symmetrical

Examples of symmetrical in the following topics:

• Skewness and the Mean, Median, and Mode

  • The histogram displays a symmetrical distribution of data.
  • A distribution is symmetrical if a vertical line can be drawn at some point in the histogram such that the shape to the left and the right of the vertical line are mirror images of each other.
  • In a perfectly symmetrical distribution, the mean and the median are the same.
  • In a symmetrical distribution that has two modes (bimodal), the two modes would be different from the mean and median.
  • is not symmetrical.

• Animal Characterization Based on Body Symmetry

  • At a very basic level of classification, true animals can be largely divided into three groups based on the type of symmetry of their body plan: radially symmetrical, bilaterally symmetrical, and asymmetrical.
  • Radially symmetrical animals have top and bottom surfaces, but no left and right sides, or front and back.
  • All true animals, except those with radial symmetry, are bilaterally symmetrical.
  • They are believed to have evolved from bilaterally symmetrical animals; thus, they are classified as bilaterally symmetrical.
  • However, the larval fish are bilaterally symmetrical.

• Symmetry of Functions

  • Two objects are symmetric to each other with respect to the invariant transformations if one object is obtained from the other by one of the transformations.
  • In the case of symmetric functions, determining symmetry is as easy as graphing the function or evaluating the function algebraically.  
  • Symmetry of a function can be a simple shift of the graph (transformation) or the function can be symmetric about a point, line or axes.
  • Functions and relations can be symmetric about a point, a line, or an axis.  

• Gene Expression in Stem Cells

  • Symmetric division maintains stem cell lines and asymmetric division yields differentiated cells.
  • To ensure self-renewal, stem cells undergo two types of cell division: symmetric and asymmetric.
  • Symmetric division gives rise to two identical daughter cells both endowed with stem cell properties.
  • It is possible that the molecular distinction between symmetric and asymmetric division lies in differential segregation of cell membrane proteins between the daughter cells.
  • This is in contrast to normal symmetric cell divisions, which give rise to daughter cells of equivalent fates.

• Gravitational Attraction of Spherical Bodies: A Uniform Sphere

  • The Shell Theorem states that a spherically symmetric object affects other objects as if all of its mass were concentrated at its center.
  • For highly symmetric shapes such as spheres or spherical shells, finding this point is simple.
  • A spherically symmetric object affects other objects gravitationally as if all of its mass were concentrated at its center,
  • If the object is a spherically symmetric shell (i.e., a hollow ball) then the net gravitational force on a body inside of it is zero.
  • That is, a mass $m$ within a spherically symmetric shell of mass $M$, will feel no net force (Statement 2 of Shell Theorem).

• Other Scales

  • For example, one class of scales that intrigues some composers is symmetrical scales.
  • The chromatic scale and whole tone scales fall into this category, but other symmetrical scales can also be constructed.
  • A diminished scale, for example, not only has the "symmetrical" quality; it is also a very useful scale if, for example, you are improvising a jazz solo over diminished chords.
  • Like chromatic and whole tone scales, a diminished scale is "symmetrical".

• Shapes of Sampling Distributions

  • The overall shape of a sampling distribution is expected to be symmetric and approximately normal.
  • Even in the relatively simple case of a mounded distribution, the distribution may be skewed to the left or skewed to the right (with symmetric corresponding to no skew).
  • As previously mentioned, the overall shape of a sampling distribution is expected to be symmetric and approximately normal.

• Trigonometric Symmetry Identities

  • Recall that even functions are symmetric about the $y$-axis, and odd functions are symmetric about the origin, $(0, 0)$.
  • Recall that cosine is an even function because it is symmetric about the $y$-axis.
  • The cosine and secant functions are symmetric about the y-axis.
  • Graphs that are symmetric about the $y$-axis represent even functions.
  • Graphs that are symmetric about the origin represent odd functions.

• Typical Shapes

  • Distributions can be symmetrical or asymmetrical depending on how the data falls.
  • In a symmetrical distribution, the two sides of the distribution are mirror images of each other.
  • A normal distribution is an example of a truly symmetric distribution of data item values.
  • When a histogram is constructed on values that are normally distributed, the shape of the columns form a symmetrical bell shape.

• Octahedral Complexes

  • Octahedral complexes have six ligands symmetrically arranged around a central atom, defining the vertices of an octahedron.
  • Octahedral molecular geometry describes the shape of compounds wherein six atoms or groups of atoms or ligands are symmetrically arranged around a central atom.