For cyclopropane, the bent bond model continues to have support despite the emergence of other theories such as Walsh orbitals, which aimed to do a better job fitting molecular orbital theory in light of spectroscopic evidence and group symmetry arguments.

Douglass found Af to be trigonal, Laue symmetry Af, with Af, Af.

However, the possible absence of a center of symmetry not only moves the hydrogen atom off Af, but also allows the oxygen atoms to become nonequivalent, with Af at Af and Af at Af ( space group Af ), where Af represents the oxygens on one side of the Af layers and Af those on the other side.

Mainly concerned with geometry and symmetry rather than individual expression.

They can all be made via Wythoff constructions from the Platonic solids with tetrahedral, octahedral and icosahedral symmetry.

Hogarth, for example, thinks that beauty consists of ( 1 ) fitness of the parts to some design ; ( 2 ) variety in as many ways as possible ; ( 3 ) uniformity, regularity or symmetry, which is only beautiful when it helps to preserve the character of fitness ; ( 4 ) simplicity or distinctness, which gives pleasure not in itself, but through its enabling the eye to enjoy variety with ease ; ( 5 ) intricacy, which provides employment for our active energies, leading the eye on " a wanton kind of chase "; and ( 6 ) quantity or magnitude, which draws our attention and produces admiration and awe.

For an object with a fixed mass that is rotating about a fixed symmetry axis, the angular momentum is expressed as the product of the moment of inertia of the object and its angular velocity vector:

For an object with a fixed mass that is rotating about a fixed symmetry axis,

Outcomes based research on quality of life improvements and psychosocial benefits associated with breast reconstruction served as the stimulus in the United States for the 1998 Women's Health and Cancer Rights Act, which mandated health care payer coverage for breast and nipple reconstruction, contralateral procedures to achieve symmetry, and treatment for the sequelae of mastectomy.

Furthermore, the symmetry of the breasts, and the general symmetry of the human body, influence what men and women consider physical attractiveness in a mate with whom to reproduce.

Therefore, because the breasts are especially sensitive to developmental interference ( genetic and environmental ), breast symmetry indicates a woman of good health and thus of good breeding stock, who shall successfully bear more ( surviving ) children than will a woman with asymmetrical breasts.

Goldstone's theorem in quantum field theory states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstone bosons.

It consists of one carbon atom surrounded by three oxygen atoms, in a trigonal planar arrangement, with D < sub > 3h </ sub > molecular symmetry.

This structure is incompatible with the observed symmetry of the ion, which implies that the three bonds are equally long and that the three oxygen atoms are equivalent.

The symmetry of a crystal is constrained by the requirement that the unit cells stack perfectly with no gaps.

The number of ligands that react with a central metal atom can be found using the 18-electron rule, saying that the valence shells of a transition metal will collectively accommodate 18 electrons, whereas the symmetry of the resulting complex can be predicted with the crystal field theory and ligand field theory.

A column with a cross section that lacks symmetry may suffer torsional buckling ( sudden twisting ) before, or in combination with, lateral buckling.

Face-centered cubic ( fcc ) structures differ from hexagonal close packed ( hcp ) structures only in stacking order: both structures have close packed atomic planes with sixfold symmetry — the atoms form equilateral triangles.

Ellipses arise from the intersection of a right circular cylinder with a plane that is not parallel to the cylinder's main axis of symmetry.

However, this work has been subject to much criticism by quantum chemists as it was concluded that the predicted I < sub > h </ sub > symmetric structure was vibrationally unstable and the resulting cage undergoes a spontaneous symmetry break, yielding a puckered cage with rare T < sub > h </ sub > symmetry ( symmetry of a volleyball ).

Aristotle had postulated a symmetry of the earth, which meant that there would be equally habitable lands south of the known world.

Magnets have north and south poles that are oriented in a specific direction, breaking rotational symmetry.

It is known that there were caves on the south west edge of Wahanga and that the symmetry of the Wahanga peak was upset by the 1886 rift.

* Monopoles, point-like defects that form when a spherical symmetry is broken, are predicted to have magnetic charge, either north or south ( and so are commonly called " magnetic monopoles ").

The building is entered through the south side through two separate doorways, each with Corinthian columns distyle in antis, thus immediately establishing symmetry within the plan of the structure.

There is a lack of symmetry to the chancel, the arches on the north and south walls do not match and half of an arch has been stopped off.

The building's main entrance, which is accessed by scaling 32 steps, uses both symmetry and transparency as themes for its large central glass walls that compose the majority of both the east and west façades of the building.

Following the 1974 season, the school's first as Boise State University, an upper deck was added to the east side ( photo-1971 )-( photo-1975 ), adding 5, 500 seats as well as symmetry to the stadium.

Other buildings significant to the design and symmetry of the triangle are the High Court and the National Gallery, located near the lake, forward of Old Parliament house and to the east, and the National Library and the National Science and Technology Centre ( or Questacon ) located forward of Old Parliament House and to the west.

" After that he realized that there is not much " symmetry between a cancer cell and a normal one.

The theory of baryogenesis was worked out by Andrei Sakharov in 1967, and requires a violation of the particle physics symmetry, called CP-symmetry, between matter and antimatter.

As in the case of the isoelectronic nitrate ion, the symmetry can be achieved by a resonance between three structures:

Therefore, the often-perceived symmetry between Mahāyāna and Hīnayāna can be deceptive, as the terms were not actually coined in relation to one another in the same era.

Consistent with the symmetry of the hyperbola, if the transverse axis is aligned with the x-axis of a Cartesian coordinate system, the slopes of the asymptotes are equal in magnitude but opposite in sign, ±, where b = a × tan ( θ ) and where θ is the angle between the transverse axis and either asymptote.

There is a symmetry between a function and its inverse.

The motion of the top can be described by three Euler angles: the tilt angle between the symmetry axis of the top and the vertical ; the azimuth of the top about the vertical ; and the rotation angle of the top about its own axis.

However, X-Pro peptide groups tend to have a roughly 3: 1 ratio, presumably because the symmetry between the and atoms of proline makes the cis and trans isomers nearly equal in energy ( See figure, below ).

where is the precession rate, is the spin rate about the axis of symmetry, is the angle between the axis of symmetry and the axis about which it precesses, is the moment of inertia about the axis of symmetry, and is moment of inertia about either of the other two perpendicular principal axes.

The piezoelectric effect is understood as the linear electromechanical interaction between the mechanical and the electrical state in crystalline materials with no inversion symmetry.

Since the strong interaction does not discriminate between different flavors of quark, QCD has approximate flavor symmetry, which is broken by the differing masses of the quarks.

* OWL adds more vocabulary for describing properties and classes: among others, relations between classes ( e. g. disjointness ), cardinality ( e. g. " exactly one "), equality, richer typing of properties, characteristics of properties ( e. g. symmetry ), and enumerated classes.

::“ there is, from the ethical point of view, no symmetry between suffering and happiness, or between pain and pleasure … In my opinion human suffering makes a direct moral appeal, namely, the appeal for help, while there is no similar call to increase the happiness of a man who is doing well anyway.

This distinction between vectors and pseudovectors is often ignored, but it becomes important in studying symmetry properties.

Crystal symmetry was first investigated experimentally by Nicolas Steno ( 1669 ), who showed that the angles between the faces are the same in every exemplar of a particular type of crystal, and by René Just Haüy ( 1784 ), who discovered that every face of a crystal can be described by simple stacking patterns of blocks of the same shape and size.

Within the sheet, the bonding is covalent and has hexagonal symmetry, but there are no covalent bonds between the sheets, making graphite easy to cleave into flakes.

Kathleen Lonsdale's 1928 structure of hexamethylbenzene established the hexagonal symmetry of benzene and showed a clear difference in bond length between the aliphatic C – C bonds and aromatic C – C bonds ; this finding led to the idea of resonance between chemical bonds, which had profound consequences for the development of chemistry.

Whilst the styles were similar, there are some notable differences between both Rococo and Baroque architecture, one of them being symmetry, since Rococo emphasised the asymmetry of forms, whilst Baroque was the opposite.

The rotational symmetry between time and space coordinate axes ( when one is taken as imaginary, another as real ) results in Lorentz transformations which in turn result in special relativity theory.