대칭

• Mouchet, Amaury. 2015. ‘Symmetry: A Bridge between Nature and Culture’. arXiv:1503.01038 [physics], February. http://arxiv.org/abs/1503.01038.

메모

• 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

노트

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