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{{Redirect|Δ|the British indie rock quartet|Alt-J|use in mathematics|Delta (disambiguation)#Mathematics{{!}}Delta (disambiguation)}}
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{{refimprove|date=February 2013}}
{{Wiktionary|Δ|δ}}
{{Greek Alphabet|letter=delta}}
'''Delta''' (uppercase Δ, lowercase δ or 𝛿; {{lang|el|Δέλτα}} ''Délta''; Modern Greek {{IPA-el|ˈðelta|}}) is the fourth letter of the [[Greek alphabet]]. In the system of [[Greek numerals]] it has a value of 4. It was derived from the [[Phoenician alphabet|Phoenician letter]] [[Dalet (letter)|dalet]] [[Image:phoenician daleth.png|20px]]. Letters that come from delta include [[Latin alphabet|Latin]] [[D]] and [[Cyrillic script|Cyrillic]] [[De (Cyrillic)|Д]].
 
A [[river delta]] (originally, the [[Nile River]] delta) is so named because its shape approximates the upper-case letter delta (the shape is a triangle). {{cn|date=October 2013}}
 
==Pronunciation and origin==
In [[Ancient Greek]], it represented a [[voiced dental plosive]] {{IPA|/d/}}. In [[Modern Greek]], it represents a [[voiced dental fricative]] {{IPA|/ð/}}, like the "th" in "that" or "this". It is [[romanization of Greek|romanized]] as ''d'' or ''dh''.<br>
The capital letter delta ('''Δ''', which has the convenient form of an [[isosceles triangle]]) is commonly used in subjects of science and mathematics, often to describe change, because delta is the initial letter of the Greek word διαφορά, ''diaphorá'', "difference" (the small [[Latin]] letter '''d''' is used in much the same way for the notation of [[derivative]]s and [[differential (mathematics)|differential]]s{{disambiguation needed|date=September 2013}}, which also describe change).
 
==Upper case==
The upper-case letter Δ can be used to denote
*[[Change (mathematics)|Change]] of any changeable quantity, in mathematics and the sciences (More specifically, the [[difference operator]]{{citation needed|date=November 2012}}); for example, in
::<math>{y_2-y_1\over x_2-x_1} = {\Delta y \over \Delta x}</math>, the average change of y per unit x, i.e. the change of y over the change of x
*The [[Laplace operator]]:
:<math>\Delta f = \sum_{i=1}^n {\frac{\partial^2 f}{\partial x_i^2}}</math>
*The [[discriminant]] of a [[polynomial]] equation, especially the [[quadratic equation]]:
:<math>\Delta = b^2 - 4ac\,\!</math>
*The [[symmetric difference]] of two sets
*A [[derivative|macroscopic change]] in the value of a variable in mathematics or science
*[[Uncertainty]] in a physical variable as seen in for instance the [[uncertainty principle]]
*An interval of possible values for a given quantity for instance across a sample{{Citation needed|date=August 2008}}
*Any of the [[Delta baryon|delta particles]] in particle physics
*The determinant of the matrix of coefficients of a set of linear equations (see [[Cramer's Rule]])
*That an associated [[locant]] number represents the location of a [[covalent bond]] in an [[organic compound]], the position of which is variant between [[isomers|isomeric]] forms
*In chemistry, it is often used to represent the addition of heat in a reaction.
*In [[legal shorthand]], it represents a [[defendant]]
*In the financial markets, it is one of the [[Greeks (finance)|Greeks]] that describes the rate of change of an option price for a given change in the underlying benchmark
*It is the symbol of the Greek inventor and architect [[Daedalus]]
*Signifies a major seventh chord in jazz music notation.
*In [[genetics]], it can stand for a [[Deletion (genetics)|gene deletion]], e.g. the [[CCR5-Δ32]] a deletion of the CCR5 at the 32nd base pair segment
*The [http://ada.org/ American Dental Association] cites it (together with omicron for "odont") as the symbol of dentistry.<ref>[http://www.ada.org/2517.aspx?currentTab=2 Caduceus, the emblem of dentistry - American Dental Association - ADA.org]</ref>
*English [[indie rock]] band [[Alt-J]] (The symbol can be typed on a [[OS X|Mac OS X]] computer system by pressing Alt-J).
 
==Lower case==
[[File:NAMA Alphabet grec.jpg|thumb|right|The [[alphabet]] on a [[black figure]] vessel, with a D-shaped delta.]]
 
The lower-case letter δ (or 𝛿) can be used to denote
*An [[differential (infinitesimal)|infinitesimal change]] in the value of a variable in [[infinitesimal calculus]]
*An auxiliary function in [[Calculus]] used to rigorously define the [[Limit of a function|limit]] or [[Continuous function|continuity]] of a given function.
*The [[Kronecker delta]] in mathematics
*The [[Dirac delta function]] in mathematics
*The boundary of a set is denoted by δA, where A is some set, in mathematics, specifically point-set topology
*The transition function in [[Finite state machine|automata]]
*[[Deflection (engineering)|Deflection]] in engineering mechanics
*The [[Compound interest|Force of Interest]] in actuarial science
*The [[chemical shift]] of [[Nuclear Magnetic Resonance]] in chemistry
*The relative [[electronegativity]] of different atoms in a molecule, δ<sup>&minus;</sup> being more electronegative than δ<sup>+</sup>
*Text requiring deletion in [[proofreading]]. The usage is said to date back to classical times
*In some of the manuscripts written by Dr. [[John Dee (mathematician)|John Dee]], the character of delta is used to represent Dee.
*Is a subunit of the F1 sector of the [[F-ATPase]]
*The [[declination]] of an object in the [[equatorial coordinate system]] of [[astronomy]]
*The dividend yield on the [[Black–Scholes]] option pricing formula
*Ratios of [[environmental isotopes]], such as <sup>18</sup>O/<sup>16</sup>O and [[Deuterium|D]]/<sup>1</sup>H from waters are displayed using [[Isotope geochemistry|delta notation]] - δ<sup>18</sup>O and δD, respectively
*The rate of depreciation of the aggregate capital stock of an economy in an [[exogenous growth model]] in [[macroeconomics]].<ref>http://econ.duke.edu/people?subpage=unit&Gurl=%2Faas%2FEconomics&cname=Masters+Students</ref>
*The angle between tension and current in High Voltage insulating testing. Measured value is "tan δ"
 
==Meteorology==
*Delta was used as a name during the [[1972 Atlantic hurricane season]] and the [[2005 Atlantic hurricane season]] as [[Tropical Storm Delta (2005)]].
 
==Computer encodings==
 
* Greek Delta / Coptic Dalda
 
{{charmap
|0394|name1=Greek Capital Letter Delta
|03B4|name2=Greek Small Letter Delta
|1F5F|name3=Modifier Letter Small Delta
|2C86|name3=Coptic Capital Letter Dalda
|2C87|name4=Coptic Small Letter Dalda
|map2=DOS Greek|map2char1=83|map2char2=9B
|map3=DOS Greek-2|map3char1=A7|map3char2=DD
|map4=Windows 1253|map4char1=C4|map4char2=E4
|namedref1=TeX|ref1char1=\Delta|ref1char2=\delta
}}
 
* Latin Delta
 
{{charmap
|1E9F|name1=Latin Small Letter Delta
|018D|name2=Latin Small Letter Turned Delta
}}
 
* Technical and Mathematical symbols
 
{{charmap
|2206|name1=Increment
|2207|name2=Nabla
|225C|name3=Delta Equal To
|234B|name4=APL Functional Symbol Delta Stile
|234D|name5=APL Functional Symbol Quad Delta
|2359|name6=APL Functional Symbol Delta Underbar
}}
 
* Mathematical Delta
 
{{charmap
|1D6AB|name1=Mathematical Bold<br />Capital Delta
|1D6C5|name2=Mathematical Bold<br />Small Delta
|1D6E5|name3=Mathematical Italic<br />Capital Delta
|1D6FF|name4=Mathematical Italic<br />Small Delta
|1D71F|name5=Mathematical Bold Italic<br />Capital Delta
|1D739|name6=Mathematical Bold Italic<br />Small Delta
}}
 
{{charmap
|1D759|name1=Mathematical Sans-Serif<br />Bold Capital Delta
|1D773|name2=Mathematical Sans-Serif<br />Bold Small Delta
|1D793|name3=Mathematical Sans-Serif<br />Bold Italic Capital Delta
|1D7AD|name4=Mathematical Sans-Serif<br />Bold Italic Small Delta
}}
 
These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.
 
==See also==
* [[D|D, d]]
* [[De (Cyrillic)|Д, д]]
* [[ẟ]] - Latin delta
* [[∂]] - the [[partial derivative]] symbol, sometimes mistaken for a lowercase Greek letter Delta.
* [[ð]] - the small [[eth]] appears similar to a small delta, and also represents a ''d'' sound in some contexts
* [[Th (digraph)]]
* [[Greek letters used in mathematics, science, and engineering]]
* ∇ - [[Nabla symbol]]
 
==References==
<references/>
 
Minishoter RS Delta: Infinity Delta, Double Delta
 
[[Category:Greek letters]]

Revision as of 22:38, 4 March 2014

Calories appear to have gotten a bad standing. How regularly are you going to hear a person state anything superior regarding calories? Poor little guys, imagine what it would seem like to be blamed with regard to anything from placing on fat to the taste of food. In cases where you have ever observed oneself thinking: Sure this tastes great, yet it includes a ton of calories, we absolutely know what I mean. Calories really can turn out to be our friends, plus I want to be capable to demonstrate how to understand plus consider them inside a different manner.

To calculate the waist-to-hip ratio (to keep an acronym it's called the WTHR), measure both a waist plus hips, and divide the waist size by the hip size. And yes, this indicator realizes the difference between guys and women, unlike the BMI. For ladies, the ratio must be no over 0.8. In additional words, a waist must be small than the hips. And for guys, it must be 1.0 or less. That signifies which a man's waist ought to be the same measurement as his hips or small. The beer-and-pizza abdomen has to go!

Some folks think it is wise to try and shed a limited pounds before computing for their body mass index. You need to remember that doing this kind of thing is synonymous to cheating during an exam at school. We should measure the real fat in purchase to receive a clear pic of how harmful we absolutely are. If you try to get rid of fat before the computation, you would receive a lower body mass index which will effectively mask the real condition. This may make you think that you don't require to go to the doctor or which we don't should lose weight at all.

I was discussing this with my family doctor plus he agreed which an simple classroom is not the place to be using a bmi calculator men. He moreover revealed that he noticed that more and more of his younger people fall inside the obese plus obese ranking than they did 5 years ago. He's acquiring himself wanting to pull out the aged bmi calculator whenever dealing with their parents. Many parents think which their kids are simply holding on their baby fat longer than before.

However maybe the researches have noticed something important. In the past, big was breathtaking. Overweight individuals were considered more appealing, more affluent, plus healthier. Because the advent of the camera, which supposedly "adds ten pounds," skinny people have become the modern idols to emulate. In Quentin Tarantino's Pulp Fiction, a woman says, "it's unfortunate what we find pleasing to the touch and pleasing to the eye is seldom the same." Is that going to change?

Anyone whom is obese shoe surely discover them selves a good doctor to discuss their weight plus overall health with. Sometimes an disease can put the hormones out of whack and cause us to gain weight. Or possibly a medication is preventing you from losing the fat or cause fatigue thus we can exercise. In any case, be sure to discuss this with the doctor plus left them recognize your plans. They may be able to provide assistance or they might should change medication plus etc.

If you don't fall in the general range, then get oneself checked with alternative (omit) methods to figure out the amount of body fat. This will provide a better perspective plus aid we to do or keep up the ideal weight.