On Symmetry and Asymmetry

WAVE SYMMETRY, 2021

In this paper, the author declares a fundamental conservation law, due to which, and the symmetry associated with it, all known interactions arise as a reaction to a change in the energy status of formed and already established material systems.

Symmetry

Symmetry can be understood in two different ways: as a property or as a principle. As Plato said, the symmetry that can be seen in nature is not random in itself, because it is a result of the symmetries of the physical laws. Thus, the principles of symmetry have been used to solve mechanical problems since antiquity. Today, these principles are still being researched; for example, in chemical engineering, the spatial symmetry properties of crystal lattices are being studied, or in electrical engineering, the temporal symmetry of the periodic processes of oscillators can be observed. This Special Issue is dedicated to symmetry in engineering sciences (electrical, mechanical, civil, and others) and aims to cover both engineering solutions related to symmetry and the search for patterns to understand the phenomena observed.

At Right Angles, 2016

This is the second part of a two-part article whose aim is to familiarise the reader with both the mathematical concept and an intrinsic idea of symmetry. The first part of the article concentrated on a ‘working definition’ of symmetry and also laid the mathematical base to understand symmetry. It discussed symmetries of figures that can be drawn on a sheet of paper and of a particular type of infinite pattern called a strip pattern or a frieze pattern In this part we will concentrate on another infinite two-dimensional pattern called the wallpaper pattern and also explore aspects of symmetry in the everyday objects around us. See http://teachersofindia.org/en/ebook/through-symmetry-lens-part-2, July 2016 pages 11-16.

2002

In this paper we examine the loss of symmetry in mechanics of mate rial To this end we rst review the so called Bromwich bounds of eigenvalues in linear algebra For illustration we revisit the hierarchy of di erent failure diagnos tics when the material properties loose symmetry Subsequently we examine the lack of symmetry in the stress and strain measures which appears in nite deforma tion analysis and in micropolar continua For de niteness we evaluate maximum and minimum values of the non symmetric second order tensors which no longer coincide with the principal eigenvalues and we discuss the special format of the trace invariants For geometric visualization we generalize Mohr s circle and the underlying transformation relations which account for the loss of symmetry in two dimensions To conclude we consider two examples of shear failure which serve as model problems to address the intricate di erences of symmetric and non symmetric stress and deformation measures

Symmetry

The symmetry concept is mainly used in two senses. The first from the aesthetic point of view of proportionality or harmony, since human beings seek symmetry in nature. Or the second, from an engineering point of view to attend to geometric regularities or to explain a repetition process or pattern in a given phenomenon. This special issue dedicated to geometry in engineering deals with this last concept, which aims to collect both the aspects of geometric solutions in engineering, which may even have a certain aesthetic character, and the aspect of the use of patterns that explain observed phenomena.

The definition of symmetry is: an object or shape involves a kind of symmetry if performing certain manipulations constantly in all it’s parts, it’s description is invariant (Murray Gell-Man) . We say that the object or phenomenon is symmetrical about these manipulations. For example rotating a cylinder around its axis leaves it unchanged, the cylinder is symmetrical with respect to it’s axis.

Foundations of Science, 2016

Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce several notions of symmetry in mathematics and explain how they can also be used in resolving different problems in the philosophy of mathematics. We use symmetry to discuss the objectivity of mathematics, the role of mathematical objects, the unreasonable effectiveness of mathematics and the relationship of mathematics to physics.

Journal of Physics: Conference Series, 2011

After an historical introduction of the concept of symmetry, the many ways in which symmetry is used today in physics are briefly reviewed. A new concept, super-symmetry, introduced in the 1970's is also briefly reviewed, and the only experimental example of supersymmetry in physics presented. The future of symmetry in physics is briefly discussed. 1. The notion of symmetry Symmetry, from the Greek σύμμετρος (well-ordered, well-proportioned) was originally introduced to describe certain properties of artifacts (Polykleitos, Περι βελοποιϊκών, IV, 2). All ancient civilizations used this concept. Two examples are shown in figures 1 and 2.

Humanistic Mathematics Network Journal, 1996

Mathematical Principles, 2022