford Encyclopedia of Philosophy , article http plato.stanford.edu entries pythagoreanism Pythagoreanism . ref He is identified as a Pythagoreanism Pythagorean of the 4th century BCE, and as a supporter of the heliocentric theory . Described as from Syracuse, Sicily Syracuse , this may or may not be the same figure as the attested Ecphantus of Croton . Notes references External links fr icon http www.cosmovisions.com Ecphante.htm DEFAULTSORT Ecphantus The Pythagorean Category 4th century BC Greek people Category 4th century BC philosophers Category Ancient Syracusians Category Ancient Greek philosophers Category Pythagoreans of Magna Graecia Category Ancient Greek astronomers Philosopher stub de Ekphantos el it Ecfanto di Siracusa pt Ecfanto, o Pitag rico ru sk Ekfantos zo Syrak z sl Ekfant ... more details
File Distorted truncated square tiling.png thumb A Pythagorean tiling File Jacob Ochtervelt Street Musicians ... Ochtervelt , 1665. As observed by Nelsen ref name rbn the floor tiles in this painting are set in the Pythagorean tiling In geometry , the Pythagorean tiling or two squares tessellation is a tessellation ... Tile Inc. date August 2008 . ref Topology and symmetry The Pythagorean tiling is the unique tiling ... b39h2mar.ps.gz volume 39 year 1998 . ref Topologically, the Pythagorean tiling has the same structure ... page 171 publisher W. H. Freeman title Tilings and Patterns year 1987 . ref The smaller squares in the Pythagorean ... tiling, while the larger squares in the Pythagorean tiling are adjacent to eight neighbors that alternate ... symmetry around the center of each tile, while the Pythagorean tiling has a smaller cyclic group cyclic ... triangles and regular hexagons, and one more, the Pythagorean tiling. ref harvtxt Gr nbaum Shephard 1987 , pp. 73 74. ref Pythagorean theorem and dissections File Pythagorean dissections.svg ... and by Henry Perigal right This tiling is called the Pythagorean tiling because it has been used as the basis of proofs of the Pythagorean theorem by the ninth century Arabic mathematicians Al Nayrizi ..., the two squares in the Pythagorean tiling have side lengths 5 and 12 units long, and the side length of the tiles in the overlaying square tiling is 13, based on the Pythagorean triple 5,12,13 . By overlaying a square grid of side length c onto the Pythagorean tiling, it may be used to generate ..., overlaying two Pythagorean tilings may be used to generate a six piece dissection of two unequal ... Aperiodic tilings File Pythagorean tiling section.svg thumb 240px An aperiodic sequence generated from tilings by two squares whose side lengths form the golden ratio Although the Pythagorean tiling ... forms a Pythagorean tiling with two squares for which the ratio between the two side lengths is an irrational ... in the Pythagorean tiling meet edge to edge, ref name mms but this fact does not violate Keller s conjecture ... more details
In musical tuning , the Orwell comma audio Orwell comma on C.mid Play is a very small musical interval of 13.07 cents music cents and frequency ratio of 1728 1715 or 2 sup 6 sup 3 sup 3 sup 5 7 sup 3 sup . ref http www.huygens fokker.org docs intervals.html List of intervals , Huygens Fokker Foundation . ref It is so named because the musical temperament temperament eliminating this comma, Orwell temperament , has an optimal generator very close to 19 steps out of 84 equal temperament this pattern of 19 84 steps is similar to the title of George Orwell Orwell s novel Nineteen Eighty Four 1984 . Citation needed date May 2011 Sources reflist Intervals state expanded Category Commas music stub ... more details
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