Chirality in the context of Figure (geometry)

A shape is a graphical representation of an object's form or its external boundary, outline, or external surface. It is distinct from other object properties, such as color, texture, or material type.In geometry, shape excludes information about the object's position, size, orientation and chirality.A figure is a representation including both shape and size (as in, e.g., figure of the Earth).

A plane shape or plane figure is constrained to lie on a plane, in contrast to solid 3D shapes.A two-dimensional shape or two-dimensional figure (also: 2D shape or 2D figure) may lie on a more general curved surface (a two-dimensional space).

Acoustic metamaterials, sometimes referred to as sonic or phononic crystals, are architected materials designed to manipulate sound waves or phonons in gases, liquids, and solids. By tailoring effective parameters such as bulk modulus (β), density (ρ), and in some cases chirality, they can be engineered to transmit, trap, or attenuate waves at selected frequencies, functioning as acoustic resonators when local resonances dominate. Within the broader field of mechanical metamaterials, acoustic metamaterials represent the dynamic branch where wave control is the primary goal. They have been applied to model large-scale phenomena such as seismic waves and earthquake mitigation, as well as small-scale phenomena such as phonon behavior in crystals through band-gap engineering. This band-gap behavior mirrors the electronic band gaps in solids, enabling analogies between acoustic and quantum systems and supporting research in optomechanics and quantum technologies. In mechanics, acoustic metamaterials are particularly relevant for designing structures that mitigate vibrations, shield against blasts, or manipulate wave propagation in civil and aerospace systems.

Murray Gell-Mann (/ˈmʌri ˈɡɛl ˈmæn/; September 15, 1929 – May 24, 2019) was an American theoretical physicist who played a preeminent role in the development of the theory of elementary particles. Gell-Mann introduced the concept of quarks as the fundamental building blocks of the strongly interacting particles, and the renormalization group as a foundational element of quantum field theory and statistical mechanics. Murray Gell-Mann received the 1969 Nobel Prize in Physics for his contributions and discoveries concerning the classification of elementary particles and their interactions.

Gell-Mann played key roles in developing the concept of chirality in the theory of the weak interactions and spontaneous chiral symmetry breaking in the strong interactions, which controls the physics of the light mesons. In the 1970s he was a co-inventor of quantum chromodynamics (QCD) which explains the confinement of quarks in mesons and baryons and forms a large part of the Standard Model of elementary particles and forces.

Proarticulata (also known as Dickinsoniomorpha) is a phylum of extinct, near-bilaterally symmetrical animals known from fossils found in the Ediacaran (Vendian) marine deposits, and dates to approximately 567 to 550 million years ago. The name comes from the Greek προ (pro-) = "before" and Articulata, i.e. prior to animals with true segmentation such as annelids and arthropods. This phylum was established by Mikhail A. Fedonkin in 1985 for such animals as Dickinsonia, Vendia, Cephalonega, Praecambridium and currently many other Proarticulata are described (see list).

Due to their simplistic morphology, their affinities and mode of life are subject to debate. They are almost universally considered to be metazoans, and due to possessing a clear central axis have been suggested to be stem-bilaterians. In the traditional interpretation, the Proarticulatan body is divided into transverse articulation (division) into isomers as distinct from the transverse articulation segments in annelids and arthropods, as their individual isomers occupy only half the width of their bodies, and are organized in an alternating pattern along the longitudinal axis of their bodies. In other words, one side is not the direct mirror image of its opposite (chirality). Opposite isomers of left and right side are located with displacement of half of their width. This phenomenon is described as the symmetry of gliding reflection. Some recent research suggests that some proarticulatans like Dickinsonia have genuine segments, and the isomerism is superficial and due to taphonomic distortion. However, other researchers dispute this. Displacement of left-right axis is known in bilaterians, notably lancelets.

Alanine (symbol Ala or A), or α-alanine, is an α-amino acid that is used in the biosynthesis of proteins. It contains an amine group and a carboxylic acid group, both attached to the central carbon atom which also carries a methyl group side chain. Consequently it is classified as a non-polar, aliphatic α-amino acid. Under biological conditions, it exists in its zwitterionic form with its amine group protonated (as −NH+3) and its carboxyl group deprotonated (as −CO−2). It is non-essential to humans as it can be synthesized metabolically and does not need to be present in the diet. It is encoded by all codons starting with GC (GCU, GCC, GCA, and GCG).

The L-isomer of alanine (left-handed) is the one that is incorporated into proteins. L-alanine is second only to L-leucine in rate of occurrence, accounting for 7.8% of the primary structure in a sample of 1,150 proteins. The right-handed form, D-alanine, occurs in peptides in some bacterial cell walls (in peptidoglycan) and in some peptide antibiotics, and occurs in the tissues of many crustaceans and molluscs as an osmolyte.

Sinistral and dextral, in some scientific fields, are the two types of chirality ("handedness") or relative direction. The terms are derived from the Latin words for "left" (sinister) and "right" (dexter). Other disciplines use different terms (such as dextro- and laevo-rotary in chemistry, or clockwise and anticlockwise in physics) or simply use left and right (as in anatomy).

Relative direction and chirality are distinct concepts. Relative direction is from the point of view of the observer; a completely symmetric object has a left side and a right side, from the observer's point of view, if the top and bottom and direction of observation are defined. Chirality, however, is observer-independent: no matter how one looks at a right-hand screw thread, it remains different from a left-hand screw thread. Therefore, a symmetric object has sinistral and dextral directions arbitrarily defined by the position of the observer, while an asymmetric object that shows chirality may have sinistral and dextral directions defined by characteristics of the object, regardless of the position of the observer.

Celestial globes show the apparent positions of the stars in the sky. They omit the Sun, Moon, and planets because the positions of these bodies vary relative to those of the stars, but the ecliptic, along which the Sun moves, is indicated.

There is an issue regarding the "handedness" of celestial globes. If the globe is constructed so that the stars are in the positions they actually occupy on the imaginary celestial sphere, then the star field will appear reversed on the surface of the globe (all the constellations will appear as their mirror images). This is because the view from Earth, positioned at the centre of the celestial sphere, is of the gnomonic projection inside of the celestial sphere, whereas the celestial globe is orthographic projection as viewed from the outside. For this reason, celestial globes are often produced in mirror image, so that at least the constellations appear as viewed from Earth. This ambiguity is famously evident in the astronomical ceiling of New York City's Grand Central Terminal, whose inconsistency was deliberately left uncorrected though it was noticed shortly after installation.

A cyclic compound (or ring compound) is a term for a compound in the field of chemistry in which one or more series of atoms in the compound is connected to form a ring. Rings may vary in size from three to many atoms, and include examples where all the atoms are carbon (i.e., are carbocycles), none of the atoms are carbon (inorganic cyclic compounds), or where both carbon and non-carbon atoms are present (heterocyclic compounds with rings containing both carbon and non-carbon). Depending on the ring size, the bond order of the individual links between ring atoms, and their arrangements within the rings, carbocyclic and heterocyclic compounds may be aromatic or non-aromatic; in the latter case, they may vary from being fully saturated to having varying numbers of multiple bonds between the ring atoms. Because of the tremendous diversity allowed, in combination, by the valences of common atoms and their ability to form rings, the number of possible cyclic structures, even of small size (e.g., < 17 total atoms) numbers in the many billions.

• Cyclic compound examples: All-carbon (carbocyclic) and more complex natural cyclic compounds
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  Cycloalkanes, the simplest carbocycles, including cyclopropane, cyclobutane, cyclopentane, and cyclohexane. Note, elsewhere an organic chemistry shorthand is used where hydrogen atoms are inferred as present to fill the carbon's valence of 4 (rather than their being shown explicitly).
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  Ingenol, a complex, terpenoid natural product, related to but simpler than the paclitaxel that follows, which displays a complex ring structure including 3-, 5-, and 7-membered non-aromatic, carbocyclic rings.
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  Paclitaxel, another complex, plant-derived terpenoid, also a natural product, displaying a complex multi-ring structure including 4-, 6-, and 8-membered rings (carbocyclic and heterocyclic, aromatic and non-aromatic).

Adding to their complexity and number, closing of atoms into rings may lock particular atoms with distinct substitution (by functional groups) such that stereochemistry and chirality of the compound results, including some manifestations that are unique to rings (e.g., configurational isomers). As well, depending on ring size, the three-dimensional shapes of particular cyclic structures – typically rings of five atoms and larger – can vary and interconvert such that conformational isomerism is displayed. Indeed, the development of this important chemical concept arose historically in reference to cyclic compounds. Finally, cyclic compounds, because of the unique shapes, reactivities, properties, and bioactivities that they engender, are the majority of all molecules involved in the biochemistry, structure, and function of living organisms, and in man-made molecules such as drugs, pesticides, etc.

The Left Hand of the Electron is a collection of seventeen nonfiction science essays by American writer and scientist Isaac Asimov, first published by Doubleday & Company in 1972. It was the ninth of a series of books collecting essays from The Magazine of Fantasy and Science Fiction. The title comes from the topic of the first section which deals with chirality of electroweak interactions and chirality of organic compounds and the possible connection between the two. Other essays in this book concern the effect of electron-spin direction on molecular structure e.g. the "Inverse Sugar" (similar to Inverted sugar syrup) in honey with philosophical reflections on the minority of left handedness in general.