# shape

This hashtag in English

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A shape is the form of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type.

Some simple shapes can be put into broad categories . For instance, polygons are classified according to their number of edges as triangles, quadrilaterals, pentagons, etc. Each of these is divided into smaller categories; triangles can be equilateral, isosceles, obtuse, acute, scalene, etc. while quadrilaterals can be rectangles, rhombi, trapezoids, squares, etc.

Other common shapes are points, lines, planes, and conic sections such as ellipses, circles, and parabolas.

Among the most common 3-dimensional shapes are polyhedra, which are shapes with flat faces; ellipsoids, which are egg-shaped or sphere-shaped objects; cylinders; and cones.

If an object falls into one of these categories exactly or even approximately, we can use it to describe the shape of the object. Thus, we say that the shape of a manhole cover is a disk, because it is approximately the same geometric object as an actual geometric disk.

A geometric shape is the geometric information which remains when location, scale, orientation and reflection are removed from the description of a geometric object. That is, the result of moving a shape around, enlarging it, rotating it, or reflecting it in a mirror is the same shape as the original, and not a distinct shape.

Many two-dimensional geometric shapes can be defined by a set of points or vertices and lines connecting the points in a closed chain, as well as the resulting interior points. Such shapes are called polygons and include triangles, squares, and pentagons. Other shapes may be bounded by curves such as the circle or the ellipse.

Many three-dimensional geometric shapes can be defined by a set of vertices, lines connecting the vertices, and two-dimensional faces enclosed by those lines, as well as the resulting interior points. Such shapes are called polyhedrons and include cubes as well as pyramids such as tetrahedrons. Other three-dimensional shapes may be bounded by curved surfaces, such as the ellipsoid and the sphere.

A shape is said to be convex if all of the points on a line segment between any two of its points are also part of the shape.

There are several ways to compare the shapes of two objects:

Sometimes, two similar or congruent objects may be regarded as having a different shape if a reflection is required to transform one into the other. For instance, the letters "b" and "d" are a reflection of each other, and hence they are congruent and similar, but in some contexts they are not regarded as having the same shape. Sometimes, only the outline or external boundary of the object is considered to determine its shape. For instance, a hollow sphere may be considered to have the same shape as a solid sphere. Procrustes analysis is used in many sciences to determine whether or not two objects have the same shape, or to measure the difference between two shapes. In advanced mathematics, quasi-isometry can be used as a criterion to state that two shapes are approximately the same.

Simple shapes can often be classified into basic geometric objects such as a point, a line, a curve, a plane, a plane figure (e.g. square or circle), or a solid figure (e.g. cube or sphere). However, most shapes occurring in the physical world are complex. Some, such as plant structures and coastlines, may be so complicated as to defy traditional mathematical description – in which case they may be analyzed by differential geometry, or as fractals.

In geometry, two subsets of a Euclidean space have the same shape if one can be transformed to the other by a combination of translations, rotations (together also called rigid transformations), and uniform scalings. In other words, the shape of a set of points is all the geometrical information that is invariant to translations, rotations, and size changes. Having the same shape is an equivalence relation, and accordingly a precise mathematical definition of the notion of shape can be given as being an equivalence class of subsets of a Euclidean space having the same shape.

Mathematician and statistician David George Kendall writes:

In this paper ‘shape’ is used in the vulgar sense, and means what one would normally expect it to mean. [...] We here define ‘shape’ informally as ‘all the geometrical information that remains when location, scale and rotational effects are filtered out from an object.’

Shapes of physical objects are equal if the subsets of space these objects occupy satisfy the definition above. In particular, the shape does not depend on the size and placement in space of the object. For instance, a "d" and a "p" have the same shape, as they can be perfectly superimposed if the "d" is translated to the right by a given distance, rotated upside down and magnified by a given factor (see Procrustes superimposition for details). However, a mirror image could be called a different shape. For instance, a "b" and a "p" have a different shape, at least when they are constrained to move within a two-dimensional space like the page on which they are written. Even though they have the same size, there's no way to perfectly superimpose them by translating and rotating them along the page. Similarly, within a three-dimensional space, a right hand and a left hand have a different shape, even if they are the mirror images of each other. Shapes may change if the object is scaled non-uniformly. For example, a sphere becomes an ellipsoid when scaled differently in the vertical and horizontal directions. In other words, preserving axes of symmetry (if they exist) is important for preserving shapes. Also, shape is determined by only the outer boundary of an object.

Objects that can be transformed into each other by rigid transformations and mirroring (but not scaling) are congruent. An object is therefore congruent to its mirror image (even if it is not symmetric), but not to a scaled version. Two congruent objects always have either the same shape or mirror image shapes, and have the same size.

Objects that have the same shape or mirror image shapes are called geometrically similar, whether or not they have the same size. Thus, objects that can be transformed into each other by rigid transformations, mirroring, and uniform scaling are similar. Similarity is preserved when one of the objects is uniformly scaled, while congruence is not. Thus, congruent objects are always geometrically similar, but similar objects may not be congruent, as they may have different size.

A more flexible definition of shape takes into consideration the fact that realistic shapes are often deformable, e.g. a person in different postures, a tree bending in the wind or a hand with different finger positions.

One way of modeling non-rigid movements is by homeomorphisms. Roughly speaking, a homeomorphism is a continuous stretching and bending of an object into a new shape. Thus, a square and a circle are homeomorphic to each other, but a sphere and a donut are not. An often-repeated mathematical joke is that topologists cannot tell their coffee cup from their donut, since a sufficiently pliable donut could be reshaped to the form of a coffee cup by creating a dimple and progressively enlarging it, while preserving the donut hole in a cup's handle.

A described shape has external lines that you can see and make up the shape. If you were putting you coordinates on and coordinate graph you could draw lines to show where you can see a shape, however not every time you put coordinates in a graph as such you can make a shape. This shape has a outline and boundary so you can see it and is not just regular dots on a regular paper.

The above-mentioned mathematical definitions of rigid and non-rigid shape have arisen in the field of statistical shape analysis. In particular, Procrustes analysis is a technique used for comparing shapes of similar objects (e.g. bones of different animals), or measuring the deformation of a deformable object. Other methods are designed to work with non-rigid (bendable) objects, e.g. for posture independent shape retrieval (see for example Spectral shape analysis).

All similar triangles have the same shape. These shapes can be classified using complex numbers u, v, w for the vertices, in a method advanced by J.A. Lester and Rafael Artzy. For example, an equilateral triangle can be expressed by the complex numbers 0, 1, (1 + i √3)/2 representing its vertices. Lester and Artzy call the ratio

the shape of triangle (u, v, w). Then the shape of the equilateral triangle is

For any affine transformation of the complex plane, ${\displaystyle z\mapsto az+b,\quad a\neq 0,}$   a triangle is transformed but does not change its shape. Hence shape is an invariant of affine geometry. The shape p = S(u,v,w) depends on the order of the arguments of function S, but permutations lead to related values. For instance,

Combining these permutations gives ${\displaystyle S(v,w,u)=(1-p)^{-1}.}$ Furthermore,

The shape of a quadrilateral is associated with two complex numbers p,q. If the quadrilateral has vertices u,v,w,x, then p = S(u,v,w) and q = S(v,w,x). Artzy proves these propositions about quadrilateral shapes:

A polygon ${\displaystyle (z_{1},z_{2},...z_{n})}$ has a shape defined by n – 2 complex numbers ${\displaystyle S(z_{j},z_{j+1},z_{j+2}),\ j=1,...,n-2.}$ The polygon bounds a convex set when all these shape components have imaginary components of the same sign.

Psychologists have theorized that humans mentally break down images into simple geometric shapes called geons. Examples of geons include cones and spheres. A wide range of other shape representations have also been investigated. Shape features seem to boil down to three basic dimensions: segmentability, compactness and spikiness.

There is also clear evidence that shapes guide human attention.

Having trouble understanding the new coronavirus variants? Here's an illustrated guide. It uses Lego parts to sho…
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The shape of Itadori's strength (via @Jujutsu_Kaisen_)
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42 in May and feel like I'm 21. More experienced, smarter, wiser, more responsible and highly blessed to be alive a…
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@Donzoao trabalhando &amp; metendo o shape
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I understand...... I'm in no shape to carry out revenge like this.
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#NowPlaying Ed Sheeran - Shape Of You | Listen Live On Stream Our 'New Release of The Week…
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@CAwkward @EmilyGould @daniel_m_lavery @stoya Thank you for the excellent answers - they helped shape this a lot!
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this is so upsetting. this should've never happened to her or any other athlete. i really, really hope that she's a…
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Shape of Water, at its TIFF premiere, with GDT and the cast, in the theatre where part of the movie was filmed
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RT @zackfox: breast implants gonna be wild when you can switch up the shape and get some hexagons just to stunt
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I gotta stop thinking that watching others workout, will get me In shape
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RT @MissMattieMac: @EricBoehlert In the shape of a Q
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@rickyjalapeno @RHonMooncalf @TheBrinz @JWilliamJames Lol that just means that the data is normalized, not that it'…
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@JustinnBih @greysweatsking Yesss 🤪 I think it depends on the shape of your vaginal canal and where your cervix sits
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Check out Jillian Michaels - Shape Up: Front (DVD, 2005) Free Shipping via @eBay #ForSale…
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I honestly find Alyssa attractive and beautiful, walang echos I wish I had her nose and the shape of her face hehe peace y'all
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RT @jimmymarks: Pretty weird flex to have your restaurant be in the shape of the one food you can never dependably provide.
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RT @plxyboihurting: Why the last shape ?
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@guytro I would love a chat with him. Last I heard, he was in bad shape. If he’s recovered enough and willing to s…
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RT @zackfox: breast implants gonna be wild when you can switch up the shape and get some hexagons just to stunt
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Some thoughts about the budget, since many in the replies, have been keen to know:: Post-COVID economic recovery is…
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Republicans think it’s normal to say, “Democrats kill babies”, but get all bent out of shape when Democrats talk ab…
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RT @noellecrombie: Link to the story:
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@TyfIow @RavenSoftware It’s bound to come back in some shape or form
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@JackPosobiec twitter needs a grumpy face to click on because i can not click on the heart shape for this
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RT @LilRJUnlimited: @TerryEr26560882 Lol in high school I took some supplements that turned out to be some weird form of steroids that cut…
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@ayysmokey42 Shape it don’t shave it😭😭😭
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RT @randyrichard2: Finally covid shape is going away and back to where I use to be !! #keepitgoing
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RT @AETCommand: During our recent virtual two-day Leadership Mentoring Symposium, leaders across the command shared their experience of bei…
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RT @IlhanMN: Republicans think it’s normal to say, “Democrats kill babies”, but get all bent out of shape when Democrats talk about how the…
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RT @Ujac4: Quick tidbit on abs. A lot of the abs is defined by the shape of the obliques and ribcage, you can't draw one without the other.…
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@SilvestriCodes @sudo_echo @NehemiahKiv this tweet and response is some virgin // chad meme shit right down to the shape of this dude's chin
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RT @CreatorsAssemb: Creators Assemble needs YOU! Seeking new Board members to help shape our 1 year old org. If you're looking for a great…
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RT @Deloitte: Words and actions can impact us both positively and negatively – they shape our stories. It is within all our power to make t…
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#sexy isnt a shape, its an attitude😉💙
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@pastoralcomical pretty flowers too
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Free printable shapes worksheets for toddlers and preschoolers. Preschool shapes activities such as find and color, tracing shapes and shapes coloring pages. #prek #preschool
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A free to download printable for engaging toddlers and create cute and funny animals with Shapes. A preschool activity for little kids, A brain teaser for little tykes, A creative way to engage the children.
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Preschool Shapes Printables - Making Shapes Fine Motor Activity #preschoolprintables #2dshapes #2dshapesprintables #planningplaytime
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FREE Ocean Preschool Centers sort the 2d shaped fish to the correct fishbowl
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Araba yolu şekiller
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Üçgen kavramı çalışma sayfası ve üçgen geometrik şekiller kavramı çalışmaları etkinliği oyunu örnekleri kağıdı indirme, çıktı yazdırma. Free triangle worksheets download printable.
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Katmerli Açma Poğaça Tarifi
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2D Şekiller
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Shape Sorting Activities for Toddlers from Minne Mama
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##### shape Pinterest Ideas
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e ëmbel po thojn 🍬 . . . . . . . #albanian #shqipe #instagram #instadaily #instalike #photo #photography #fancy #mood #details #openbacksweater #promotion #motivation #inspiration #makeup #fashion #fashioninspiration #outfit #outfitoftheday #zara #lucieandleo #levis #levisjeans #swarovski #fitness #fitnessmotivation #body #shape #skin
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Ehh to nie do końca był mój tydzień i chyba dobrze, że się kończy... A zapowiadał się całkiem fajnie. Niestety są rzeczy, na które nie do końca mamy wpływ, #sibo w tym tygodniu pokazało rożki ☹️ na pocieszenie dziś wpadła #cardiomasakra i jakoś tak samopoczucie od razu lepsze 😉 . #training #gym #gymtime #siłownia #weekend #bodybuilding #stepbystep #shape #fitbody #strongbody #strongwomen #abs #athlete #personaltrainer #cardio #model #muscle #bodyinprogress #selfie #instafit #fitfam #sportstyle #lifestyle #legs #gymfreak #bodygoals #followｍe #fitness
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OC Sexy and badass✨ Follow me for more (what you think??) I love comments 💪🏻 @itsajart . . . . #beautiful #model #drawing #sketch #explore #art #hiddentalent #instagram #supportmme #talent #itsajart #girl #shape
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Training partner ✊🙏💪 . Tu n'as pas besoin d être au top pour commencer, mais TU dois COMMENCER pour être au TOP . #motivation #girlpower #fitnessgirl . @CROSSBOX1000 🔥🔥 #crossbox1000 #sportlife #anderlecht #belgium #instagram #fitness #fit #shape
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#custom #decoart #shape #shapes #surfboard #lovesea #surf #surfboards #desing #surfing #colors #board #indoor #home #vintage #retro #valenciasurf #windsurf #customsurfboard #slap #flow #shapesurfboard #foam #hands #worldsurf #surfworld #decosurf #art #interiorismo #decoration
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„𝑯𝒂𝒑𝒑𝒊𝒏𝒆𝒔𝒔 𝒊𝒔, 𝒘𝒉𝒆𝒏 𝒖 𝒇𝒆𝒆𝒍 𝒈𝒐𝒐𝒅 𝒂𝒃𝒐𝒖𝒕 𝒚𝒐𝒖𝒓𝒔𝒆𝒍𝒇 𝒘𝒊𝒕𝒉𝒐𝒖𝒕 𝒇𝒆𝒆𝒍𝒊𝒏𝒈 𝒕𝒉𝒆 𝒏𝒆𝒆𝒅 𝒇𝒐𝒓 𝒂𝒏𝒚𝒐𝒏𝒆 𝒆𝒍𝒔𝒆‘𝒔 𝒂𝒑𝒑𝒓𝒐𝒗𝒂𝒍.“ ________________________________________ Das Leben nach einer Beziehung mit einem Narzissten. Da ich so unfassbar viel positive Resonanz von beiden Geschlechtern bekommen habe, werde ich ein kleines Tagebuch (was Insta für mich ja eh schon ist) über meinen Weg zur Freiheit führen, nachdem ich der missbräuchlichen Beziehung entflohen bin. Wie geht es nun eigentlich weiter, nachdem man der Hölle entkommen konnte? Ganz einfach , man muss den Kontakt KOMPLETT abbrechen, und dann gehts Schritt für Schritt weiter. Ich wurde während der gemeinsamen Zeit für meine Verhältnisse extrem isoliert / habe in einer neuen Stadt keine wirklichen Freundschaften geschlossen und bis aufs gym auch keine sozialen Kontakte gehabt. Und selbst die im Studio wurden massiv eingeschränkt, da ich bei normalem smalltalk schon capslock sms bekam, warum ich mit XY rede. Ja, irgendwelche Menschen haben mich beobachtet und alles weitergeleitet. Das Fußvolk der Narzissten gibt es überall. Je mehr Terror kam, umso mehr habe ich mich weiter zurückgezogen. Nicht zu vergessen, dass der Narzisst sich in seiner freien Zeit mit allen möglichen Frauen getroffen hat. Aber er selber rechtfertigt ja alles irgendwie. Nun gut, das Wichtigste am Anfang ist eine Struktur. Ich ging zur Arbeit, ins Gym und mit meinen Hunden raus. Durch die lange psychische Abhängigkeit, die der Narzisst geschaffen hat, erscheint einem das Leben alleine völlig leer und es dauert, bis man die seelischen Splitter wieder zusammensetzen kann. Ich habe mich auf mich selbst konzentriert, Dinge unternommen, auch wenn mir nicht danach war, und neue Kontakte zu neuen Menschen aufgebaut - die der Narzisst NICHT zu seinen Bekannten zählen kann. Aber die Wichtigste Zutat ist: Zeit. Am Anfang denkt man, man würde nie wieder glücklich und sitzt in einem tiefen Loch. Unvorstellbar, dass man sich je wieder „heil“ fühlen, oder sich neu verlieben könnte. Aber es wird gut - das kann ich bestätigen. Ich bin heute glücklicher denn je. ♥️
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#frenchgirl #french #girl #bordeaux #bordeauxmaville #blonde #blondie #blondegirl #blondehair #longhair #shape #fitgirl #fitnessgirl #bikini #happy #smile #picoftheday #potd #summer #laurafitness
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Always in shape with my favorite meal prep @megafitmeals 🔥🔥🔥#fitness #motivation #meals #shape
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Suite de cette série avec la charmante Adeline  avec qui j'ai eu le plaisir de faire ce cliché à Angers @insta_promo.ig ', . : ' .  #fitfrenchies #french #photographeangers #fitfrenchie #lingerie #lingeriefitness #fitnesslingerie #fitnessmodel #fitnesslifestyle #fitnessgirl #fitness #trening #girlmotivation #shape #fitbody #muscles #fitshape #lovesport #stronggirl #healthy #fit  #fitnessgirl #gymgirl #brunette #hobbymodel #beautyportraits #womanmodel #modelwerk #indoorphotography #modeltime #modelshooting
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