In architecture

Symmetry is found in architecture at all scales, from the general external views of buildings such as Gothic cathedrals and the White House, through the design of floor plans "Plan (architecture)"), and to the design of individual building elements such as tile mosaics. Islamic buildings such as the Taj Mahal and the Lotfollah Mosque make elaborate use of symmetry in both their structure and ornamentation.[6]​[7]​ Moorish buildings such as the Alhambra are ornamented with complex patterns made using translational and reflective symmetries, as well as rotations.[8]​.

Modernist architecture, beginning with the International Style, is instead based on "wings and balance of masses."[9]​.

in drawing

In drawing there are five important symmetries that are translational, rotational, enlargement, bilateral, and depression symmetry.

On carpets and rugs

A long tradition of using symmetry in rugs spans a variety of cultures. The American Navajo Indians used bold diagonals and rectangular motifs. Many oriental rugs have intricate centers and mirrored edges that translate a pattern. Not surprisingly, rectangular rugs typically have the symmetries of a rectangle, that is, motifs that are reflected in both the horizontal and vertical axis.[10]​[11]​.

in quilts

As quilts are made from square blocks (usually 9, 16, or 25 pieces per block) and each smaller piece usually consists of triangles of fabric, the craft lends itself easily to the application of symmetry.[12]​.

In other arts and crafts

Symmetries appear in the design of objects of all kinds. Examples include beads, furniture, sand paintings, knotwork, masks, and musical instruments. Symmetries are central to the art of M. C. Escher and the many applications of mosaic in art and craft forms such as wallpaper, ceramic tiles as well as in Islamic geometric decoration, batik, ikat, rug making and many types of textile patterns and embroidery.[13]​.

Symmetry is also used in logo design.[14] By creating a logo on a grid and using the theory of symmetry, designers can organize their work, create a symmetrical or asymmetrical design, determine the spacing between letters, determine how much negative space is required in the design, and how to accentuate parts of the logo to make it stand out.

In aesthetics

The relationship of symmetry with aesthetics is complex. Humans find bilateral symmetry in faces physically attractive;[15]​ indicates health and genetic fitness.[16]​[17]​ Contrary to this is the tendency for excessive symmetry to be perceived as boring or uninteresting. People prefer shapes that have some symmetry, but with enough complexity to make them interesting.[18]​.

in literature

Symmetry can be found in various forms in literature, a simple example is the palindrome where a short text reads the same thing forwards or backwards. Stories can have a symmetrical structure, as in the rise/fall pattern of Beowulf.[19]​.

In physics the concept of symmetry can be formulated in a non-geometric form. If K is a set of mathematical objects of the same type (functions, geometric shapes, equations, ...) that represent some properties of a physical system and G is a group of transformations that acts on K in such a way that:.

An element is said to have symmetry if:[20]​.

Thus, for example, several conservation laws of physics are a consequence of the existence of abstract symmetries of the Lagrangian, as shown by Noether's theorem. In that case K would represent the set of admissible Lagrangians, k the Lagrangian of the system under study and G can represent spatial translations (conservation of linear momentum), temporal translations (conservation of energy), rotations (conservation of angular momentum) or other types of abstract symmetries (conservation of electric charge, lepton number, parity "Parity (physics)", etc.).

These two previous examples are cases of Noether's theorem, a general result that states that if there exists a uniparametric symmetry group G for the Lagrangian such that:.

Then the scalar quantity:

Being v the vector field that generates the uniparametric group of symmetry transformations, and p the conjugate moments of the generalized position coordinates.

Symmetry is important to chemistry (particularly organic chemistry) because it underlies essentially all specific interactions between molecules in nature (i.e., through the interaction of natural and artificial chiral molecules with inherently chiral biological systems). Controlling the symmetry of molecules produced in modern chemical synthesis contributes to scientists' ability to deliver therapeutic interventions with minimal side effects. A rigorous understanding of symmetry explains fundamental observations in quantum chemistry and in the applied areas of spectroscopy and crystallography. The theory and application of symmetry to these areas of physical science is based largely on the mathematical area of ​​group theory.[21] Additionally, the dipole moment can be predicted or explained from the symmetry of the molecule.

The symmetries that appear in chemistry are associated with finite groups of isometries, specifically they are point groups of isometry transformations.

Contenido

Simetría en biología es la equilibrada distribución en el cuerpo de los organismos de aquellas partes que aparecen duplicadas. Los planes corporales de la mayoría de organismos pluricelulares exhiben alguna forma de simetría, bien sea simetría radial "Simetría radial (biología)") o simetría bilateral. Una pequeña minoría no presenta ningún tipo de simetría (son asimétricos).

radial symmetry

Radial symmetry is the symmetry defined by a heteropolar axis (different at its two ends). The end that contains the mouth is called oral side, and its opposite aboral side or abactinal.

On this axis, main planes of symmetry are established; two perpendiculars that define the per-radial positions. Structures in other planes (bisectors of the per-radials) remain in inter-radial positions. The zone between the per-radials and the inter-radials is the ad-radial zone.

Bilateral symmetry

The majority of animal species have bilateral symmetry and therefore belong to the Bilateria group, although there are species such as hedgehogs and starfish, which have secondary radial symmetry "Radial symmetry (biology)" (early development phases and larvae have bilateral symmetry that is later lost in the adult).

Bilateral symmetry allows the definition of a body axis in the direction of movement, which favors the formation of a centralized nervous system and cephalization...

To a human observer, some types of symmetry are more salient than others, in particular the most salient is a reflection with a vertical axis, such as that present in the human face. Ernst Mach made this observation in his book "The Analysis of Sensations",[22] and this implies that the perception of symmetry is not a general response to all types of regularities. Both behavioral and neurophysiological studies have confirmed special sensitivity to reflective symmetry in humans and also other animals.[23] Early studies within the Gestalt tradition suggested that bilateral symmetry was one of the key factors in perceptual grouping. This is known as the principle of symmetry. The role of symmetry in grouping and figure/ground organization has been confirmed in many studies. For example, detection of reflection symmetry is faster when this is a property of a single object.[24] Studies of human perception and psychophysics have shown that symmetry detection is fast, efficient, and robust to perturbations. For example, symmetry can be detected with presentations between 100 and 150 milliseconds.[25]​.

More recent neuroimaging studies have documented which brain regions are active during symmetry perception. Sasaki et al[26]​ used functional magnetic resonance imaging (fMRI) to compare the responses of patterns with symmetrical or random dots. There was strong activity in the extrastriate regions of the occipital cortex, but not in the primary visual cortex. Extrastriate regions included V3A, V4, V7, and the lateral occipital complex (LOC). Electrophysiological studies have found a late posterior negativity originating in the same areas.[27]​ Overall, a large part of the visual system appears to be involved in the processing of visual symmetry, and these areas involve networks similar to those responsible for detecting and recognizing objects.[28]​.

En música clásica, existen composiciones en las que podemos encontrar distribuciones de las notas generadas mediante simetría bilateral, traslación o giros de media vuelta. Algunos ejemplos de composiciones, son: el Preludio de Johann Sebastian Bach, la Sonata en Sol mayor de Domenico Scarlatti, Lotosblume de Robert Schumann, o Die Meistersinger de Richard Wagner.

pitch structures

Symmetry is also an important consideration in the formation of scales and chords, since traditional or tonal music is made up of non-symmetrical tone groups, such as the diatonic scale or major chord. Symmetrical scales or chords, such as the whole tone scale, the augmented chord"), or the diminished seventh chord, are said to lack direction or sense of forward motion, are ambiguous as to key or tonal center, and have less specific diatonic functionality. However, composers such as Alban Berg, Béla Bartók, and George Perle have used axes of symmetry and/or interval cycles in ways analogous to the non-tonal keys or tonal centers.[29]​.

Interval cycles are symmetrical and therefore non-diatonic. However, a seven-tone segment of C5 (the cycle of fifths, which are enharmonic with the cycle of fourths) will produce the diatonic major scale. The cyclical tonal progressions in the works of Romantic composers such as Gustav Mahler and Richard Wagner form a link with the cyclical tonal successions in the atonal music of modernists such as Bartók, Alexander Scriabin, Edgard Varèse and the Vienna School. At the same time, these progressions signal the end of the key.[29]​[30]​.

The first extended composition based consistently on symmetrical tonal relationships was probably Alban Berg's Quartet, Op. 3 (1910).[30]​.

In the context of radio frequency electronics, we speak of a symmetrical supply of alternating current when none of the conductors is grounded. When one of the conductors is grounded and the other experiences voltage variations, the power supply is said to be asymmetrical.

There are important technological applications based on symmetrical feeding, since symmetrical feeding has the great advantage that the power loss in the transmission line is an order of magnitude less than asymmetrical feeding over coaxial cable.

Symmetrical feeding is therefore the preferred feeding in QRP operation and EME mode, modes where every dB of gain counts.

Literature

http://recursosbiblio.url.edu.gt/tesisjcem/2016/03/05/Letona-Diana-Investigacion.pdf.

https://www.um.es/analesps/v17/v17_2/12-17_2.pdf.

In architecture

Symmetry is found in architecture at all scales, from the general external views of buildings such as Gothic cathedrals and the White House, through the design of floor plans "Plan (architecture)"), and to the design of individual building elements such as tile mosaics. Islamic buildings such as the Taj Mahal and the Lotfollah Mosque make elaborate use of symmetry in both their structure and ornamentation.[6]​[7]​ Moorish buildings such as the Alhambra are ornamented with complex patterns made using translational and reflective symmetries, as well as rotations.[8]​.

Modernist architecture, beginning with the International Style, is instead based on "wings and balance of masses."[9]​.

in drawing

In drawing there are five important symmetries that are translational, rotational, enlargement, bilateral, and depression symmetry.

On carpets and rugs

A long tradition of using symmetry in rugs spans a variety of cultures. The American Navajo Indians used bold diagonals and rectangular motifs. Many oriental rugs have intricate centers and mirrored edges that translate a pattern. Not surprisingly, rectangular rugs typically have the symmetries of a rectangle, that is, motifs that are reflected in both the horizontal and vertical axis.[10]​[11]​.

in quilts

As quilts are made from square blocks (usually 9, 16, or 25 pieces per block) and each smaller piece usually consists of triangles of fabric, the craft lends itself easily to the application of symmetry.[12]​.

In other arts and crafts

Symmetries appear in the design of objects of all kinds. Examples include beads, furniture, sand paintings, knotwork, masks, and musical instruments. Symmetries are central to the art of M. C. Escher and the many applications of mosaic in art and craft forms such as wallpaper, ceramic tiles as well as in Islamic geometric decoration, batik, ikat, rug making and many types of textile patterns and embroidery.[13]​.

Symmetry is also used in logo design.[14] By creating a logo on a grid and using the theory of symmetry, designers can organize their work, create a symmetrical or asymmetrical design, determine the spacing between letters, determine how much negative space is required in the design, and how to accentuate parts of the logo to make it stand out.

In aesthetics

The relationship of symmetry with aesthetics is complex. Humans find bilateral symmetry in faces physically attractive;[15]​ indicates health and genetic fitness.[16]​[17]​ Contrary to this is the tendency for excessive symmetry to be perceived as boring or uninteresting. People prefer shapes that have some symmetry, but with enough complexity to make them interesting.[18]​.

in literature

Symmetry can be found in various forms in literature, a simple example is the palindrome where a short text reads the same thing forwards or backwards. Stories can have a symmetrical structure, as in the rise/fall pattern of Beowulf.[19]​.

In physics the concept of symmetry can be formulated in a non-geometric form. If K is a set of mathematical objects of the same type (functions, geometric shapes, equations, ...) that represent some properties of a physical system and G is a group of transformations that acts on K in such a way that:.

An element is said to have symmetry if:[20]​.

Thus, for example, several conservation laws of physics are a consequence of the existence of abstract symmetries of the Lagrangian, as shown by Noether's theorem. In that case K would represent the set of admissible Lagrangians, k the Lagrangian of the system under study and G can represent spatial translations (conservation of linear momentum), temporal translations (conservation of energy), rotations (conservation of angular momentum) or other types of abstract symmetries (conservation of electric charge, lepton number, parity "Parity (physics)", etc.).

These two previous examples are cases of Noether's theorem, a general result that states that if there exists a uniparametric symmetry group G for the Lagrangian such that:.

Then the scalar quantity:

Being v the vector field that generates the uniparametric group of symmetry transformations, and p the conjugate moments of the generalized position coordinates.

Symmetry is important to chemistry (particularly organic chemistry) because it underlies essentially all specific interactions between molecules in nature (i.e., through the interaction of natural and artificial chiral molecules with inherently chiral biological systems). Controlling the symmetry of molecules produced in modern chemical synthesis contributes to scientists' ability to deliver therapeutic interventions with minimal side effects. A rigorous understanding of symmetry explains fundamental observations in quantum chemistry and in the applied areas of spectroscopy and crystallography. The theory and application of symmetry to these areas of physical science is based largely on the mathematical area of ​​group theory.[21] Additionally, the dipole moment can be predicted or explained from the symmetry of the molecule.

The symmetries that appear in chemistry are associated with finite groups of isometries, specifically they are point groups of isometry transformations.

Contenido

Simetría en biología es la equilibrada distribución en el cuerpo de los organismos de aquellas partes que aparecen duplicadas. Los planes corporales de la mayoría de organismos pluricelulares exhiben alguna forma de simetría, bien sea simetría radial "Simetría radial (biología)") o simetría bilateral. Una pequeña minoría no presenta ningún tipo de simetría (son asimétricos).

radial symmetry

Radial symmetry is the symmetry defined by a heteropolar axis (different at its two ends). The end that contains the mouth is called oral side, and its opposite aboral side or abactinal.

On this axis, main planes of symmetry are established; two perpendiculars that define the per-radial positions. Structures in other planes (bisectors of the per-radials) remain in inter-radial positions. The zone between the per-radials and the inter-radials is the ad-radial zone.

Bilateral symmetry

The majority of animal species have bilateral symmetry and therefore belong to the Bilateria group, although there are species such as hedgehogs and starfish, which have secondary radial symmetry "Radial symmetry (biology)" (early development phases and larvae have bilateral symmetry that is later lost in the adult).

Bilateral symmetry allows the definition of a body axis in the direction of movement, which favors the formation of a centralized nervous system and cephalization...

To a human observer, some types of symmetry are more salient than others, in particular the most salient is a reflection with a vertical axis, such as that present in the human face. Ernst Mach made this observation in his book "The Analysis of Sensations",[22] and this implies that the perception of symmetry is not a general response to all types of regularities. Both behavioral and neurophysiological studies have confirmed special sensitivity to reflective symmetry in humans and also other animals.[23] Early studies within the Gestalt tradition suggested that bilateral symmetry was one of the key factors in perceptual grouping. This is known as the principle of symmetry. The role of symmetry in grouping and figure/ground organization has been confirmed in many studies. For example, detection of reflection symmetry is faster when this is a property of a single object.[24] Studies of human perception and psychophysics have shown that symmetry detection is fast, efficient, and robust to perturbations. For example, symmetry can be detected with presentations between 100 and 150 milliseconds.[25]​.

More recent neuroimaging studies have documented which brain regions are active during symmetry perception. Sasaki et al[26]​ used functional magnetic resonance imaging (fMRI) to compare the responses of patterns with symmetrical or random dots. There was strong activity in the extrastriate regions of the occipital cortex, but not in the primary visual cortex. Extrastriate regions included V3A, V4, V7, and the lateral occipital complex (LOC). Electrophysiological studies have found a late posterior negativity originating in the same areas.[27]​ Overall, a large part of the visual system appears to be involved in the processing of visual symmetry, and these areas involve networks similar to those responsible for detecting and recognizing objects.[28]​.

En música clásica, existen composiciones en las que podemos encontrar distribuciones de las notas generadas mediante simetría bilateral, traslación o giros de media vuelta. Algunos ejemplos de composiciones, son: el Preludio de Johann Sebastian Bach, la Sonata en Sol mayor de Domenico Scarlatti, Lotosblume de Robert Schumann, o Die Meistersinger de Richard Wagner.

pitch structures

Symmetry is also an important consideration in the formation of scales and chords, since traditional or tonal music is made up of non-symmetrical tone groups, such as the diatonic scale or major chord. Symmetrical scales or chords, such as the whole tone scale, the augmented chord"), or the diminished seventh chord, are said to lack direction or sense of forward motion, are ambiguous as to key or tonal center, and have less specific diatonic functionality. However, composers such as Alban Berg, Béla Bartók, and George Perle have used axes of symmetry and/or interval cycles in ways analogous to the non-tonal keys or tonal centers.[29]​.

Interval cycles are symmetrical and therefore non-diatonic. However, a seven-tone segment of C5 (the cycle of fifths, which are enharmonic with the cycle of fourths) will produce the diatonic major scale. The cyclical tonal progressions in the works of Romantic composers such as Gustav Mahler and Richard Wagner form a link with the cyclical tonal successions in the atonal music of modernists such as Bartók, Alexander Scriabin, Edgard Varèse and the Vienna School. At the same time, these progressions signal the end of the key.[29]​[30]​.

The first extended composition based consistently on symmetrical tonal relationships was probably Alban Berg's Quartet, Op. 3 (1910).[30]​.

In the context of radio frequency electronics, we speak of a symmetrical supply of alternating current when none of the conductors is grounded. When one of the conductors is grounded and the other experiences voltage variations, the power supply is said to be asymmetrical.

There are important technological applications based on symmetrical feeding, since symmetrical feeding has the great advantage that the power loss in the transmission line is an order of magnitude less than asymmetrical feeding over coaxial cable.

Symmetrical feeding is therefore the preferred feeding in QRP operation and EME mode, modes where every dB of gain counts.

Literature

http://recursosbiblio.url.edu.gt/tesisjcem/2016/03/05/Letona-Diana-Investigacion.pdf.

https://www.um.es/analesps/v17/v17_2/12-17_2.pdf.