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
- The simplest symmetry is Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry).[1]
- Continuous and discrete transformations give rise to corresponding types of symmetries.[2]
- The sphere is said to exhibit spherical symmetry.[2]
- Continuous spacetime symmetries are symmetries involving transformations of space and time.[2]
- A discrete symmetry is a symmetry that describes non-continuous changes in a system.[2]
- , where they might be given the following shapes and asked to draw lines of symmetry on them.[3]
- In, children are asked to identify lines of symmetry in 2D shapes presented in different orientations.[3]
- They may be asked to look at these regular shapes and think about how many lines of symmetry they can find.[3]
- In general, every kind of structure in mathematics will have its own kind of symmetry.[4]
- In biology, the notion of symmetry is mostly used explicitly to describe body shapes.[4]
- Early studies within the Gestalt tradition suggested that bilateral symmetry was one of the key factors in perceptual grouping.[4]
- The role of symmetry in grouping and figure/ground organization has been confirmed in many studies.[4]
- There's a lot of symmetry between the moon and Earth, most commonly seen in a phenomena known as tidal locking.[5]
- Written as 10/10/2020, the date bore a certain digital symmetry and numerological fascination.[5]
- The symmetry of the numbers appealed to him as a mathematician.[5]
- It’s the sort of blunt symmetry that was always Sorkin’s calling card.[5]
- Consequently, we expect that deviations from exact symmetries to be relatively ‘small’.[6]
- \({P}_{\varepsilon }\) approximates an exact symmetry in the ideal limit \(\varepsilon \to 0\).[6]
- Any line splitting a shape into two parts such that the two parts are the same is called a line of symmetry.[7]
- Can we have more than one line of symmetry?[7]
- Example 4: Given below is a left part of a picture and its line of symmetry.[7]
- We look at each vertex of the yellow part and measure its distance from the line of symmetry.[7]
- 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]
- The black dot represents the original point and the colored dots demonstrate the four types of symmetry.[8]
- : 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]
- : 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]
- And now that answer is only helpful if we know what a line of symmetry is.[9]
- A line of symmetry is a line where we can fold the image and have both halves match exactly.[9]
- 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]
- Maybe this could be our line of symmetry.[9]
- Welcome to the world of symmetry![10]
- The next few pages introduce each of these symmetry elements with example molecules having each type of symmetry.[10]
- 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]
- The pictures and patterns have vertical lines of symmetry while the shapes include both vertical and horizontal lines of symmetry.[11]
- For further practise on symmetry try our Symmetry Sorting game.[11]
- Thus, only one plane of symmetry will divide a bilateral animal into symmetrical halves, the median longitudinal, or sagittal, plane.[12]
- The concept of symmetry is also applied in botany.[12]
- In this perspective, we summarized these advanced achievements obtained through utilizing symmetry and asymmetry in thermoelectrics.[13]
- We also work out the explicit form of our condition for the dihedral group of symmetries of a regular polygon.[14]
- It is this transformation of an object so that the result is indistinguishable from the original that defines a symmetry.[15]
- A symmetry requires that the transformation not alter the size or shape of the object.[15]
- Now we can continue our analysis of the symmetries of a square.[15]
- Of course it’s impossible to tell, precisely because of the criteria for a symmetry.[15]
- This symmetry is lower than expected for DNIC with low-molecular-weight thiols, which have axial symmetry (see above).[16]
- This low symmetry is plausibly rationalized by BSA molecule contributing only one thiol group to the DNIC.[16]
- Thus, the different nature of the two anionic ligands could lower the symmetry of the complex from axial to rhombic.[16]
- At room temperature, this complex shows an axially symmetric EPR spectrum, as distinct from the rhombic symmetry of DNIC-BSA.[16]
- As we will see below, there are various types of symmetry.[17]
- We are going to begin with the most well-known, symmetry with respect to a line or axial symmetry.[17]
- To better understand what symmetry is with respect to an axis, take a look at this video of one of our interactive tutorials.[17]
- is the one that divides an object or figure in two using , in other words, by an axis of symmetry.[17]
- Our discussion of symmetry in crystallography should begin with a description of crystals.[18]
- 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]
- In the tetragonal, trigonal, and hexagonal systems, one axis contains higher symmetry.[18]
- Generally higher metric symmetry is identified by computer programs.[18]
- Asymmetrical balance refers to a kind of balance that does not rely on symmetry.[19]
- The architecture for interaction classifies behavior according to its symmetry.[19]
- The mutual exchange of reciprocity is based on the principle of symmetry interpreted as fair exchange.[19]
- The golden rule expresses the importance of maintaining symmetry and balance as we encounter others.[19]
- Proteins can adopt a range of different symmetries.[20]
- The most common one is cyclic symmetry which involves n-fold rotation around a symmetry axis (Cn symmetry).[20]
- Another common group is the Dihedral symmetries that combine one n-fold symmetry axis with perpendicular twofold symmetry axis.[20]
- For example D2 symmetry involves a dimer of dimers.[20]
- But in mathematics, symmetry has been given a more precise meaning.[21]
- An equilateral triangle has six symmetries, shown above.[21]
- Suffice it to say that the mathematical concept of a group captures the essence of symmetry in abstract terms.[21]
- The focus is on the operation that reveals the symmetry.[21]
- This latter notion of symmetry developed, via several steps, into the concept found today in modern science.[22]
- The group-theoretic notion of symmetry is the one that has proven so successful in modern science.[22]
- As we have seen, the scientific notion of symmetry (the one we are interested in here) is a recent one.[22]
- The second is between the two main ways of using symmetry.[22]
소스
- ↑ Reflection and Rotation
- ↑ 2.0 2.1 2.2 2.3 Symmetry (physics)
- ↑ 3.0 3.1 3.2 What is symmetry?
- ↑ 4.0 4.1 4.2 4.3 Wikipedia
- ↑ 5.0 5.1 5.2 5.3 Definition of Symmetry by Merriam-Webster
- ↑ 6.0 6.1 Symmetry group factorization reveals the structure-function relation in the neural connectome of Caenorhabditis elegans
- ↑ 7.0 7.1 7.2 7.3 Definition, Facts and Examples
- ↑ 8.0 8.1 8.2 8.3 college algebra
- ↑ 9.0 9.1 9.2 9.3 Identifying symmetrical figures
- ↑ 10.0 10.1 Symmetry Tutorial - Introduction
- ↑ 11.0 11.1 11.2 Reflective symmetry game for 4 to 8 year olds
- ↑ 12.0 12.1 Symmetry | biology
- ↑ Symmetry and asymmetry in thermoelectrics
- ↑ meaning in the Cambridge English Dictionary
- ↑ 15.0 15.1 15.2 15.3 Quanta Magazine
- ↑ 16.0 16.1 16.2 16.3 Symmetry - an overview
- ↑ 17.0 17.1 17.2 17.3 Symmetry: Definiton, Types, Exercises & Examples
- ↑ 18.0 18.1 18.2 18.3 Symmetry in Crystallography Notes
- ↑ 19.0 19.1 19.2 19.3 Emotional Competency
- ↑ 20.0 20.1 20.2 20.3 Symmetry User's Guide.
- ↑ 21.0 21.1 21.2 21.3 The Power of Symmetry
- ↑ 22.0 22.1 22.2 22.3 Symmetry and Symmetry Breaking (Stanford Encyclopedia of Philosophy)