# All Words Glossary

Glossary of Math Terms
beginning with letter E
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 eccentric
noun
1. A disk or wheel with its axis off centre, giving a reciprocating motion.
2. One who does not behave like others.
3. (slang) a kook
1. Not at or in the centre.
2. Not perfectly circular
an eccentric or elliptical orbit
1. Having a different center.
2. Deviating from the norm; behaving unexpectedly or differently.
"He has become really eccentric over the years."
1. (physiology) (of a motion) against or in the opposite direction of contraction of a muscle. (E.g. flexion of the lower arm while flexing the tricep; opening of the jaw while flexing the masseter). (Antonym: Concentric)
 eigenfunction
noun
1. (math) A function &phi; such that, for a generic linear operator D (e.g. differential one), D&phi; = &lambda;&phi; where &lambda; is an eigenvalue of the operator.
2. (quantum) Any eigenfunction of the Hamiltonian operator, representing a quantum state whose energy level is given by the corresponding eigenvalue.
 eigenvalue
noun
1. (linearalg) The change in magnitude of a vector that is not rotated under a given linear transformation; formally, a scalar $\lambda$ such that, for a particular matrix $A$, $A x = \lambda x$ for some nonzero vector $x$, an eigenvector of the matrix; thus, a value of $\lambda$ such that $\mathrm{det}(A - \lambda I) = 0$ for a given square matrix $A$, where $I$ is the identity matrix and $\mathrm{det}$ is the determinant operator.
 eigenvector
noun (pluraleigenvectors)
1. (linearalg) A vector that is not rotated under a given linear transformation; a left eigenvector, left or right eigenvector depending on context.
2. (context, physics, engineering) A right eigenvector; a nonzero vector $x$ such that, for a particular matrix $A$, $A x = \lambda x$ for some scalar $\lambda$ which is its eigenvalue and an eigenvalue of the matrix.
 element
noun
1. (chemistry) Any one of the simplest chemical substances that cannot be decomposed in a chemical reaction or by any chemical means and made up of atoms all having the same number of protons.
2. One of the four basic building blocks of matter in theories of ancient philosophers and alchemists: water, earth, fire, and air.
3. Something small.
an of doubt
1. A place or state of being that an individual or object is better suited towards.
be in one's own
1. A required aspect or component of a cause of action. A deed is regarded a violation of law only if each element can be proved.
2. (set theory) One of the objects in a set.
3. A group of people within a larger group having a particular common characteristic.
You sometimes find the hooligan at football matches.
1. A short form of heating element, a component in electrical equipment, often in the form of a coil, having a high resistance, thereby generating heat when a current is passed through it.
The in this electric kettle can heat the water in under a minute.
 elementary function
noun (wikipedia, elementary function (differential algebra))
1. (mathematics) Any function that is composed of algebraic functions, trigonometric functions, exponential functions and/or logarithmic functions, combined using addition, subtraction, multiplication and/or division
 eliminate
verb (eliminat, ing)
1. (transitive) To completely destroy (something) so that it no longer exists.
2. (slang) To kill (a person or animal).
 elimination
noun
1. The act of eliminating, expelling or throwing off
2. the act of discharging or excreting waste products or foreign substances through the various emunctories.
3. Act of causing a quantity to disappear from an equation; especially, in the operation of deducing from several equations containing several unknown quantities a less number of equations containing a less number of unknown quantities.
4. The act of obtaining by separation, or as the result of eliminating; deduction. See Eliminate, 4.
 ellipse
noun
1. (geometry) A closed curve, the locus of a point such that the sum of the distances from that point to two other fixed points (called the focus, foci of the ellipse) is constant; equivalently, the conic section that is the intersection of a cone with a plane that does not intersect the base of the cone.
verb (ellips, ed)
1. (context, grammar) To remove from a phrase a word which is grammatically needed, but which is clearly understood without having to be stated.
In the exchange:- (A.Would you like to go out?, B.I'd love to), the ellipsed words are <u>go out.</u>
 ellipsograph
noun
1. A mechanical instrument used to trace out an ellipse. Applied to draw, cut, etc mathematically correct ellipses (rather than general ovals).
 ellipsoid
noun
1. (mathematics) a surface, all of whose cross sections are elliptic or circular (includes the sphere)
1. (mathematics) of or pertaining to an ellipse; ellipsoidal
 ellipsoidal
1. (mathematics) of or pertaining to an ellipse or an ellipsoid
 elliptic function
noun
1. (mathematics) Any function of a complex variable which is periodic in two directions
 embed
verb (embed, d, ing)
1. To lay as in a bed; to lay in surrounding matter; to bed; as, to embed a thing in clay, mortar, or sand.
 embedding
noun
1. (mathematics) A map which maps a subspace (smaller structure) to the whole space (larger structure).
verb
1. (present participle of, embed)
 empty
noun (empt, ies)
1. A bottle previously containing some liquid, especially a drink, and that is now empty.
Put the empties out to be recycled.
verb (empties, emptying, emptied)
1. (transitive) (ergative) to make empty; to void; to remove the contents of
1. devoid of content
 endomorphism
noun
1. (geology) The assimilation of surrounding rock by an intrusive igneous rock
2. (mathematics) A homomorphism that maps a system to itself
 enneagon
noun
1. (geometry) a polygon with nine sides; a nonagon.
 entire function
noun
1. (mathematics) Any function of a complex variable that is holomorphic throughout the complex plane
 envelope
noun (pluralenvelopes)
1. A paper or cardboard wrapper used to enclose and small, flat items, especially letters, for mailing.
2. Something that envelops; a wrapping
3. A bag containing the lifting gas of a balloon or airship.
4. (geometry) A mathematical curve, surface, or higher-dimensional object that is the tangent to a given family of lines, curves, surfaces, or higher-dimensional objects.
5. (electronics) A curve that bounds another curve or set of curves, as the modulation envelope of an amplitude-modulated carrier wave in electronics.
6. (music) The shape of a sound, which may be controlled by a synthesizer or sampler.
7. (computing) The information used for routing an email that is transmitted with the email but not part of its contents.
8. (biology) An enclosing structure or cover, such as a membrane.
9. (engineering) The set of limitations within which a technological system can perform safely and effectively.
 epicycle
noun
1. (astronomy) (in Ptolemaic cosmology) a small circle, moving around the circumference of a larger circle having the earth at its centre; the supposed orbit of a planet
2. (mathematics) any circle whose circumference rolls around that of another circle, thus creating a hypocycloid or epicycloid
 epicycloid
noun (pluralepicycloids)
1. (geometry) The locus of a point on the circumference of a circle that rolls without slipping on the circumference of another circle.
 epsilon
noun
1. The name for the fifth letter of the Greek alphabet, Îµ or Î•, preceded by delta (Î", Î´) and followed by zeta (Î–, Î¶).
2. (context, phonetics) In International Phonetic Alphabet, IPA, the phonetic symbol that represents the w:open-mid front unrounded vowel, open-mid front unrounded vowel. Represented in SAMPA as E.
3. (context, mathematics) An arbitrarily small quantity.
4. (context, computing, colloquial) A negligible effect.
• Yes, we have to convert all the symbol names to upper case at startup, but that"s .
 equality
noun (equalities, -)
1. (uncountable) The fact of being equal.
2. (uncountable) (mathematics) The fact of being equal, of having the same value.
3. (uncountable) The equal treatment of people irrespective of social or cultural differences.
 equal sign
noun (pluralequal signs)
1. A symbol ( = ) used in mathematics to indicate that two values are the same, and elsewhere in various other ways, such as (formerly) to separate the signature from the content of a telegram.
<!--NOTE: "equal sign" is not a computing term. In computing, = represents either the assignment operator or the equality operator, depending on the language. It is never properly called "the equal(s) sign".
Note also that other USES of this symbol do not provide other SENSES of the term, as the symbol remains the same one.-->
 equation
noun
1. (math) An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; from which one is to determine a particular quantity.
 equiangular
1. (geometry) Referring to a polygon all of whose interior angles are equal. This is not necessarily a regular polygon, since that would also be equilateral; a rectangle is equiangular but not equilateral, unless it is a square. Translations
• : équiangle
• : equiangolo
 equidistant
1. occupying a position midway between two ends or sides
2. occupying a position that is an equal distance between several points. Note that in a one-dimensional space this position can be identified with two points, in a two-dimensional space with three points (not on the same straight line), and in a three-dimensional space with four points (not in the same plane).
1. (cartography) Describing a map projection that preserves scale. No map can show scale correctly throughout the entire map but some can show true scale between one or two points and every point or along every meridian and these are referred to as equidistant.
 equilateral
1. (geometry): Referring to a polygon all of whose sides are of equal length. Not necessarily a regular polygon since the angles can still differ (a regular polygon would also be equiangular).
 equivalence class
noun (pluralequivalence classes)
1. (settheory) Any one of the subsets into which an equivalence relation partitions a set, each of these subsets containing all the elements of the set that are equivalent under the equivalence relation.
 equivalence relation
noun (pluralequivalence relations)
1. (settheory) A binary relation that is reflexive, symmetric and transitive.
 equivalent
noun
1. anything that is virtually equal to another
2. (chemistry) an equivalent weight
1. similar or identical in value, meaning or effect; virtually equal
2. (mathematics) of two sets, having a one-to-one relationship
3. (mathematics) relating to the corresponding elements of an equivalence relation
4. (chemistry) having the equal ability to combine
5. (cartography) of a map, equal-area
 erect
verb (erects, erecting, erected)
1. (transitive) To put up by the fitting together of materials or parts.
2. (transitive) To cause to stand up or out.
1. upright, Upright; vertical or reaching broadly upwards.
2. rigid, Rigid, firm; standing out perpendicularly.
 error
noun
1. (countable) A mistake.
2. (mathematics) The difference between a measured or calculated value and a true one.
3. (baseball, countable) A play which is scored as having been made incorrectly.
4. (context, appellate, _, law, uncountable) One or more mistakes in a trial that could be grounds for review of the judgement.
verb
1. (non-standard) To make a mistake; to result in an error.
• 1993 December, Arie Kaufman (editor), Rendering, Visualization, and Rasterization Hardware, Springer-Verlag New York LLC
• :Pixels which are mathematically outside of a triangle, but which are included for anti-aliasing purposes can be generated with colour and depth information outside of the valid range. The ADE should identify these cases and clamp the output to the minimum or maximum value depending on the direction it has errored in.
• 2000 December, Randy W. Kamphaus, Clinical Assessment of Child And Adolescent Intelligence, Allyn & Bacon
• :By doing so examiners are erroring in the direction of drawing hypotheses based on greater evidence of reliability and validity.
• 2001 November, Daniel D. Dancer, Shards and Circles: Artistic Adventures in Spirit and Ecology, Trafford Publishing
• :Error is not just permitted by diversity; it is what permits diversity.... The beetle had "errored" beautifully
• 2002 May, Sylvain Beauregard, Passion Celine Dion the Book: The Ultimate Guide for the Fan!, Trafford Publishing
• :Many other celebrities errored in the political comments area...
 Euclidean
1. Of or relating to w:Euclid, Euclid's w:Euclid's Elements, Elements, especially to Euclidean geometry.
 Euclidean algorithm
noun
1. (algebra) a method based on the division algorithm for finding the greatest common divisor (gcd) of two given integers.
 Euclidean geometry
noun (uncountable)
1. (geometry) The familiar geometry of the real world, based on the postulate that through any two points there is exactly one straight line.
 Euclidean group
noun
1. (mathematics) the set of rigid motions that are also affine transformations
 Euclidean space
noun
1. Ordinary two-dimensional, two- or three-dimensional space, characterised by an infinite extent along each dimension and a constant distance between any pair of parallel lines.
2. (mathematics) any vector space on which a real-valued inner product is defined.
 evaluate
verb (evaluat, ing)
1. to draw conclusions from by examine, examining
It will take several weeks to the material gathered in the survey.
2. (math)to compute an expression
Evaluate this polynomial
 even
noun
1. (context, archaic, or, poetic) evening, Evening.
verb
1. To make flat and level.
We need to even this playing field; the west goal is too low.
1. Flat and level.
Clear out those rocks. The surface must be even.
1. Without great variation.
Despite her fear, she spoke in an even voice.
1. Equal in proportion, quantity, size etc.
The distribution of food must be even.
1. (arithmetic) (no comparative or superlative) Leaving no remainder when divided by 2.
Four, fourteen and forty are even numbers.
1. (context, archaic or rhetorical) exactly, just, fully
I fulfilled my instructions as I had promised.
You are leaving tonight? &mdash; Even so.
1. Implying an extreme example in the case mentioned, as compared to the implied reality
Even a blind squirrel finds an acorn sometimes.
Did you make it through the front door?
That was before I was born.
1. Emphasising a comparative
I was strong before; but now I am stronger.
 evolution
noun
1. (context, general) A gradual process of development, formation, or growth, esp. one leading to a more advanced or complex form.
2. (biology) The change in the genetic composition of a population over successive generations.
3. (mathematics) The extraction of a root from a quantity.
4. (military) One of a series of ordered movements.
 exact
verb
1. (transitive) Demand and enforce the payment or performance of.
2. (transitive) Make desirable or necessary.
3. (transitive) Extract forcibly.
to revenge
1. Precisely agreeing with a standard, a fact, or the truth; perfectly conforming; neither exceeding nor falling short in any respect.
The clock keeps time.
He paid the debt.
an copy of a letter
accounts
1. Habitually careful to agree with a standard, a rule, or a promise; accurate; methodical; punctual
a man in observing an appointment
In my doings I was .
1. Precisely or definitely conceived or stated; strict.
 example
noun
1. Something that is representative of all such things in a group.
2. Something that serves to explain or illustrate a rule.
3. Something that serves as a pattern of behaviour to be imitated (a good example) or not to be imitated (a bad example).
• "Learn from me, if not by my precepts, then at least by my example, how dangerous is the acquirement of knowledge" - Mary Shelley, Frankenstein
1. A person punished as a warning to others.
2. A parallel or closely similar case, especially when serving as a precedent or model.
3. An instance (as a problem to be solved) serving to illustrate the rule or precept or to act as an exercise in the application of the rule.
 exp.
abbreviation
1. experience
2. expiration
 explicit
1. very specific, clear, or detailed
I gave instructions for him to stay here, but he followed me, anyway.
2. containing material (e.g. language or film footage) that might be deemed offensive or graphic
The film had several scenes including language and sex.
 exponent
noun
1. One who expounds, represents or advocates
2. (mathematics) The power to which a number, symbol or expression is to be raised. As in the "3" in x3.
 exponential function
noun
1. (mathematics) Any function in which an independent variable is in the form of an exponent; they are the inverse functions of logarithms
 exponentiation
noun
1. (context, mathematics, arithmetic, uncountable) The process of calculating a power by multiplying together a number of equal factors, where the exponent specifies the number of factors to multiply.
In 54, the factors are all 5, the power is 4 and gives the result 625.
1. (context, mathematics, arithmetic, countable) A mathematical problem involving exponentiation.
 expression
noun
1. A particular way of phrase, phrasing an idea.
2. A colloquialism or idiom.
The "break a leg!" should not be taken literally.
1. A facial appearance usually associated with an emotion.
2. (math) A set of symbols denoting values and operations performed on them.
3. (biology) The process of translating a gene into a protein.
4. (context, programming) A piece of code in a high-level language that returns a value.
5. The process of expressing milk
 extension
noun
1. The act of extending or the state of being extended; a stretching out; enlargement in breadth or continuation of length; increase; augmentation; expansion.
2. That property of a body by which it occupies a portion of space (or time, e.g. "spatiotemporal extension")
3. Capacity of a concept or general term to include a greater or smaller number of objects; -- correlative of intension. Synonymous with denotation.
4. A written engagement on the part of a creditor, allowing a debtor further time to pay a debt.
5. The operation of stretching a broken bone so as to bring the fragments into the same straight line.
6. (weightlifting) An exercise in which an arm or leg is straightened against resistance.
7. (fencing) A simple offensive action, consisting of extending the weapon arm forward.
8. A numerical code used to specify a specific telephone in a telecommunication network.
 exterior
noun
1. the outside parts or surface of something
It was written on the exterior
1. foreign lands
She is our new minister of the exterior
1. relating to the outside parts or surface of something
2. being from outside a country, foreign
3. outdoor
 exterior angle
noun
1. (context, Geometry) An angle formed between one side of a polygon and an extension of an adjacent side.
 extremum
noun (pl=extrema, pl2=extremums)
1. (mathematics) a point, or value, which is a maximum or a minimum

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