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Symmetry
Published in Michael Hann, The Grammar of Pattern, 2019
So, in popular understanding, the word ‘symmetry’ is used to refer specifically to reflection symmetry, particularly where all parts on the left-hand side of an imaginary (two-sided) mirror are reflections to all parts on the right-hand side. This is known as ‘reflection symmetry’, with one reflection only. However, higher orders of reflection symmetry are possible, using two, three or more reflection axes. Visualisation is helped if each object, motif or figure is imagined as inscribed within a circle; each successive reflection axis reflects from two sides and is imagined as passing through the centre of that circle. So, in the popular imagination, at least, shapes or objects may be described as ‘symmetrical’ if they can be split into two or more reflected parts.
A novel mathematical model to measure individuals’ perception of the symmetry level of building facades
Published in Architectural Engineering and Design Management, 2020
Yusuf Cihat Aydin, Parham A. Mirzaei
Visual symmetry can simply be defined as the self-similarity of a visual stimulus under transformations. There are different types of symmetries and these can be grouped under three main headings, namely, reflectional, rotational, and translational symmetry (Wagemans, 1997). Visual demonstration of symmetry typologies is given in Figure 1. Reflection symmetry, also known as a mirror, line, bilateral symmetry, is the reflection of a visual stimulus around a line (e.g. vertical (Figure 1(A)), horizontal (Figure 1(B)) or diagonal-oblique (Figure 1(C))), the visual stimulus can have more than one symmetry line (multiple symmetries) (see Figure 1(D)). Rotational symmetry occurs when the visual stimulus is rotated relative to a specific pivot point (centric (Figure 1(E)) or decentralized (Figure 1(F))) without any change in its form. When the visual stimulus is moved or slide without any change in its form, this called translational symmetry (Figure 1(G)).
Unique solutions, stability and travelling waves for some generalized fractional differential problems
Published in Applied Mathematics in Science and Engineering, 2023
Mahdi Rakah, Yazid Gouari, Rabha W. Ibrahim, Zoubir Dahmani, Hasan Kahtan
Traveling waves can exhibit different types of symmetry, depending on the characteristics of the wave and the medium through which it travels. Here are some examples of symmetry in travelling waves: Reflection symmetry: A wave has reflection symmetry if it looks the same when reflected in a line or plane. For example, a sinusoidal wave that travels along a string has reflection symmetry because it looks the same when reflected in the string.Translational symmetry: A wave has translational symmetry if it looks the same after it has been shifted by a fixed distance. For example, a wave that travels along an infinitely long string has translational symmetry because it looks the same at any point along the string.Rotational symmetry: A wave has rotational symmetry if it looks the same after it has been rotated around a fixed point. For example, a circular wave that travels outward from a point source has rotational symmetry because it looks the same when viewed from any angle around the source. Time-reversal symmetry: A wave has time-reversal symmetry if it looks the same when time is reversed. For example, an electromagnetic wave that travels through free space has time-reversal symmetry because it looks the same whether it is moving forward or backward in time. In addition, the Duffing equation is symmetric under the transformation , which is known as the parity transformation. This means that if the displacement x of the oscillator is replaced with its negative, the equation remains unchanged.