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Centroid in Scrabble and Meaning

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What does centroid mean? Is centroid a Scrabble word?

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Is centroid a Scrabble word?

Yes. The word centroid is a Scrabble US word. The word centroid is worth 11 points in Scrabble:

C3E1N1T1R1O1I1D2

Is centroid a Scrabble UK word?

Yes. The word centroid is a Scrabble UK word and has 11 points:

C3E1N1T1R1O1I1D2

Is centroid a Words With Friends word?

Yes. The word centroid is a Words With Friends word. The word centroid is worth 13 points in Words With Friends (WWF):

C4E1N2T1R1O1I1D2

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Valid words made from Centroid

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8-letter words (2 found)

CENTROID,DOCTRINE,

7-letter words (7 found)

COINTER,CORDITE,CTENOID,DEONTIC,NOTICED,NOTICER,RECTION,

6-letter words (44 found)

CINDER,CITRON,CODEIN,COEDIT,COINED,COINER,CONDER,CONDIE,CORNED,CORNET,CORTIN,CREDIT,CRETIN,CRINED,CRONET,DINERO,DIRECT,DITONE,DOCENT,DOTIER,EDITOR,EROTIC,INTOED,IRONED,NERDIC,NOETIC,NORDIC,NORITE,NOTICE,OINTED,ORCEIN,ORCINE,ORIENT,RECOIN,RIDENT,RIOTED,RODENT,ROINED,TERCIO,TINDER,TONIER,TRICED,TRINED,TRIODE,

5-letter words (70 found)

CENTO,CIDER,CITED,CITER,CODEN,CODER,CONED,CONTE,CORED,CORNI,COTED,CREDO,CRIED,CRINE,CRONE,DECOR,DICER,DICOT,DINER,DONER,DORIC,DOTER,DRENT,DRICE,DROIT,DRONE,EDICT,IDENT,INERT,INTER,INTRO,IRONE,NICER,NIDOR,NITER,NITRE,NITRO,NOTED,NOTER,ONCER,ONCET,ONTIC,ORCIN,RECIT,RECON,RECTI,RECTO,REDON,RICED,RONDE,RONTE,ROTED,TEIND,TENOR,TICED,TINED,TIRED,TONDI,TONED,TONER,TONIC,TORIC,TREND,TRICE,TRIDE,TRIED,TRINE,TRODE,TRONC,TRONE,

4-letter words (115 found)

CEDI,CENT,CERO,CERT,CIDE,CINE,CION,CIRE,CITE,CITO,CODE,COED,COID,COIN,COIR,COIT,COND,CONE,CONI,CORD,CORE,CORN,COTE,CRED,CRIT,CRON,DECO,DENI,DENT,DERN,DERO,DICE,DICT,DIET,DINE,DINO,DINT,DIRE,DIRT,DITE,DOEN,DOER,DOIT,DONE,DORE,DORT,DOTE,ECOD,EDIT,ERIC,ETIC,ICED,ICER,ICON,INRO,INTO,IRED,IRON,NERD,NICE,NIDE,NIED,NITE,NODE,NODI,NOIR,NORI,NOTE,ODIC,OINT,ONCE,ONER,ONIE,OTIC,REDO,REIN,REND,RENO,RENT,RICE,RIDE,RIND,RINE,RIOT,RITE,RODE,ROED,ROID,ROIN,RONE,RONT,ROTE,ROTI,TEIN,TEND,TERN,TICE,TIDE,TIED,TIER,TIND,TINE,TIRE,TIRO,TOED,TONE,TORC,TORE,TORI,TORN,TRIE,TRIN,TRIO,TROD,TRON,

3-letter words (63 found)

CID,CIT,COD,CON,COR,COT,DEI,DEN,DIE,DIN,DIT,DOC,DOE,DON,DOR,DOT,ECO,END,EON,ERN,ICE,IDE,ION,IRE,NED,NET,NID,NIE,NIT,NOD,NOR,NOT,ODE,ONE,ORC,ORD,ORE,ORT,REC,RED,REI,REN,REO,RET,RID,RIN,RIT,ROC,ROD,ROE,ROT,TEC,TED,TEN,TIC,TID,TIE,TIN,TOC,TOD,TOE,TON,TOR,

2-letter words (22 found)

DE,DI,DO,ED,EN,ER,ET,ID,IN,IO,IT,NE,NO,OD,OE,OI,ON,OR,RE,TE,TI,TO,

1-letter words (1 found)

E,

You can make 324 words from centroid according to the Scrabble US and Canada dictionary.

Definitions and meaning of centroid

centroid

Etymology

From centre +‎ -oid. From 1844, used as a replacement for the older terms "centre of gravity" and "centre of mass" in situations described in purely geometrical terms, and subsequently used for further generalisations.

Noun

centroid (plural centroids)

  1. (geometry, physics, engineering, of an object or a geometrical figure) The point at which gravitational force (or other universally and uniformly acting force) may be supposed to act on a given rigid, uniformly dense body; the centre of gravity or centre of mass.
    • 2020, Cheng Zhang, Qiuchi Li, Lingyu Hua, Dawei Song, Assessing the Memory Ability of Recurrent Neural Networks, Giuseppe De Giacomo, et al. (editors), ECAI 2020: 24th European Conference on Artificial Intelligence, IOS Press, page 1660,
      In R n {\displaystyle \mathbb {R} ^{n}} , a centroid is the mean position of all the points in all of the coordinate directions. The centroid of a subset X {\displaystyle {\mathcal {X}}} of R n {\displaystyle \mathbb {R} ^{n}} is computed as follows:
      Centroid ⁡ ( X ) = ∫ x g ( x ) d x ∫ g ( x ) d x ( 6 ) {\displaystyle \operatorname {Centroid} ({\mathcal {X}})={\frac {\int xg(x)dx}{\int g(x)dx}}\quad \quad \quad \quad \quad \quad (6)}
      where the integrals are taken over the whole space R n {\displaystyle \mathbb {R} ^{n}} , and g {\displaystyle g} is the characteristic function of the subset, which is 1 inside X {\displaystyle {\mathcal {X}}} and 0 outside it [27].
  2. (geometry, specifically, of a triangle) The point of intersection of the three medians of a given triangle; the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of the three vertices.
  3. (of a finite set of points) the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of a given finite set of points.
  4. (mathematical analysis, of a function) An analogue of the centre of gravity of a nonuniform body in which local density is replaced by a specified function (which can take negative values) and the place of the body's shape is taken by the function's domain.
  5. (statistics, cluster analysis, of a cluster of points) the arithmetic mean (alternatively, median) position of a cluster of points in a coordinate system based on some application-dependent measure of distance.
  6. (graph theory, of a tree) Given a tree of n nodes, either (1) a unique node whose removal would split the tree into subtrees of fewer than n/2 nodes, or (2) either of a pair of adjacent nodes such that removal of the edge connecting them would split the tree into two subtrees of exactly n/2 nodes.
    • 1974 [Prentice-Hall], Narsingh Deo, Graph Theory with Applications to Engineering and Computer Science, 2017, Dover, page 248,
      Just as in the case of centers of a tree (Section 3-4), it can be shown that every tree has either one centroid or two centroids. It can also be shown that if a tree has two centroids, the centroids are adjacent.
    • 2009, Hao Yuan, Patrick Eugster, An Efficient Algorithm for Solving the Dyck-CFL Reachability Problem on Trees, Giuseppe Castagna (editor), Programming Languages and Systems: 18th European Symposium, Proceedings, Springer, LNCS 5502, page 186,
      A node x {\displaystyle x} in a tree T {\displaystyle T} is called a centroid of T {\displaystyle T} if the removal of x {\displaystyle x} will make the size of each remaining connected component no greater than | T | / 2 {\displaystyle \vert T\vert /2} . A tree may have at most two centroids, and if there are two then one must be a neighbor of the other [6, 5]. Throughout this paper, we specify the centroid to be the one whose numbering is lexicographically smaller (i.e, we number the nodes from 1 to n {\displaystyle n} ). There exists a linear time algorithm to compute the centroid of a tree due to the work of Goldman [21]. We use CT ⁡ ( T ) {\displaystyle \operatorname {CT} (T)} to denote the centroid of T {\displaystyle T} computed by the linear time algorithm.

Usage notes

(centre of gravity and related senses):

  • The term centroid is an approximate synonym of centre of gravity and centre of mass, applied in mathematically abstract situations where the concepts of mass and gravity are not invoked. It may also be called centre of area or centre of volume.
  • Another near synonym is barycentre, which is differently nuanced. It tends to be used in situations where mass is relevant:
    • In geometry, barycentre is a synonym of centroid.
    • In physics, barycentre refers to the centre of gravity of an object that is not (or is not assumed to be) of uniform density.
    • Specifically in astronomy and astrophysics, barycentre refers to the centre of gravity in a system of (usually two, but possibly more) objects that are in orbit around each other. See also Two-body problem on Wikipedia.Wikipedia
  • In geography, the geographical centre of a region of the Earth's surface is the centroid of the radial projection of said region onto sea level. (Depending on the size of the region, it may in fact be significantly below sea level.)

(graph theory: type of node in a tree):

  • Any given tree has either one centroid or two. A tree with one centroid is said to be centroidal; one that has two is bicentroidal.

Synonyms

  • (centre of gravity of a uniform, rigid object): barycentre, centre of area, centre of gravity, centre of mass, centre of volume, geometric centre, geometric centroid
  • (centre of gravity of a set of points of equal mass): barycentre, centre of gravity, centre of mass
  • (centroid of a function): function centroid
  • (cluster theory: arithmetic mean or median position of points in a cluster):
  • (graph theory: type of node in a tree): tree centroid

Derived terms

  • bicentroidal
  • centroidal
  • centroiding
  • function centroid
  • geometric centroid

Translations

See also

  • barycentre / barycenter
  • geographical centre

References

Further reading

  • Center of mass on Wikipedia.Wikipedia
  • List of centroids on Wikipedia.Wikipedia
  • Barycenter on Wikipedia.Wikipedia
  • Euler line on Wikipedia.Wikipedia
  • Triangle center on Wikipedia.Wikipedia
  • Locating the center of mass on Wikipedia.Wikipedia
  • k-means clustering on Wikipedia.Wikipedia
  • Barycentric coordinate system on Wikipedia.Wikipedia
  • Cluster analysis on Wikipedia.Wikipedia
  • Fréchet mean on Wikipedia.Wikipedia
  • Centroid on Encyclopedia of Mathematics
  • Geometric Centroid on Wolfram MathWorld
  • Centroid Point on Wolfram MathWorld
  • Triangle Centroid on Wolfram MathWorld
  • Function Centroid on Wolfram MathWorld

Anagrams

  • Crediton, doctrine, on credit

Source: wiktionary.org