Symmetry.pptx
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Symmetry is a mathematical concept where an object appears identical after some transformation such as reflection, rotation, or translation. Geometric shapes with symmetry appeal to our visual perception. Tessellations are patterns made of shapes that fit together without gaps. Symmetry is important in fields like chemistry for understanding molecular structures, in art for creating balance, and in music where symmetrical patterns can sound pleasing. The document discusses definitions of different types of symmetry and applications in areas like science, art, and music to highlight symmetry's significance.
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Symmetry
This document discusses different types of symmetry, including line symmetry and rotational symmetry. It provides examples of line symmetry in letters of the alphabet and examples of rotational symmetry in shapes like triangles, squares, and pentagons. It also discusses symmetry in architecture, flags, and natural phenomena. Symmetry is a fundamental organizing principle in nature and art that involves preserving certain properties when an object is transformed in some way.
Symmetry
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")[1] in everyday language refers to a sense of harmonious and beautiful proportion and balance.[2][3][a] In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, theoretic models, language, music and even knowledge itself.[4][b]
This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry.
In geometry[edit]
Main article: Symmetry (geometry)
The triskelion has 3-fold rotational symmetry.
A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion.[5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. The type of symmetry is determined by the way the pieces are organized, or by the type of transformation:
An object has reflectional symmetry (line or mirror symmetry) if there is a line going through it which divides it into two pieces which are mirror images of each other.[6]
An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.[7]
An object has translational symmetry if it can be translated without changing its overall shape.[8]
An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.[9]
An object has scale symmetry if it does not change shape when it is expanded or contracted.[10] Fractals also exhibit a form of scale symmetry, where small portions of the fractal are similar in shape to large portions.[11]
Line symmetry for 7th std
The document discusses line symmetry in nature, architecture, and shapes. It provides examples of line symmetry in shells, starfish, crabs, masks, the human face, reflections in water, and structures like the Taj Mahal. Specific animals and objects mentioned include butterflies, shells found at the beach, crab shells, starfish, masks from different cultures, and the famous artwork by Leonardo Da Vinci depicting human proportions. Geometric shapes like equilateral triangles, squares, pentagons, hexagons, and octagons are analyzed and their number of internal angles and lines of symmetry identified.
Unit 3 symmetry
The document discusses symmetry in nature, architecture, and art. It defines symmetry as a spatial relationship where one half of a shape is the mirror image of the other half. There are different types of symmetrical lines including horizontal, vertical, and diagonal. Symmetry can be classified as axial or radial depending on whether equal elements are equidistant from a central axis or point.
Line symmetry
Line symmetry is the most common type of symmetry where an object can be folded along a central line so that one half is an exact mirror image of the other. Examples of objects that exhibit line symmetry include many creatures, plants, human faces, bodies, letters of the alphabet, and artworks which can be folded along a central line to form two congruent mirror images. Line symmetry is found throughout nature and in human-made objects.
Symmetry
This document discusses different types of symmetry found in shapes, letters, numbers, objects, and designs. It provides examples of rotational symmetry, including some letters that have order 2 rotational symmetry like H, I, O, and Z. It also gives examples of shapes, flags, road signs, buildings and monuments that demonstrate various kinds of line and rotational symmetry.
Symmetry in mathematics
This presentation discusses different types of symmetry. It defines symmetry as identical parts facing each other or around an axis. There are two main types of symmetry discussed - line symmetry, where a figure does not change upon reflection, and rotational symmetry, where an object looks the same after rotation. Examples are given of different geometric shapes and their number of lines of symmetry, ranging from 1 line to many lines to no lines of symmetry. Mirror images are also introduced as reflected duplications that appear identical but reversed.
Symmetry
The document discusses two types of symmetry: rotational symmetry and reflectional symmetry. Rotational symmetry occurs when a shape appears identical after being rotated, while reflectional symmetry occurs when a shape is the same on both sides of a mirror line. The document provides examples of shapes with different orders of rotational symmetry and numbers of lines of reflectional symmetry. It also introduces the concept of plane symmetry in solid objects.
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Symmetry
This document discusses different types of symmetry, including line symmetry and rotational symmetry. It provides examples of line symmetry in letters of the alphabet and examples of rotational symmetry in shapes like triangles, squares, and pentagons. It also discusses symmetry in architecture, flags, and natural phenomena. Symmetry is a fundamental organizing principle in nature and art that involves preserving certain properties when an object is transformed in some way.
Symmetry
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")[1] in everyday language refers to a sense of harmonious and beautiful proportion and balance.[2][3][a] In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, theoretic models, language, music and even knowledge itself.[4][b]
This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry.
In geometry[edit]
Main article: Symmetry (geometry)
The triskelion has 3-fold rotational symmetry.
A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion.[5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object but doesn't change the overall shape. The type of symmetry is determined by the way the pieces are organized, or by the type of transformation:
An object has reflectional symmetry (line or mirror symmetry) if there is a line going through it which divides it into two pieces which are mirror images of each other.[6]
An object has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.[7]
An object has translational symmetry if it can be translated without changing its overall shape.[8]
An object has helical symmetry if it can be simultaneously translated and rotated in three-dimensional space along a line known as a screw axis.[9]
An object has scale symmetry if it does not change shape when it is expanded or contracted.[10] Fractals also exhibit a form of scale symmetry, where small portions of the fractal are similar in shape to large portions.[11]
Line symmetry for 7th std
The document discusses line symmetry in nature, architecture, and shapes. It provides examples of line symmetry in shells, starfish, crabs, masks, the human face, reflections in water, and structures like the Taj Mahal. Specific animals and objects mentioned include butterflies, shells found at the beach, crab shells, starfish, masks from different cultures, and the famous artwork by Leonardo Da Vinci depicting human proportions. Geometric shapes like equilateral triangles, squares, pentagons, hexagons, and octagons are analyzed and their number of internal angles and lines of symmetry identified.
Unit 3 symmetry
The document discusses symmetry in nature, architecture, and art. It defines symmetry as a spatial relationship where one half of a shape is the mirror image of the other half. There are different types of symmetrical lines including horizontal, vertical, and diagonal. Symmetry can be classified as axial or radial depending on whether equal elements are equidistant from a central axis or point.
Line symmetry
Line symmetry is the most common type of symmetry where an object can be folded along a central line so that one half is an exact mirror image of the other. Examples of objects that exhibit line symmetry include many creatures, plants, human faces, bodies, letters of the alphabet, and artworks which can be folded along a central line to form two congruent mirror images. Line symmetry is found throughout nature and in human-made objects.
Symmetry
This document discusses different types of symmetry found in shapes, letters, numbers, objects, and designs. It provides examples of rotational symmetry, including some letters that have order 2 rotational symmetry like H, I, O, and Z. It also gives examples of shapes, flags, road signs, buildings and monuments that demonstrate various kinds of line and rotational symmetry.
Symmetry in mathematics
This presentation discusses different types of symmetry. It defines symmetry as identical parts facing each other or around an axis. There are two main types of symmetry discussed - line symmetry, where a figure does not change upon reflection, and rotational symmetry, where an object looks the same after rotation. Examples are given of different geometric shapes and their number of lines of symmetry, ranging from 1 line to many lines to no lines of symmetry. Mirror images are also introduced as reflected duplications that appear identical but reversed.
Symmetry
The document discusses two types of symmetry: rotational symmetry and reflectional symmetry. Rotational symmetry occurs when a shape appears identical after being rotated, while reflectional symmetry occurs when a shape is the same on both sides of a mirror line. The document provides examples of shapes with different orders of rotational symmetry and numbers of lines of reflectional symmetry. It also introduces the concept of plane symmetry in solid objects.
Line symmetry
This document discusses line symmetry in various contexts. It explains that an object has line symmetry if it can be divided into two mirror image halves by a line. Letters of the alphabet, road signs, monuments, and flags are provided as examples of objects that do or do not exhibit line symmetry. Regular polygons from triangles to octagons are also described as having a specific number of lines of symmetry corresponding to their number of sides and internal angles.
Line symmetry
This PowerPoint presentation discusses line symmetry in nature, animals, humans, architecture, and 2D shapes. Some key examples provided include butterflies, shells, starfish, human faces, Leonardo da Vinci's drawing of human proportions, the Taj Mahal, and regular polygons like triangles, squares, and hexagons. The presentation shows how line symmetry exists all around us and is considered aesthetically pleasing, appearing commonly in both natural and man-made structures.
Line symmetry
This PowerPoint presentation discusses symmetry in nature, architecture, and geometry. It provides examples of line symmetry in animals like butterflies, shells, crabs, and starfish. Symmetry is also seen in human faces and bodies, as well as architectural structures like the Taj Mahal. Different 2D shapes have varying numbers of lines of symmetry: equilateral triangles have 3, squares have 4, regular pentagons have 5, and so on.
Crystallographic and geometric symmetry
The document discusses symmetry in geometry and crystallography. There are three elements of crystallographic symmetry: axis of symmetry, where a crystal can be rotated around an imaginary line to fill the same space multiple times; plane of symmetry, where an imaginary plane divides a crystal into mirror image halves; and center of symmetry, where points on the crystal are equidistant from the center along an imaginary line. Symmetry is a balanced similarity found in two halves of an object, and it is a fundamental property of the orderly arrangements of atoms in crystalline solids.
Mather nature
The document discusses two types of symmetry found in nature: bilateral symmetry and rotational symmetry. Bilateral symmetry refers to shapes that can be folded along an imaginary line so that opposite sides match, like many insects and animals. Rotational symmetry involves shapes that look the same when rotated around their central point, exemplified by snowflakes, flowers, and starfish. The document provides examples and images to illustrate these two fundamental forms of symmetry exhibited in the natural world.
Symmetry 131015035956-phpapp01 (1) (1)
This document discusses different types of symmetry seen in shapes, letters, numbers, flags, religious symbols, and more. It provides examples of objects with various orders of rotational symmetry, such as flowers with order 5 rotational symmetry and pizza with order 6 rotational symmetry. It also examines which letters and symbols have lines of symmetry and which do not, such as H, N, S, X, I, O, and Z not having any lines of symmetry.
Fractals and symmetry by group 3
Symmetry is the correspondence of form and configuration on opposite sides of a dividing line or plane. It is present in many areas including geometry, mathematics, science, and nature. Fractals are self-similar patterns that repeat at different scales and often have non-integer fractal dimensions. Benoît Mandelbrot coined the term fractal and studied fractals like the Mandelbrot set, which demonstrate iterative processes that lead to increasingly complex patterns appearing as one zooms in. Fractals are used in computer graphics, geography, art and other applications to model real-world irregular forms and processes.
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Radial, bilateral, translational, and wallpaper symmetries are prevalent in nature. Examples include starfish with dihedral symmetry, trees with translational strip patterns, hexagonal structures like honeycombs and the Giant's Causeway that tessellate plane patterns, and the approximate bilateral symmetry found in human faces. Symmetry represents a balance and order that is reflected in both man-made and natural designs.
HO MMW Lecture 2 -Mathematics in our Modern World lecture 2
Mathematics helps organize and predict patterns in nature. Some common patterns include symmetry, fractals, and spirals. Symmetry refers to an object being invariant under transformations like reflection or rotation, and can be bilateral or radial. Fractals are never-ending patterns that repeat themselves at different scales. Spirals are curved patterns that revolve around a central point in circular shapes. Mathematics allows us to describe these patterns found throughout nature.
Fractals and symmetry group 3
Fractals and symmetry are closely related concepts in mathematics. Fractals exhibit a repeating pattern that displays at every scale and often have non-integer fractal dimensions. Some key fractals include the Mandelbrot set, Julia set, and Koch snowflake. Symmetry refers to an object having identical corresponding parts on opposite sides of a dividing line or plane. There are several types of symmetry such as reflection, rotation, translation, and scale symmetry which fractals demonstrate. Benoit Mandelbrot coined the term "fractal" and studied their properties, finding their applications in fields like art, geography, and physics.
H0.2b Line Symmetry2
This document discusses different types of symmetry found in nature, architecture, and shapes. It provides examples of line symmetry in shells, crabs, starfish, masks, the human face, reflections in water, and the Taj Mahal. It also examines the number of lines of symmetry in different polygons, finding that an equilateral triangle has 3 lines of symmetry, a square has 4, a regular pentagon has 5, a regular hexagon has 6, and a regular octagon has 8.
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Radial symmetry
Radial symmetry is a type of balance where parts of an object are arranged around a central point. There are three types of balance: radial symmetry, mirror/bilateral symmetry, and asymmetry. Radial symmetry is seen in both natural objects like snowflakes and human-made objects like mandalas, kaleidoscopes, and rose windows in cathedrals. To create radial symmetry, a circle is divided into equal sections and the same pattern is repeated in each section.
Rotational symmetry
An object with rotational symmetry, also known in biological contexts as radial symmetry, is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted.
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X-ray crystallography uses X-rays to determine the three-dimensional structure of molecules. Symmetry elements like centers of symmetry and planes of symmetry describe the repeating patterns in a crystal lattice. Bragg's law relates the wavelength of X-rays to the diffraction pattern produced when X-rays interact with the regular array of atoms in a crystal and bounce off the lattice planes.
Line symmetry
This PowerPoint presentation introduces the concept of line symmetry through examples found in nature, architecture, art, and everyday objects. It explains that line symmetry exists when one half of a shape is the mirror image of the other half. Examples discussed include butterflies, human faces and bodies, shells on the beach, underwater creatures like crabs and starfish, animal shapes, reflections in water, and architectural structures like the Taj Mahal. The presentation also examines line symmetry in 2D shapes like triangles, squares, pentagons, hexagons, and octagons.
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Line symmetry exists when one half of a shape is the mirror image of the other half. Many common shapes and structures exhibit line symmetry, including letters of the alphabet, road signs, polygons, and architectural landmarks like the Taj Mahal. The document explores line symmetry through examples, activities identifying symmetrical shapes, and explanations of what qualifies as a line of symmetry.
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3) The Fibonacci sequence is a number pattern where each number is the sum of the two preceding numbers. This sequence is often seen in nature, such as the number of flower petals. The ratio of numbers in the Fibonacci sequence approaches the Golden Ratio of 1.618:1.
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Symmetry refers to the orderly and proportionate arrangement of parts that produces a balanced form. It is important in biology, mathematics, and mineralogy. In biology, symmetry can be bilateral around a central axis or radial around a central point. In geometry, symmetry involves transformations that produce identical or mirror images of shapes. In mineralogy, crystal structures are classified based on their symmetry properties. Symmetry in physics refers to systems that remain unchanged under transformations like mirroring or time reversal, and relates to conservation laws.
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Line symmetry
This document discusses line symmetry in various contexts. It explains that an object has line symmetry if it can be divided into two mirror image halves by a line. Letters of the alphabet, road signs, monuments, and flags are provided as examples of objects that do or do not exhibit line symmetry. Regular polygons from triangles to octagons are also described as having a specific number of lines of symmetry corresponding to their number of sides and internal angles.
Line symmetry
This PowerPoint presentation discusses line symmetry in nature, animals, humans, architecture, and 2D shapes. Some key examples provided include butterflies, shells, starfish, human faces, Leonardo da Vinci's drawing of human proportions, the Taj Mahal, and regular polygons like triangles, squares, and hexagons. The presentation shows how line symmetry exists all around us and is considered aesthetically pleasing, appearing commonly in both natural and man-made structures.
Line symmetry
This PowerPoint presentation discusses symmetry in nature, architecture, and geometry. It provides examples of line symmetry in animals like butterflies, shells, crabs, and starfish. Symmetry is also seen in human faces and bodies, as well as architectural structures like the Taj Mahal. Different 2D shapes have varying numbers of lines of symmetry: equilateral triangles have 3, squares have 4, regular pentagons have 5, and so on.
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The document discusses symmetry in geometry and crystallography. There are three elements of crystallographic symmetry: axis of symmetry, where a crystal can be rotated around an imaginary line to fill the same space multiple times; plane of symmetry, where an imaginary plane divides a crystal into mirror image halves; and center of symmetry, where points on the crystal are equidistant from the center along an imaginary line. Symmetry is a balanced similarity found in two halves of an object, and it is a fundamental property of the orderly arrangements of atoms in crystalline solids.
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The document discusses two types of symmetry found in nature: bilateral symmetry and rotational symmetry. Bilateral symmetry refers to shapes that can be folded along an imaginary line so that opposite sides match, like many insects and animals. Rotational symmetry involves shapes that look the same when rotated around their central point, exemplified by snowflakes, flowers, and starfish. The document provides examples and images to illustrate these two fundamental forms of symmetry exhibited in the natural world.
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This document discusses different types of symmetry seen in shapes, letters, numbers, flags, religious symbols, and more. It provides examples of objects with various orders of rotational symmetry, such as flowers with order 5 rotational symmetry and pizza with order 6 rotational symmetry. It also examines which letters and symbols have lines of symmetry and which do not, such as H, N, S, X, I, O, and Z not having any lines of symmetry.
Fractals and symmetry by group 3
Symmetry is the correspondence of form and configuration on opposite sides of a dividing line or plane. It is present in many areas including geometry, mathematics, science, and nature. Fractals are self-similar patterns that repeat at different scales and often have non-integer fractal dimensions. Benoît Mandelbrot coined the term fractal and studied fractals like the Mandelbrot set, which demonstrate iterative processes that lead to increasingly complex patterns appearing as one zooms in. Fractals are used in computer graphics, geography, art and other applications to model real-world irregular forms and processes.
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Radial, bilateral, translational, and wallpaper symmetries are prevalent in nature. Examples include starfish with dihedral symmetry, trees with translational strip patterns, hexagonal structures like honeycombs and the Giant's Causeway that tessellate plane patterns, and the approximate bilateral symmetry found in human faces. Symmetry represents a balance and order that is reflected in both man-made and natural designs.
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Mathematics helps organize and predict patterns in nature. Some common patterns include symmetry, fractals, and spirals. Symmetry refers to an object being invariant under transformations like reflection or rotation, and can be bilateral or radial. Fractals are never-ending patterns that repeat themselves at different scales. Spirals are curved patterns that revolve around a central point in circular shapes. Mathematics allows us to describe these patterns found throughout nature.
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Fractals and symmetry are closely related concepts in mathematics. Fractals exhibit a repeating pattern that displays at every scale and often have non-integer fractal dimensions. Some key fractals include the Mandelbrot set, Julia set, and Koch snowflake. Symmetry refers to an object having identical corresponding parts on opposite sides of a dividing line or plane. There are several types of symmetry such as reflection, rotation, translation, and scale symmetry which fractals demonstrate. Benoit Mandelbrot coined the term "fractal" and studied their properties, finding their applications in fields like art, geography, and physics.
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This document discusses different types of symmetry found in nature, architecture, and shapes. It provides examples of line symmetry in shells, crabs, starfish, masks, the human face, reflections in water, and the Taj Mahal. It also examines the number of lines of symmetry in different polygons, finding that an equilateral triangle has 3 lines of symmetry, a square has 4, a regular pentagon has 5, a regular hexagon has 6, and a regular octagon has 8.
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Rotational symmetry
An object with rotational symmetry, also known in biological contexts as radial symmetry, is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted.
X ray crystallography
X-ray crystallography uses X-rays to determine the three-dimensional structure of molecules. Symmetry elements like centers of symmetry and planes of symmetry describe the repeating patterns in a crystal lattice. Bragg's law relates the wavelength of X-rays to the diffraction pattern produced when X-rays interact with the regular array of atoms in a crystal and bounce off the lattice planes.
Line symmetry
This PowerPoint presentation introduces the concept of line symmetry through examples found in nature, architecture, art, and everyday objects. It explains that line symmetry exists when one half of a shape is the mirror image of the other half. Examples discussed include butterflies, human faces and bodies, shells on the beach, underwater creatures like crabs and starfish, animal shapes, reflections in water, and architectural structures like the Taj Mahal. The presentation also examines line symmetry in 2D shapes like triangles, squares, pentagons, hexagons, and octagons.
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Line symmetry exists when one half of a shape is the mirror image of the other half. Many common shapes and structures exhibit line symmetry, including letters of the alphabet, road signs, polygons, and architectural landmarks like the Taj Mahal. The document explores line symmetry through examples, activities identifying symmetrical shapes, and explanations of what qualifies as a line of symmetry.
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This is for UG students. In this unit concept of stereochemistry is explain in easy way. The content are shown below:
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1) Patterns are found throughout nature and can be described mathematically. The natural world exhibits intricate shapes, colors, and patterns.
2) Common patterns in nature include symmetry, fractals, spots/stripes on animals, flower petals exhibiting Fibonacci numbers, and number sequences like the Fibonacci sequence.
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Symmetry
Symmetry refers to the orderly and proportionate arrangement of parts that produces a balanced form. It is important in biology, mathematics, and mineralogy. In biology, symmetry can be bilateral around a central axis or radial around a central point. In geometry, symmetry involves transformations that produce identical or mirror images of shapes. In mineralogy, crystal structures are classified based on their symmetry properties. Symmetry in physics refers to systems that remain unchanged under transformations like mirroring or time reversal, and relates to conservation laws.
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Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
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Symmetry.pptx
- 1. Symmetry Discover the beauty of symmetry in mathematics and its importance in our world! By Charithraa A.R
- 2. Symmetry Definition Symmetry also known as reflection symmetry, an object is reflected across a specific line and appears identical to the original.
- 3. Symmetry in Geometry Symmetry in Shapes Geometric shapes that have symmetry are pleasing to our eyes. Fractals are one of the key examples of naturally occurring symmetry in shapes. Tessellations A repeated pattern made up of a variety of geometric shapes, without any gaps or overlaps. Tessellations can have a variety of symmetry types.
- 4. Symmetry Definition Mirror Symmetry Also known as reflection symmetry, an object is reflected across a specific line and appears identical to the original. Rotational Symmetry When an object can be rotated by a certain angle and it appears identical to the original. Translational Symmetry When an object appears to be shifted without any change.
- 5. Applications of Symmetry 1 Chemistry The study of crystalline structures, bonding, and molecular symmetry is important in understanding the behavior of chemicals. 2 Art Artists use symmetry in their work to create balance and harmony. Examples of this can be seen in architecture as well as other art forms. 3 Music Music that is considered symmetrical can be pleasing to the ear and mind. Symmetry in music can be observed in note patterns, rhythms, and beats.
- 6. Conclusion 1 Summary of Key Points Symmetry is a fascinating mathematical concept with many different applications in science, art, and music. 2 Importance of Symmetry Symmetry is part of our everyday life. Its use can be seen in both the natural and the human-made world, which highlights its importance.