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(새 문서: * Mouchet, Amaury. 2015. ‘Symmetry: A Bridge between Nature and Culture’. arXiv:1503.01038 [physics], February. http://arxiv.org/abs/1503.01038.)
 
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* Mouchet, Amaury. 2015. ‘Symmetry: A Bridge between Nature and Culture’. arXiv:1503.01038 [physics], February. http://arxiv.org/abs/1503.01038.
 
* Mouchet, Amaury. 2015. ‘Symmetry: A Bridge between Nature and Culture’. arXiv:1503.01038 [physics], February. http://arxiv.org/abs/1503.01038.
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== 메모 ==
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* Noson S. Yanofsky, Mark Zelcer, The Role of Symmetry in Mathematics, arXiv:1502.07803[math.HO], February 27 2015, http://arxiv.org/abs/1502.07803v2, 10.1007/s10699-016-9486-7, http://dx.doi.org/10.1007/s10699-016-9486-7, Published in Foundations of Science, March 2016
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== 노트 ==
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# The simplest symmetry is Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry).<ref name="ref_6b8b">[https://www.mathsisfun.com/geometry/symmetry.html Reflection and Rotation]</ref>
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# Continuous and discrete transformations give rise to corresponding types of symmetries.<ref name="ref_d906">[https://en.wikipedia.org/wiki/Symmetry_(physics) Symmetry (physics)]</ref>
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# The sphere is said to exhibit spherical symmetry.<ref name="ref_d906" />
 +
# Continuous spacetime symmetries are symmetries involving transformations of space and time.<ref name="ref_d906" />
 +
# A discrete symmetry is a symmetry that describes non-continuous changes in a system.<ref name="ref_d906" />
 +
# , where they might be given the following shapes and asked to draw lines of symmetry on them.<ref name="ref_e697">[https://www.theschoolrun.com/what-is-symmetry What is symmetry?]</ref>
 +
# In, children are asked to identify lines of symmetry in 2D shapes presented in different orientations.<ref name="ref_e697" />
 +
# They may be asked to look at these regular shapes and think about how many lines of symmetry they can find.<ref name="ref_e697" />
 +
# In general, every kind of structure in mathematics will have its own kind of symmetry.<ref name="ref_a3f4">[https://en.wikipedia.org/wiki/Symmetry Wikipedia]</ref>
 +
# In biology, the notion of symmetry is mostly used explicitly to describe body shapes.<ref name="ref_a3f4" />
 +
# Early studies within the Gestalt tradition suggested that bilateral symmetry was one of the key factors in perceptual grouping.<ref name="ref_a3f4" />
 +
# The role of symmetry in grouping and figure/ground organization has been confirmed in many studies.<ref name="ref_a3f4" />
 +
# There's a lot of symmetry between the moon and Earth, most commonly seen in a phenomena known as tidal locking.<ref name="ref_b1c6">[https://www.merriam-webster.com/dictionary/symmetry Definition of Symmetry by Merriam-Webster]</ref>
 +
# Written as 10/10/2020, the date bore a certain digital symmetry and numerological fascination.<ref name="ref_b1c6" />
 +
# The symmetry of the numbers appealed to him as a mathematician.<ref name="ref_b1c6" />
 +
# It’s the sort of blunt symmetry that was always Sorkin’s calling card.<ref name="ref_b1c6" />
 +
# Consequently, we expect that deviations from exact symmetries to be relatively ‘small’.<ref name="ref_3270">[https://www.nature.com/articles/s41467-019-12675-8 Symmetry group factorization reveals the structure-function relation in the neural connectome of Caenorhabditis elegans]</ref>
 +
# \({P}_{\varepsilon }\) approximates an exact symmetry in the ideal limit \(\varepsilon \to 0\).<ref name="ref_3270" />
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# Any line splitting a shape into two parts such that the two parts are the same is called a line of symmetry.<ref name="ref_a96d">[https://www.splashlearn.com/math-vocabulary/geometry/symmetry Definition, Facts and Examples]</ref>
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# Can we have more than one line of symmetry?<ref name="ref_a96d" />
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# Example 4: Given below is a left part of a picture and its line of symmetry.<ref name="ref_a96d" />
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# We look at each vertex of the yellow part and measure its distance from the line of symmetry.<ref name="ref_a96d" />
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# This last one is particularly helpful when we move into three-dimensional graphs and symmetry is harder to tell by looking at a shape.<ref name="ref_dd8e">[http://www.mesacc.edu/~marfv02121/readings/symmetry/ college algebra]</ref>
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# The black dot represents the original point and the colored dots demonstrate the four types of symmetry.<ref name="ref_dd8e" />
 +
# : Use the test for symmetry about the y-axis to determine if the graph of y - 5x2 = 4 is symmetric about the y-axis.<ref name="ref_dd8e" />
 +
# : Use the test for symmetry about the x-axis to determine if the graph of y - 5x2 = 4 is symmetric about the x-axis.<ref name="ref_dd8e" />
 +
# And now that answer is only helpful if we know what a line of symmetry is.<ref name="ref_1434">[https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/line-of-symmetry/v/identifying-symmetrical-figures Identifying symmetrical figures]</ref>
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# A line of symmetry is a line where we can fold the image and have both halves match exactly.<ref name="ref_1434" />
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# This line is a line of symmetry if we can take one side of the line and fold it onto the other and have them match exactly.<ref name="ref_1434" />
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# Maybe this could be our line of symmetry.<ref name="ref_1434" />
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# Welcome to the world of symmetry!<ref name="ref_a908">[http://faculty.otterbein.edu/djohnston/sym/tutorial/index.html Symmetry Tutorial - Introduction]</ref>
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# The next few pages introduce each of these symmetry elements with example molecules having each type of symmetry.<ref name="ref_a908" />
 +
# Symmetry Matching is a tablet-friendly maths game for 4 to 8 year olds which involves mirroring an image along a line of symmetry.<ref name="ref_693c">[https://www.topmarks.co.uk/symmetry/symmetry-matching Reflective symmetry game for 4 to 8 year olds]</ref>
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# The pictures and patterns have vertical lines of symmetry while the shapes include both vertical and horizontal lines of symmetry.<ref name="ref_693c" />
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# For further practise on symmetry try our Symmetry Sorting game.<ref name="ref_693c" />
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# Thus, only one plane of symmetry will divide a bilateral animal into symmetrical halves, the median longitudinal, or sagittal, plane.<ref name="ref_c965">[https://www.britannica.com/science/symmetry-biology Symmetry | biology]</ref>
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# The concept of symmetry is also applied in botany.<ref name="ref_c965" />
 +
# In this perspective, we summarized these advanced achievements obtained through utilizing symmetry and asymmetry in thermoelectrics.<ref name="ref_35f3">[https://pubs.rsc.org/en/content/articlelanding/2020/tc/d0tc03270k Symmetry and asymmetry in thermoelectrics]</ref>
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# We also work out the explicit form of our condition for the dihedral group of symmetries of a regular polygon.<ref name="ref_278d">[https://dictionary.cambridge.org/dictionary/english/symmetry meaning in the Cambridge English Dictionary]</ref>
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# It is this transformation of an object so that the result is indistinguishable from the original that defines a symmetry.<ref name="ref_7c31">[https://www.quantamagazine.org/symmetry-algebra-and-the-monster-20170817/ Quanta Magazine]</ref>
 +
# A symmetry requires that the transformation not alter the size or shape of the object.<ref name="ref_7c31" />
 +
# Now we can continue our analysis of the symmetries of a square.<ref name="ref_7c31" />
 +
# Of course it’s impossible to tell, precisely because of the criteria for a symmetry.<ref name="ref_7c31" />
 +
# This symmetry is lower than expected for DNIC with low-molecular-weight thiols, which have axial symmetry (see above).<ref name="ref_0652">[https://www.sciencedirect.com/topics/chemistry/symmetry Symmetry - an overview]</ref>
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# This low symmetry is plausibly rationalized by BSA molecule contributing only one thiol group to the DNIC.<ref name="ref_0652" />
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# Thus, the different nature of the two anionic ligands could lower the symmetry of the complex from axial to rhombic.<ref name="ref_0652" />
 +
# At room temperature, this complex shows an axially symmetric EPR spectrum, as distinct from the rhombic symmetry of DNIC-BSA.<ref name="ref_0652" />
 +
# As we will see below, there are various types of symmetry.<ref name="ref_5d66">[https://www.smartick.com/blog/math/geometry/symmetry/ Symmetry: Definiton, Types, Exercises & Examples]</ref>
 +
# We are going to begin with the most well-known, symmetry with respect to a line or axial symmetry.<ref name="ref_5d66" />
 +
# To better understand what symmetry is with respect to an axis, take a look at this video of one of our interactive tutorials.<ref name="ref_5d66" />
 +
# is the one that divides an object or figure in two using , in other words, by an axis of symmetry.<ref name="ref_5d66" />
 +
# Our discussion of symmetry in crystallography should begin with a description of crystals.<ref name="ref_81f8">[http://xrayweb.chem.ou.edu/notes/symmetry.html Symmetry in Crystallography Notes]</ref>
 +
# If other symmetry considerations do not override, then the cell is chosen so that a ≤ b ≤ c, and α, β, and γ all < 90 ° or all ≥ 90 °.<ref name="ref_81f8" />
 +
# In the tetragonal, trigonal, and hexagonal systems, one axis contains higher symmetry.<ref name="ref_81f8" />
 +
# Generally higher metric symmetry is identified by computer programs.<ref name="ref_81f8" />
 +
# Asymmetrical balance refers to a kind of balance that does not rely on symmetry.<ref name="ref_b91f">[http://www.emotionalcompetency.com/symmetry.htm Emotional Competency]</ref>
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# The architecture for interaction classifies behavior according to its symmetry.<ref name="ref_b91f" />
 +
# The mutual exchange of reciprocity is based on the principle of symmetry interpreted as fair exchange.<ref name="ref_b91f" />
 +
# The golden rule expresses the importance of maintaining symmetry and balance as we encounter others.<ref name="ref_b91f" />
 +
# Proteins can adopt a range of different symmetries.<ref name="ref_2385">[https://www.rosettacommons.org/docs/latest/rosetta_basics/structural_concepts/symmetry Symmetry User's Guide.]</ref>
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# The most common one is cyclic symmetry which involves n-fold rotation around a symmetry axis (Cn symmetry).<ref name="ref_2385" />
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# Another common group is the Dihedral symmetries that combine one n-fold symmetry axis with perpendicular twofold symmetry axis.<ref name="ref_2385" />
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# For example D2 symmetry involves a dimer of dimers.<ref name="ref_2385" />
 +
# But in mathematics, symmetry has been given a more precise meaning.<ref name="ref_8ef9">[https://www.americanscientist.org/article/the-power-of-symmetry The Power of Symmetry]</ref>
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# An equilateral triangle has six symmetries, shown above.<ref name="ref_8ef9" />
 +
# Suffice it to say that the mathematical concept of a group captures the essence of symmetry in abstract terms.<ref name="ref_8ef9" />
 +
# The focus is on the operation that reveals the symmetry.<ref name="ref_8ef9" />
 +
# This latter notion of symmetry developed, via several steps, into the concept found today in modern science.<ref name="ref_811a">[https://plato.stanford.edu/entries/symmetry-breaking/ Symmetry and Symmetry Breaking (Stanford Encyclopedia of Philosophy)]</ref>
 +
# The group-theoretic notion of symmetry is the one that has proven so successful in modern science.<ref name="ref_811a" />
 +
# As we have seen, the scientific notion of symmetry (the one we are interested in here) is a recent one.<ref name="ref_811a" />
 +
# The second is between the two main ways of using symmetry.<ref name="ref_811a" />
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===소스===
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<references />

2020년 12월 17일 (목) 20:07 기준 최신판

메모

노트

  1. The simplest symmetry is Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry).[1]
  2. Continuous and discrete transformations give rise to corresponding types of symmetries.[2]
  3. The sphere is said to exhibit spherical symmetry.[2]
  4. Continuous spacetime symmetries are symmetries involving transformations of space and time.[2]
  5. A discrete symmetry is a symmetry that describes non-continuous changes in a system.[2]
  6. , where they might be given the following shapes and asked to draw lines of symmetry on them.[3]
  7. In, children are asked to identify lines of symmetry in 2D shapes presented in different orientations.[3]
  8. They may be asked to look at these regular shapes and think about how many lines of symmetry they can find.[3]
  9. In general, every kind of structure in mathematics will have its own kind of symmetry.[4]
  10. In biology, the notion of symmetry is mostly used explicitly to describe body shapes.[4]
  11. Early studies within the Gestalt tradition suggested that bilateral symmetry was one of the key factors in perceptual grouping.[4]
  12. The role of symmetry in grouping and figure/ground organization has been confirmed in many studies.[4]
  13. There's a lot of symmetry between the moon and Earth, most commonly seen in a phenomena known as tidal locking.[5]
  14. Written as 10/10/2020, the date bore a certain digital symmetry and numerological fascination.[5]
  15. The symmetry of the numbers appealed to him as a mathematician.[5]
  16. It’s the sort of blunt symmetry that was always Sorkin’s calling card.[5]
  17. Consequently, we expect that deviations from exact symmetries to be relatively ‘small’.[6]
  18. \({P}_{\varepsilon }\) approximates an exact symmetry in the ideal limit \(\varepsilon \to 0\).[6]
  19. Any line splitting a shape into two parts such that the two parts are the same is called a line of symmetry.[7]
  20. Can we have more than one line of symmetry?[7]
  21. Example 4: Given below is a left part of a picture and its line of symmetry.[7]
  22. We look at each vertex of the yellow part and measure its distance from the line of symmetry.[7]
  23. This last one is particularly helpful when we move into three-dimensional graphs and symmetry is harder to tell by looking at a shape.[8]
  24. The black dot represents the original point and the colored dots demonstrate the four types of symmetry.[8]
  25. : Use the test for symmetry about the y-axis to determine if the graph of y - 5x2 = 4 is symmetric about the y-axis.[8]
  26. : Use the test for symmetry about the x-axis to determine if the graph of y - 5x2 = 4 is symmetric about the x-axis.[8]
  27. And now that answer is only helpful if we know what a line of symmetry is.[9]
  28. A line of symmetry is a line where we can fold the image and have both halves match exactly.[9]
  29. This line is a line of symmetry if we can take one side of the line and fold it onto the other and have them match exactly.[9]
  30. Maybe this could be our line of symmetry.[9]
  31. Welcome to the world of symmetry![10]
  32. The next few pages introduce each of these symmetry elements with example molecules having each type of symmetry.[10]
  33. Symmetry Matching is a tablet-friendly maths game for 4 to 8 year olds which involves mirroring an image along a line of symmetry.[11]
  34. The pictures and patterns have vertical lines of symmetry while the shapes include both vertical and horizontal lines of symmetry.[11]
  35. For further practise on symmetry try our Symmetry Sorting game.[11]
  36. Thus, only one plane of symmetry will divide a bilateral animal into symmetrical halves, the median longitudinal, or sagittal, plane.[12]
  37. The concept of symmetry is also applied in botany.[12]
  38. In this perspective, we summarized these advanced achievements obtained through utilizing symmetry and asymmetry in thermoelectrics.[13]
  39. We also work out the explicit form of our condition for the dihedral group of symmetries of a regular polygon.[14]
  40. It is this transformation of an object so that the result is indistinguishable from the original that defines a symmetry.[15]
  41. A symmetry requires that the transformation not alter the size or shape of the object.[15]
  42. Now we can continue our analysis of the symmetries of a square.[15]
  43. Of course it’s impossible to tell, precisely because of the criteria for a symmetry.[15]
  44. This symmetry is lower than expected for DNIC with low-molecular-weight thiols, which have axial symmetry (see above).[16]
  45. This low symmetry is plausibly rationalized by BSA molecule contributing only one thiol group to the DNIC.[16]
  46. Thus, the different nature of the two anionic ligands could lower the symmetry of the complex from axial to rhombic.[16]
  47. At room temperature, this complex shows an axially symmetric EPR spectrum, as distinct from the rhombic symmetry of DNIC-BSA.[16]
  48. As we will see below, there are various types of symmetry.[17]
  49. We are going to begin with the most well-known, symmetry with respect to a line or axial symmetry.[17]
  50. To better understand what symmetry is with respect to an axis, take a look at this video of one of our interactive tutorials.[17]
  51. is the one that divides an object or figure in two using , in other words, by an axis of symmetry.[17]
  52. Our discussion of symmetry in crystallography should begin with a description of crystals.[18]
  53. If other symmetry considerations do not override, then the cell is chosen so that a ≤ b ≤ c, and α, β, and γ all < 90 ° or all ≥ 90 °.[18]
  54. In the tetragonal, trigonal, and hexagonal systems, one axis contains higher symmetry.[18]
  55. Generally higher metric symmetry is identified by computer programs.[18]
  56. Asymmetrical balance refers to a kind of balance that does not rely on symmetry.[19]
  57. The architecture for interaction classifies behavior according to its symmetry.[19]
  58. The mutual exchange of reciprocity is based on the principle of symmetry interpreted as fair exchange.[19]
  59. The golden rule expresses the importance of maintaining symmetry and balance as we encounter others.[19]
  60. Proteins can adopt a range of different symmetries.[20]
  61. The most common one is cyclic symmetry which involves n-fold rotation around a symmetry axis (Cn symmetry).[20]
  62. Another common group is the Dihedral symmetries that combine one n-fold symmetry axis with perpendicular twofold symmetry axis.[20]
  63. For example D2 symmetry involves a dimer of dimers.[20]
  64. But in mathematics, symmetry has been given a more precise meaning.[21]
  65. An equilateral triangle has six symmetries, shown above.[21]
  66. Suffice it to say that the mathematical concept of a group captures the essence of symmetry in abstract terms.[21]
  67. The focus is on the operation that reveals the symmetry.[21]
  68. This latter notion of symmetry developed, via several steps, into the concept found today in modern science.[22]
  69. The group-theoretic notion of symmetry is the one that has proven so successful in modern science.[22]
  70. As we have seen, the scientific notion of symmetry (the one we are interested in here) is a recent one.[22]
  71. The second is between the two main ways of using symmetry.[22]

소스

  1. ↑ Reflection and Rotation
  2. ↑ 2.0 2.1 2.2 2.3 Symmetry (physics)
  3. ↑ 3.0 3.1 3.2 What is symmetry?
  4. ↑ 4.0 4.1 4.2 4.3 Wikipedia
  5. ↑ 5.0 5.1 5.2 5.3 Definition of Symmetry by Merriam-Webster
  6. ↑ 6.0 6.1 Symmetry group factorization reveals the structure-function relation in the neural connectome of Caenorhabditis elegans
  7. ↑ 7.0 7.1 7.2 7.3 Definition, Facts and Examples
  8. ↑ 8.0 8.1 8.2 8.3 college algebra
  9. ↑ 9.0 9.1 9.2 9.3 Identifying symmetrical figures
  10. ↑ 10.0 10.1 Symmetry Tutorial - Introduction
  11. ↑ 11.0 11.1 11.2 Reflective symmetry game for 4 to 8 year olds
  12. ↑ 12.0 12.1 Symmetry | biology
  13. ↑ Symmetry and asymmetry in thermoelectrics
  14. ↑ meaning in the Cambridge English Dictionary
  15. ↑ 15.0 15.1 15.2 15.3 Quanta Magazine
  16. ↑ 16.0 16.1 16.2 16.3 Symmetry - an overview
  17. ↑ 17.0 17.1 17.2 17.3 Symmetry: Definiton, Types, Exercises & Examples
  18. ↑ 18.0 18.1 18.2 18.3 Symmetry in Crystallography Notes
  19. ↑ 19.0 19.1 19.2 19.3 Emotional Competency
  20. ↑ 20.0 20.1 20.2 20.3 Symmetry User's Guide.
  21. ↑ 21.0 21.1 21.2 21.3 The Power of Symmetry
  22. ↑ 22.0 22.1 22.2 22.3 Symmetry and Symmetry Breaking (Stanford Encyclopedia of Philosophy)
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