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mathematics
     1. n. An abstract representational system used in the study of numbers, shapes, structure, change and the relationships between these concepts.
     2. n. A person's ability to count, calculate, and use different systems of mathematics at differing levels.
           My mathematics is always improving.
a
     1. art. One; any indefinite example of; used to denote a singular item of a group.
           There was a man here looking for you yesterday.
     2. art. Used in conjunction with the adjectives score, dozen, hundred, thousand, and million, as a function word.
           I've seen it happen a hundred times.
     3. art. One certain or particular; any single.Brown, Lesley, (2003)
           We've received an interesting letter from a Mrs. Miggins of London.
     4. art. The same; one.
           We are of a mind on matters of morals.
     5. art. Any, every; used before a noun which has become modified to limit its scope; also used with a negative to indicate not a single one.Lindberg, Christine A. (2007)
           A man who dies intestate leaves his children troubles and difficulties.
           He fell all that way, and hasn't a bump on his head?
     6. art. Used before plural nouns modified by few, good many, couple, great many, etc.
     7. art. Someone or something like; similar to; Used before a proper noun to create an example out of it.
           The center of the village was becoming a Times Square.
     8. prep. (archaic) To do with position or direction; In, on, at, by, towards, onto.
           Stand a tiptoe.
     9. prep. To do with separation; In, into.
           Torn a pieces.
     10. prep. To do with time; Each, per, in, on, by.
           I brush my teeth twice a day.
     11. prep. (obsolete) To do with method; In, with.
     12. prep. (obsolete) To do with role or capacity; In.
           A God’s name.
     13. prep. To do with status; In.
           King James Bible (II Chronicles 2:18)
             To set the people a worke.
     14. prep. (archaic) To do with process, with a passive verb; In the course of, experiencing.
           1964, Bob Dylan, The Times They Are a-Changin’
             The times, they are a-changin'.
     15. prep. (archaic) To do with an action, an active verb; Engaged in.
           1611, King James Bible, Hebrews 11-21
             Jacob, when he was a dying
     16. prep. (archaic) To do with an action/movement; To, into.
     17. v. (archaic, or slang) Have.
           I'd a come, if you'd a asked.
     18. pron. (obsolete, outside, England, and Scotland dialects) He.
     19. interj. A meaningless syllable; ah.
     20. prep. (archaic, slang) Of.
           The name of John a Gaunt.
     21. adv. (chiefly Scotland) All.
     22. adj. (chiefly Scotland) All.
region
     1. n. Any considerable and connected part of a space or surface; specifically, a tract of land or sea of considerable but indefinite extent; a country; a district; in a broad sense, a place without special
           the equatorial regions
           the temperate regions
           the polar regions
           the upper regions of the atmosphere
     2. n. An administrative subdivision of a city, a territory, a country or the European Union.
     3. n. (historical) Such a division of the city of Rome and of the territory about Rome, of which the number varied at different times; a district, quarter, or ward.
     4. n. (figuratively) The inhabitants of a region or district of a country.
     5. n. (anatomy) A place in or a part of the body in any way indicated.
           the abdominal regions
     6. n. (obsolete) Place; rank; station; dignity.
     7. n. (obsolete) The space from the earth's surface out to the orbit of the moon: properly called the elemental region.
of
     1. prep. Expressing distance or motion.
     2. prep.          (now obsolete, or dialectal) From (of distance, direction), "off".
     3. prep.          (obsolete except in phrases) Since, from (a given time, earlier state etc.).
     4. prep.          From, away from (a position, number, distance etc.).
                    There are no shops within twenty miles of the cottage.
     5. prep.          (North America, Scotland, Ireland) Before (the hour); to.
                    What's the time? / Nearly a quarter of three.
     6. prep. Expressing separation.
     7. prep.          (Indicating removal, absence or separation, with the action indicated by a transitive verb and the quality or substance by a grammatical object.)
                    Finally she was relieved of the burden of caring for her sick husband.
     8. prep.          (Indicating removal, absence or separation, with resulting state indicated by an adjective.)
                    He seemed devoid of human feelings.
     9. prep.          (obsolete) (Indicating removal, absence or separation, construed with an intransitive verb.)
     10. prep. Expressing origin.
     11. prep.          (Indicating an ancestral source or origin of descent.)
                    The word is believed to be of Japanese origin.
     12. prep.          (Indicating a (non-physical) source of action or emotion; introducing a cause, instigation); from, out of, as an expression of.
                    The invention was born of necessity.
     13. prep.          (following an intransitive verb) (Indicates the source or cause of the verb.)
                    It is said that she died of a broken heart.
     14. prep.          (following an adjective) (Indicates the subject or cause of the adjective.)
                    I am tired of all this nonsense.
     15. prep. Expressing agency.
     16. prep.          (following a passive verb) (Indicates the agent (for most verbs, now usually expressed with by).)
                    I am not particularly enamoured of this idea.
     17. prep.          (Used to introduce the "subjective genitive"; following a noun to form the head of a postmodifying noun phrase) (see also 'Possession' senses below).
                    The contract can be terminated at any time with the agreement of both parties.
     18. prep.          (following an adjective) (Used to indicate the agent of something described by the adjective.)
                    It was very brave of you to speak out like that.
     19. prep. Expressing composition, substance.
     20. prep.          (after a verb expressing construction, making etc.) (Used to indicate the material or substance used.)
                    Many 'corks' are now actually made of plastic.
     21. prep.          (directly following a noun) (Used to indicate the material of the just-mentioned object.)
                    She wore a dress of silk.
     22. prep.          (Indicating the composition of a given collective or quantitative noun.)
                    What a lot of nonsense!
     23. prep.          (Used to link a given class of things with a specific example of that class.)
                   Welcome to the historic town of Harwich.
     24. prep.          (Links two nouns in near-apposition, with the first qualifying the second); "which is also".
                    I'm not driving this wreck of a car.
     25. prep. Introducing subject matter.
     26. prep.          (Links an intransitive verb, or a transitive verb and its subject (especially verbs to do with thinking, feeling, expressing etc.), with its subject-ma
                    I'm always thinking of you.
     27. prep.          (following a noun (now chiefly nouns of knowledge, communication etc.)) (Introduces its subject matter); about, concerning.
                    He told us the story of his journey to India.
     28. prep.          (following an adjective) (Introduces its subject matter.)
                    This behaviour is typical of teenagers.
     29. prep. Having partitive effect.
     30. prep.          (following a number or other quantitive word) (Introduces the whole for which is indicated only the specified part or segment); "from among".
                    Most of these apples are rotten.
     31. prep.          (following a noun) (Indicates a given part.)
     32. prep.          (now archaic, literary, with preceding partitive word assumed, or as a predicate after to be) Some, an amount of, one of.
                    On the whole, they seem to be of the decent sort.
     33. prep.          (Links to a genitive noun or possessive pronoun, with partitive effect (though now often merged with possessive senses, below).)
                    He is a friend of mine.
     34. prep. Expressing possession.
     35. prep.          Belonging to, existing in, or taking place in a given location, place or time. Compare "origin" senses, above.
                    He was perhaps the most famous scientist of the twentieth century.
     36. prep.          Belonging to (a place) through having title, ownership or control over it.
                    The owner of the nightclub was arrested.
     37. prep.          Belonging to (someone or something) as something they possess or have as a characteristic; (the "possessive genitive". (With abstract nouns, this inter
                    Keep the handle of the saucepan away from the flames.
     38. prep. Forming the "objective genitive".
     39. prep.          (Follows an agent noun, verbal noun or noun of action.)
                    She had a profound distrust of the police.
     40. prep. Expressing qualities or characteristics.
     41. prep.          (now archaic, or literary) (Links an adjective with a noun or noun phrase to form a quasi-adverbial qualifier); in respect to, as regards.
                    My companion seemed affable and easy of manner.
     42. prep.          (Indicates a quality or characteristic); "characterized by".
                    Pooh was said to be a bear of very little brain.
     43. prep.          (Indicates quantity, age, price, etc.)
                    We have been paying interest at a rate of 10%.
     44. prep.          (US, informal considered incorrect by some) (Used to link singular indefinite nouns (preceded by the indefinite article) and attributive adjectives mod
                    It's not that big of a deal.
     45. prep. Expressing a point in time.
     46. prep.          (chiefly regional) During the course of (a set period of time, day of the week etc.), now specifically with implied repetition or regularity.
                    Of an evening, we would often go for a stroll along the river.
     47. prep.          (UK dialectal, chiefly in negative constructions) For (a given length of time).
                    I've not tekken her out of a goodly long while.
     48. prep.          (after a noun) (Indicates duration of a state, activity etc.)
                    After a delay of three hours, the plane finally took off.
the
     1. art. Definite grammatical article that implies necessarily that an entity it articulates is presupposed; something already mentioned, or completely specified later in that same sentence, or assumed already
           I’m reading the book. (Compare I’m reading a book.)
           The street in front of your house. (Compare A street in Paris.)
           The men and women watched the man give the birdseed to the bird.
     2. art.          Used before a noun modified by a restrictive relative clause, indicating that the noun refers to a single referent defined by the relative clause.
                    The street that runs through my hometown.
     3. art. Used before an object considered to be unique, or of which there is only one at a time.
           No one knows how many galaxies there are in the universe.
           God save the Queen!
     4. art. Used before a superlative or an ordinal number modifying a noun, to indicate that the noun refers to a single item.
           That was the best apple pie ever.
     5. art.          Added to a superlative or an ordinal number to make it into a substantive.
                    That apple pie was the best.
     6. art. Introducing a singular term to be taken generically: preceding a name of something standing for a whole class.
     7. art. Used before an adjective, indicating all things (especially persons) described by that adjective.
           Feed the hungry, clothe the naked, comfort the afflicted, and afflict the comfortable.
     8. art. Used to indicate a certain example of (a noun) which is usually of most concern or most common or familiar.
           No one in the whole country had seen it before.
           I don't think I'll get to it until the morning.
     9. art. Used before a body part (especially of someone previously mentioned), as an alternative to a possessive pronoun.
           A stone hit him on the head. (= “A stone hit him on his head.”)
     10. art. When stressed, indicates that it describes an object which is considered to be best or exclusively worthy of attention.
           That is the hospital to go to for heart surgery.
     11. adv. 1=With a comparative ormore and a verb phrase, establishes a parallel with one or more other such comparatives.
           The hotter the better.
           The more I think about it, the weaker it looks.
           The more money donated, the more books purchased, and the more happy children.
           It looks weaker and weaker, the more I think about it.
     12. adv. 1=With a comparative, and often withfor it, indicates a result more like said comparative. This can be negated withnone.
           It was a difficult time, but I’m the wiser for it.
           It was a difficult time, and I’m none the wiser for it.
           I'm much the wiser for having had a difficult time like that.
projection
     1. n. Something which projects, protrudes, juts out, sticks out, or stands out.
           The face of the cliff had many projections that were big enough for birds to nest on.
     2. n. The action of projecting or throwing or propelling something.
     3. n. The display of an image by devices such as movie projector, video projector, overhead projector or slide projector.
     4. n. A forecast or prognosis obtained by extrapolation
     5. n. (psychology) A belief or assumption that others have similar thoughts and experiences as oneself
     6. n. (photography) The image that a translucent object casts onto another object.
     7. n. (cartography) Any of several systems of intersecting lines that allow the curved surface of the earth to be represented on a flat surface. The set of mathematics used to calculate coordinate positions
     8. n. (geometry) An image of an object on a surface of fewer dimensions.
     9. n. (linear algebra) An idempotent linear transformation which maps vectors from a vector space onto a subspace.
     10. n. (mathematics) A transformation which extracts a fragment of a mathematical object.
     11. n. (category theory) A morphism from a categorical product to one of its (two) components.
of
     1. prep. Expressing distance or motion.
     2. prep.          (now obsolete, or dialectal) From (of distance, direction), "off".
     3. prep.          (obsolete except in phrases) Since, from (a given time, earlier state etc.).
     4. prep.          From, away from (a position, number, distance etc.).
                    There are no shops within twenty miles of the cottage.
     5. prep.          (North America, Scotland, Ireland) Before (the hour); to.
                    What's the time? / Nearly a quarter of three.
     6. prep. Expressing separation.
     7. prep.          (Indicating removal, absence or separation, with the action indicated by a transitive verb and the quality or substance by a grammatical object.)
                    Finally she was relieved of the burden of caring for her sick husband.
     8. prep.          (Indicating removal, absence or separation, with resulting state indicated by an adjective.)
                    He seemed devoid of human feelings.
     9. prep.          (obsolete) (Indicating removal, absence or separation, construed with an intransitive verb.)
     10. prep. Expressing origin.
     11. prep.          (Indicating an ancestral source or origin of descent.)
                    The word is believed to be of Japanese origin.
     12. prep.          (Indicating a (non-physical) source of action or emotion; introducing a cause, instigation); from, out of, as an expression of.
                    The invention was born of necessity.
     13. prep.          (following an intransitive verb) (Indicates the source or cause of the verb.)
                    It is said that she died of a broken heart.
     14. prep.          (following an adjective) (Indicates the subject or cause of the adjective.)
                    I am tired of all this nonsense.
     15. prep. Expressing agency.
     16. prep.          (following a passive verb) (Indicates the agent (for most verbs, now usually expressed with by).)
                    I am not particularly enamoured of this idea.
     17. prep.          (Used to introduce the "subjective genitive"; following a noun to form the head of a postmodifying noun phrase) (see also 'Possession' senses below).
                    The contract can be terminated at any time with the agreement of both parties.
     18. prep.          (following an adjective) (Used to indicate the agent of something described by the adjective.)
                    It was very brave of you to speak out like that.
     19. prep. Expressing composition, substance.
     20. prep.          (after a verb expressing construction, making etc.) (Used to indicate the material or substance used.)
                    Many 'corks' are now actually made of plastic.
     21. prep.          (directly following a noun) (Used to indicate the material of the just-mentioned object.)
                    She wore a dress of silk.
     22. prep.          (Indicating the composition of a given collective or quantitative noun.)
                    What a lot of nonsense!
     23. prep.          (Used to link a given class of things with a specific example of that class.)
                   Welcome to the historic town of Harwich.
     24. prep.          (Links two nouns in near-apposition, with the first qualifying the second); "which is also".
                    I'm not driving this wreck of a car.
     25. prep. Introducing subject matter.
     26. prep.          (Links an intransitive verb, or a transitive verb and its subject (especially verbs to do with thinking, feeling, expressing etc.), with its subject-ma
                    I'm always thinking of you.
     27. prep.          (following a noun (now chiefly nouns of knowledge, communication etc.)) (Introduces its subject matter); about, concerning.
                    He told us the story of his journey to India.
     28. prep.          (following an adjective) (Introduces its subject matter.)
                    This behaviour is typical of teenagers.
     29. prep. Having partitive effect.
     30. prep.          (following a number or other quantitive word) (Introduces the whole for which is indicated only the specified part or segment); "from among".
                    Most of these apples are rotten.
     31. prep.          (following a noun) (Indicates a given part.)
     32. prep.          (now archaic, literary, with preceding partitive word assumed, or as a predicate after to be) Some, an amount of, one of.
                    On the whole, they seem to be of the decent sort.
     33. prep.          (Links to a genitive noun or possessive pronoun, with partitive effect (though now often merged with possessive senses, below).)
                    He is a friend of mine.
     34. prep. Expressing possession.
     35. prep.          Belonging to, existing in, or taking place in a given location, place or time. Compare "origin" senses, above.
                    He was perhaps the most famous scientist of the twentieth century.
     36. prep.          Belonging to (a place) through having title, ownership or control over it.
                    The owner of the nightclub was arrested.
     37. prep.          Belonging to (someone or something) as something they possess or have as a characteristic; (the "possessive genitive". (With abstract nouns, this inter
                    Keep the handle of the saucepan away from the flames.
     38. prep. Forming the "objective genitive".
     39. prep.          (Follows an agent noun, verbal noun or noun of action.)
                    She had a profound distrust of the police.
     40. prep. Expressing qualities or characteristics.
     41. prep.          (now archaic, or literary) (Links an adjective with a noun or noun phrase to form a quasi-adverbial qualifier); in respect to, as regards.
                    My companion seemed affable and easy of manner.
     42. prep.          (Indicates a quality or characteristic); "characterized by".
                    Pooh was said to be a bear of very little brain.
     43. prep.          (Indicates quantity, age, price, etc.)
                    We have been paying interest at a rate of 10%.
     44. prep.          (US, informal considered incorrect by some) (Used to link singular indefinite nouns (preceded by the indefinite article) and attributive adjectives mod
                    It's not that big of a deal.
     45. prep. Expressing a point in time.
     46. prep.          (chiefly regional) During the course of (a set period of time, day of the week etc.), now specifically with implied repetition or regularity.
                    Of an evening, we would often go for a stroll along the river.
     47. prep.          (UK dialectal, chiefly in negative constructions) For (a given length of time).
                    I've not tekken her out of a goodly long while.
     48. prep.          (after a noun) (Indicates duration of a state, activity etc.)
                    After a delay of three hours, the plane finally took off.
a
     1. art. One; any indefinite example of; used to denote a singular item of a group.
           There was a man here looking for you yesterday.
     2. art. Used in conjunction with the adjectives score, dozen, hundred, thousand, and million, as a function word.
           I've seen it happen a hundred times.
     3. art. One certain or particular; any single.Brown, Lesley, (2003)
           We've received an interesting letter from a Mrs. Miggins of London.
     4. art. The same; one.
           We are of a mind on matters of morals.
     5. art. Any, every; used before a noun which has become modified to limit its scope; also used with a negative to indicate not a single one.Lindberg, Christine A. (2007)
           A man who dies intestate leaves his children troubles and difficulties.
           He fell all that way, and hasn't a bump on his head?
     6. art. Used before plural nouns modified by few, good many, couple, great many, etc.
     7. art. Someone or something like; similar to; Used before a proper noun to create an example out of it.
           The center of the village was becoming a Times Square.
     8. prep. (archaic) To do with position or direction; In, on, at, by, towards, onto.
           Stand a tiptoe.
     9. prep. To do with separation; In, into.
           Torn a pieces.
     10. prep. To do with time; Each, per, in, on, by.
           I brush my teeth twice a day.
     11. prep. (obsolete) To do with method; In, with.
     12. prep. (obsolete) To do with role or capacity; In.
           A God’s name.
     13. prep. To do with status; In.
           King James Bible (II Chronicles 2:18)
             To set the people a worke.
     14. prep. (archaic) To do with process, with a passive verb; In the course of, experiencing.
           1964, Bob Dylan, The Times They Are a-Changin’
             The times, they are a-changin'.
     15. prep. (archaic) To do with an action, an active verb; Engaged in.
           1611, King James Bible, Hebrews 11-21
             Jacob, when he was a dying
     16. prep. (archaic) To do with an action/movement; To, into.
     17. v. (archaic, or slang) Have.
           I'd a come, if you'd a asked.
     18. pron. (obsolete, outside, England, and Scotland dialects) He.
     19. interj. A meaningless syllable; ah.
     20. prep. (archaic, slang) Of.
           The name of John a Gaunt.
     21. adv. (chiefly Scotland) All.
     22. adj. (chiefly Scotland) All.
knot
     1. n. A looping of a piece of string or of any other long, flexible material that cannot be untangled without passing one or both ends of the material through its loops.
           Climbers must make sure that all knots are both secure and of types that will not weaken the rope.
     2. n. (of hair, etc) A tangled clump.
           The nurse was brushing knots from the protesting child's hair.
     3. n. A maze-like pattern.
     4. n. (mathematics) A non-self-intersecting closed curve in (e.g., three-dimensional) space that is an abstraction of a knot (in sense 1 above).
           A knot can be defined as a non-self-intersecting broken line whose endpoints coincide: when such a knot is constrained to lie in a plane, then it is simply a polygon.
               A knot in its original sense can be modeled as a mathematical knot (or link) as follows: if the knot is made with a single piece of rope, then abstract the shape of that
     5. n. A difficult situation.
           I got into a knot when I inadvertently insulted a policeman.
     6. n. The whorl left in lumber by the base of a branch growing out of the tree's trunk.
           When preparing to tell stories at a campfire, I like to set aside a pile of pine logs with lots of knots, since they burn brighter and make dramatic pops and cracks.
     7. n. Local swelling in a tissue area, especially skin, often due to injury.
           Jeremy had a knot on his head where he had bumped it on the bedframe.
     8. n. A protuberant joint in a plant.
     9. n. Any knob, lump, swelling, or protuberance.
     10. n. the swelling of the Bulbus Glandis in members of the dog family; Canidae
     11. n. The point on which the action of a story depends; the gist of a matter.
           the knot of the tale
     12. n. (engineering) A node.
     13. n. A kind of epaulet; a shoulder knot.
     14. n. A group of people or things.
     15. n. A bond of union; a connection; a tie.
     16. n. (nautical) A unit of speed, equal to one nautical mile per hour. (From the practice of counting the number of knots in the log-line (as it plays out) in a standard time. Traditionally spaced at one ev
           Cedric claimed his old yacht could make 12 knots.
     17. n. (slang) A nautical mile (incorrectly)
     18. v. To form into a knot; to tie with a knot or knots.
           We knotted the ends of the rope to keep it from unravelling.
     19. v. To form wrinkles in the forehead, as a sign of concentration, concern, surprise, etc.
           She knotted her brow in concentration while attempting to unravel the tangled strands.
     20. v. To unite closely; to knit together.
     21. v. (obsolete, rare) To entangle or perplex; to puzzle.
     22. n. One of a variety of shore birds; the red-breasted sandpiper (variously Calidris canutus or).
such
     1. det. (demonstrative) Like this, that, these, those; used to make a comparison with something implied by context.
           I’ve never seen such clouds in the sky before.  Such is life.
     2. det. (particularly used in formal documents) Any.
           the above address or at such other address as may notify
     3. det. Used as an intensifier; roughly equivalent to very much of.
           The party was such a bore.
     4. det. (obsolete) A certain; representing the object as already particularized in terms which are not mentioned.
     5. pron. A person, a thing, people or things like the one or ones already mentioned.
     6. n. (philosophy) Something being indicated that is similar to something else.
that
     1. conj. Introducing a clause which is the subject or object of a verb (such as one involving reported speech), or which is a complement to a previous statement.
           He told me that the book is a good read.
           I believe that it is true. — She is convinced that he is British.
     2. conj. Introducing a subordinate clause expressing a reason or cause: because, in that.
           Be glad that you have enough to eat.
     3. conj. (now uncommon) Introducing a subordinate clause that expresses an aim, purpose or goal ("final"), and usually contains the auxiliaries may, might or should: so, so that.
     4. conj. Introducing — especially, but not exclusively, with an antecedent like so or such — a subordinate clause expressing a result, consequence or effect.
           The noise was so loud that she woke up.
           The problem was sufficiently important that it had to be addressed.
     5. conj. (archaic, or poetic) Introducing a premise or supposition for consideration: seeing as; inasmuch as; given that; as would appear from the fact that.
     6. conj. Introducing a subordinate clause modifying an adverb.
           Was John there? — Not that I saw.
           How often did she visit him? — Twice that I saw.
     7. conj. Introducing an exclamation expressing a desire or wish.
     8. conj. Introducing an exclamation expressing a strong emotion such as sadness or surprise.
     9. det. The (thing, person, idea, etc) indicated or understood from context, especially if more remote physically, temporally or mentally than one designated as "this", or if expressing distinction.
           That book is a good read. This one isn't.
           That battle was in 1450.
           That cat of yours is evil.
     10. pron. (demonstrative) The thing, person, idea, quality, event, action or time indicated or understood from context, especially if more remote geographically, temporally or mentally than one designated as "t
           He went home, and after that I never saw him again.
     11. pron. The known (thing); (used to refer to something just said).
           They're getting divorced. What do you think about that?
     12. pron. (demonstrative) The aforementioned quality; used together with a verb and pronoun to emphatically repeat a previous statement.
           The water is so cold! — That it is.
     13. pron. (relative) (plural that) Which, who; (representing a subject, direct object, indirect object, or object of a preposition).
           The CPR course that she took really came in handy.
           The house that he lived in was old and dilapidated.
     14. pron. (colloquial) (Used in place of relative adverbs such as where or when; often omitted.)
           the place that = where or to which I went last year
           the last time that = when I went to Europe
     15. adv. (degree) To a given extent or degree.
           "The ribbon was that thin." "I disagree, I say it was not that thin, it was thicker... or maybe thinner...".
     16. adv. (degree) To a great extent or degree; very, particularly (in negative constructions).
           I'm just not that sick.
           I did the run last year, and it wasn't that difficult.
     17. adv. (obsolete, outside, dialects) To such an extent; so. (in positive constructions).
           Ooh, I was that happy I nearly kissed her.
     18. n. (philosophy) Something being indicated that is there; one of those.
the
     1. art. Definite grammatical article that implies necessarily that an entity it articulates is presupposed; something already mentioned, or completely specified later in that same sentence, or assumed already
           I’m reading the book. (Compare I’m reading a book.)
           The street in front of your house. (Compare A street in Paris.)
           The men and women watched the man give the birdseed to the bird.
     2. art.          Used before a noun modified by a restrictive relative clause, indicating that the noun refers to a single referent defined by the relative clause.
                    The street that runs through my hometown.
     3. art. Used before an object considered to be unique, or of which there is only one at a time.
           No one knows how many galaxies there are in the universe.
           God save the Queen!
     4. art. Used before a superlative or an ordinal number modifying a noun, to indicate that the noun refers to a single item.
           That was the best apple pie ever.
     5. art.          Added to a superlative or an ordinal number to make it into a substantive.
                    That apple pie was the best.
     6. art. Introducing a singular term to be taken generically: preceding a name of something standing for a whole class.
     7. art. Used before an adjective, indicating all things (especially persons) described by that adjective.
           Feed the hungry, clothe the naked, comfort the afflicted, and afflict the comfortable.
     8. art. Used to indicate a certain example of (a noun) which is usually of most concern or most common or familiar.
           No one in the whole country had seen it before.
           I don't think I'll get to it until the morning.
     9. art. Used before a body part (especially of someone previously mentioned), as an alternative to a possessive pronoun.
           A stone hit him on the head. (= “A stone hit him on his head.”)
     10. art. When stressed, indicates that it describes an object which is considered to be best or exclusively worthy of attention.
           That is the hospital to go to for heart surgery.
     11. adv. 1=With a comparative ormore and a verb phrase, establishes a parallel with one or more other such comparatives.
           The hotter the better.
           The more I think about it, the weaker it looks.
           The more money donated, the more books purchased, and the more happy children.
           It looks weaker and weaker, the more I think about it.
     12. adv. 1=With a comparative, and often withfor it, indicates a result more like said comparative. This can be negated withnone.
           It was a difficult time, but I’m the wiser for it.
           It was a difficult time, and I’m none the wiser for it.
           I'm much the wiser for having had a difficult time like that.
knot
     1. n. A looping of a piece of string or of any other long, flexible material that cannot be untangled without passing one or both ends of the material through its loops.
           Climbers must make sure that all knots are both secure and of types that will not weaken the rope.
     2. n. (of hair, etc) A tangled clump.
           The nurse was brushing knots from the protesting child's hair.
     3. n. A maze-like pattern.
     4. n. (mathematics) A non-self-intersecting closed curve in (e.g., three-dimensional) space that is an abstraction of a knot (in sense 1 above).
           A knot can be defined as a non-self-intersecting broken line whose endpoints coincide: when such a knot is constrained to lie in a plane, then it is simply a polygon.
               A knot in its original sense can be modeled as a mathematical knot (or link) as follows: if the knot is made with a single piece of rope, then abstract the shape of that
     5. n. A difficult situation.
           I got into a knot when I inadvertently insulted a policeman.
     6. n. The whorl left in lumber by the base of a branch growing out of the tree's trunk.
           When preparing to tell stories at a campfire, I like to set aside a pile of pine logs with lots of knots, since they burn brighter and make dramatic pops and cracks.
     7. n. Local swelling in a tissue area, especially skin, often due to injury.
           Jeremy had a knot on his head where he had bumped it on the bedframe.
     8. n. A protuberant joint in a plant.
     9. n. Any knob, lump, swelling, or protuberance.
     10. n. the swelling of the Bulbus Glandis in members of the dog family; Canidae
     11. n. The point on which the action of a story depends; the gist of a matter.
           the knot of the tale
     12. n. (engineering) A node.
     13. n. A kind of epaulet; a shoulder knot.
     14. n. A group of people or things.
     15. n. A bond of union; a connection; a tie.
     16. n. (nautical) A unit of speed, equal to one nautical mile per hour. (From the practice of counting the number of knots in the log-line (as it plays out) in a standard time. Traditionally spaced at one ev
           Cedric claimed his old yacht could make 12 knots.
     17. n. (slang) A nautical mile (incorrectly)
     18. v. To form into a knot; to tie with a knot or knots.
           We knotted the ends of the rope to keep it from unravelling.
     19. v. To form wrinkles in the forehead, as a sign of concentration, concern, surprise, etc.
           She knotted her brow in concentration while attempting to unravel the tangled strands.
     20. v. To unite closely; to knit together.
     21. v. (obsolete, rare) To entangle or perplex; to puzzle.
     22. n. One of a variety of shore birds; the red-breasted sandpiper (variously Calidris canutus or).
crosses
     1. n. plural of cross
     2. n. plural of crosse
     3. v. third-person singular present indicative of cross
     cross
          1. n. A geometrical figure consisting of two straight lines or bars intersecting each other such that at least one of them is bisected by the other.
                Put a cross for a wrong answer and a tick for a right one.
          2. n. (heraldry) Any geometric figure having this or a similar shape, such as a cross of Lorraine or a Maltese cross.
          3. n. A wooden post with a perpendicular beam attached and used (especially in the Roman Empire) to execute criminals (by crucifixion).
                Criminals were commonly executed on a wooden cross.
          4. n. (usually with the) The cross on which Christ was crucified.
          5. n. (Christianity) A hand gesture made in imitation of the shape of the Cross.
                She made the cross after swearing.
          6. n. (Christianity) A modified representation of the crucifixion stake, worn as jewellery or displayed as a symbol of religious devotion.
                She was wearing a cross on her necklace.
          7. n. (figurative, from Christ's bearing of the cross) A difficult situation that must be endured.
                It's a cross I must bear.
          8. n. The act of going across; the act of passing from one side to the other
                A quick cross of the road.
          9. n. (biology) An animal or plant produced by crossbreeding or cross-fertilization.
          10. n. (by extension) A hybrid of any kind.
          11. n. (boxing) A hook thrown over the opponent's punch.
          12. n. (football) A pass in which the ball travels from by one touchline across the pitch.
          13. n. A place where roads intersect and lead off in four directions; a crossroad (common in UK and Irish place names such as Gerrards Cross).
          14. n. A monument that marks such a place. (Also common in UK or Irish place names such as Charing Cross)
          15. n. (obsolete) A coin stamped with the figure of a cross, or that side of such a piece on which the cross is stamped; hence, money in general.
          16. n. (obsolete, Ireland) Church lands.
          17. n. A line drawn across or through another line.
          18. n. (surveying) An instrument for laying of offsets perpendicular to the main course.
          19. n. A pipe-fitting with four branches whose axes usually form a right angle.
          20. n. (Rubik's Cube) Four edge cubies of one side that are in their right places, forming the shape of a cross.
          21. n. (cartomancy) The thirty-sixth Lenormand card.
          22. adj. Transverse; lying across the main direction.
                At the end of each row were cross benches which linked the rows.
          23. adj. (archaic) Opposite, opposed to.
                His actions were perversely cross to his own happiness.
          24. adj. (now rare) Opposing, adverse; being contrary to what one would hope or wish for.
          25. adj. Bad-tempered, angry, annoyed.
                She was rather cross about missing her train on the first day of the job.
                Please don't get cross at me. (or) Please don't get cross with me.
          26. adj. Made in an opposite direction, or an inverse relation; mutually inverse; interchanged.
                cross interrogatories
                cross marriages, as when a brother and sister marry persons standing in the same relation to each other
          27. prep. (archaic) across
                She walked cross the mountains.
          28. prep. cross product of the previous vector and the following vector.
                The Lorentz force is q times v cross B.
          29. v. To make or form a cross.
          30. v.          To place across or athwart; to cause to intersect.
                        She frowned and crossed her arms.
          31. v.          To lay or draw something across, such as a line.
                        to cross the letter t
          32. v.          To mark with an X.
                        Cross the box which applies to you.
          33. v.          To write lines at right angles.W
          34. v.          (reflexive, to cross oneself) To make the sign of the cross over oneself.
          35. v. To move relatively.
          36. v.          To go from one side of (something) to the other.
                        Why did the chicken cross the road?
                        You need to cross the street at the lights.
          37. v.          (intransitive) To travel in a direction or path that will intersect with that of another.
                        Ships crossing from starboard have right-of-way.
          38. v.          To pass, as objects going in an opposite direction at the same time.
          39. v.          (sports) Relative movement by a player or of players.
          40. v.         # (cricket, reciprocally) Of both batsmen, to pass each other when running between the wickets in order to score runs.
          41. v.         # (football) To pass the ball from one side of the pitch to the other side.
                   #     He crossed the ball into the penalty area.
          42. v.         # (rugby) To score a try.
          43. v. (social) To oppose.
          44. v.          To contradict (another) or frustrate the plans of.
                        "You'll rue the day you tried to cross me, Tom Hero!" bellowed the villain.
          45. v.          (transitive, obsolete) To interfere and cut off; to debar.
          46. v.          (legal) To conduct a cross examination; to question a hostile witness.
          47. v. (biology) To cross-fertilize or crossbreed.
                They managed to cross a sheep with a goat.
          48. v. To stamp or mark a cheque in such a way as to prevent it being cashed, thus requiring it to be deposited into a bank account.
its
     1. det. Belonging to it.
     2. pron. The one (or ones) belonging to it.
     3. n. plural of it
perimeter
     1. n. (mathematics) The sum of the distance of all the lengths of the sides of an object.
     2. n. (mathematics) The length of such a boundary.
     3. n. The outer limits of an area. (syndiff, en, circumference)
     4. n. A fortified strip or boundary usually protecting a military position.
     5. n. An instrument for determining the extent and shape of the field of vision.
exactly
     1. adv. (manner) without approximation; precisely.
           Measure exactly so we can be sure it is right.
           The edge is not exactly straight.
     2. adv. (focus) Used to provide emphasis.
           It was exactly an Eastern gray squirrel.
           He divided the coins exactly in half.
           He did it that way exactly to prove the point.
           His complaint was exactly that she failed to meet the deadline by four days.
     3. interj. Signifies agreement or recognition.
           So you're saying that we have only three days left? / Yes, exactly!
four
     1. num. (cardinal) A numerical value equal to 4; the number after three and before five; two plus two. This many dots (••••)
           There are four seasons: winter, spring, summer and autumn.
     2. num. Describing a set or group with four elements.
     3. n. The digit or figure 4; an occurrence thereof.
     4. n. Anything measuring four units, as length.
           Do you have any more fours? I want to make this a little taller.
     5. n. A person who is four years old.
           I'll take the threes, fours and fives and go to the playground.
     6. n. (cricket) An event whereby a batsman hits a ball which bounces on the ground before passing over a boundary in the air, resulting in an award of 4 runs for the batting team. If the ball does not bounc
     7. n. (basketball) A power forward.
     8. n. (rowing) Quadruple sculls.
     9. n. (obsolete) A four-pennyworth of spirits.
times
     1. n. plural of time
     2. n. The circumstances of a certain time.
           Modern times are so very different from the past.
     3. n. A person's experiences or biography.
           The Life and Times of Rosie the Riveter.
     4. prep. (mathematics) multiplied by
           Four times five is twenty.
           One times one is one.
     5. v. third-person singular present indicative of time
     6. v. (informal, arithmetic) To multiply.
     time
          1. n. The inevitable progression into the future with the passing of present events into the past.
                Time stops for nobody.   the ebb and flow of time
          2. n.          (physics, usually) A dimension of spacetime with the opposite metric signature to space dimensions; the fourth dimension.
                        Both science-fiction writers and physicists have written about travel through time.
          3. n.          (physics) Change associated with the second law of thermodynamics; the physical and psychological result of increasing entropy.
                        Time slows down when you approach the speed of light.
          4. n.          (physics, reductionistic definition) The property of a system which allows it to have more than one distinct configuration.
                        An essential definition of time should entail neither speed nor direction, just change.
          5. n. A duration of time.
          6. n.          A quantity of availability of duration.
                        More time is needed to complete the project.   You had plenty of time, but you waited until the last minute.   Are you finish
          7. n.          A measurement of a quantity of time; a numerical or general indication of a length of progression.
                        a long time;  Record the individual times for the processes in each batch.   Only your best time is compared with the other compet
          8. n.          (slang) The serving of a prison sentence.
                        The judge leniently granted a sentence with no hard time.   He is not living at home because he is doing time.
          9. n.          An experience.
                        We had a wonderful time at the party.
          10. n.          An era; (with the, sometimes in plural) the current era, the current state of affairs.
                        Roman times;  the time of the dinosaurs
          11. n.          (with possessive) A person's youth or young adulthood, as opposed to the present day.
                        In my time, we respected our elders.
          12. n.          (only in singular, sports) Time out; temporary, limited suspension of play.
          13. n. An instant of time.
          14. n.          How much of a day has passed; the moment, as indicated by a clock or similar device.
                        Excuse me, have you got the time?   What time is it, do you guess? Ten o’clock?   A computer keeps time using a clock battery
          15. n.          A particular moment or hour; the appropriate moment or hour for something (especially with prepositional phrase or imperfect subjunctive).
                        it’s time for bed;  it’s time to sleep;  we must wait for the right time;  it's time we were going
          16. n.          A numerical indication of a particular moment.
                        at what times do the trains arrive?;  these times were erroneously converted between zones
          17. n.          An instance or occurrence.
                        When was the last time we went out? I don’t remember.
                        see you another time;  that’s three times he’s made the same mistake
                        Okay, but this is the last time. No more after that!
          18. n.          (of pubs) Closing time.
                        Last call: it's almost time.
          19. n.          The hour of childbirth.
          20. n.          (as someone's time) The end of someone's life, conceived by the speaker as having been predestined.
                         It was his time.
          21. n. The measurement under some system of region of day or moment.
                Let's synchronize our watches so we're not on different time.
          22. n. Ratio of comparison.
                your car runs three times faster than mine;  that is four times as heavy as this
          23. n. (grammar, dated) Tense.
                the time of a verb
          24. n. (music) The measured duration of sounds; measure; tempo; rate of movement; rhythmical division.
                common or triple time;   the musician keeps good time.
          25. v. To measure or record the time, duration, or rate of.
                I used a stopwatch to time myself running around the block.
          26. v. To choose when something begins or how long it lasts.
                The President timed his speech badly, coinciding with the Super Bowl.
                The bomb was timed to explode at 9:20 p.m.
          27. v. (obsolete) To keep or beat time; to proceed or move in time.
          28. v. (obsolete) To pass time; to delay.
          29. v. To regulate as to time; to accompany, or agree with, in time of movement.
          30. v. To measure, as in music or harmony.
          31. interj. (tennis) Reminder by the umpire for the players to continue playing after their pause.
Dictionary entries from Wiktionary