Nature uses symmetry to make things beautiful. For example, consider the pictures of the butterfly and the leaf. Recommend 2 Comment 0. Symmetry is often seen everyday by people of all ages in nature. Symmetry that we see everyday in nature is most often Bilateral Symmetry.
This means that the two halves of an object are exactly mirror images of each other. Symmetry in humans the human face has a line of symmetry in some places, but some faces are more symmetrical than others. The more symmetrical your face the prettier your face will appear. A perfect example of this is supermodels and actresses.
Another example of human symmetry is the kidneys, lungs, and the brain. If you draw a line or slice these organs in half, you will have a mirror image of the other. In flowers there are roughly identical petals, sepals, stamens, and leaves. While at the beach there are a wide variety of shells and underwater life with a line of symmetry, an example of this is a crab, a lobster, octopus, and starfish.
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We learn in daily lives, area in daily life as understand mathematics problems related to clipboard. Moving in daily lives and symmetries of personality from? How is this related to symmetry? A geometric figure that we wish to study is usually given as a set of points existing in some ambient space. For example, a tiling pattern may be given as a collection of line segments in the plane. Thus, in inaction, we see action. But a symmetry transformation is not just any action; it must leave the pattern as a set of points invariant.
Thus, what is important to us is that in this action the transformation , we are able to see inaction the invariance of the set of points making up the pattern.
This is the seed of all that I want students to know about symmetry: action and inaction, a transformation and its invariants, what changes and what stays the same.
With this, the students gain a unifying perspective on the concept of symmetry that can help them understand it initially and that can later help them simplify and unify all the occurrences of this concept as they are met and eventually understand symmetry groups, invariants, and so on.
This theme can also help students connect all instances of symmetry that they have already seen to this one unifying perspective. For example, in the commutative and associative properties of arithmetic, the positions of the numbers or parentheses change, but the answer does not change. For a tiling, the Euclidean plane can be rotated, reflected or translated in certain ways, but the pattern remains the same. A knot can be moved and redrawn, but its Conway polynomial is invariant, and so on.
This verse from the Bhagavad-Gita not only captures the essence of symmetry, it also helps students understand the importance of invariants wherever they might see them. This silent level of life is the source of the active levels of life; it is subtler and more abstract than the active levels, but more powerful and more important.
Elsewhere, Maharishi explains this using an analogy of the ocean. The ocean is silent at its depths and the dynamism of the waves is just the natural expression of the silent levels; the silent, nonchanging level is more fundamental.
Thus, it is the invariants of a transformation that will be useful to us, even though at first they may seem difficult to grasp because of their subtlety or abstraction. For students at Maharishi International University, this understanding takes on a very personal meaning in terms of their practice of the Transcendental Meditation technique, which allows the active thinking mind to settle down to the silent, nonactive state of consciousness at its source. In their own experience, they see that their consciousness has two aspects, active and silent, and that the silent level is more fundamental and more powerful than the dynamic level.
In a very concrete way, they are able to connect the ideas of symmetry transformation and invariants to their own personal experience. Nevertheless, they will have seen symmetry in many forms already: nature, manufactured objects, art and architecture, and even in mathematics commutativity, circles and squares, odd and even functions, and so on. It is good for students to have an understanding of symmetry that includes all the examples that they have seen and lays a foundation for further study.
I want to introduce them to the idea of symmetry transformation, even though they may not know what a function is, so that they will remember it, feel that it is important, and be able to make some use of it. Students should realize that symmetry locates some underlying property that may be more abstract and less obvious but is more unifying and more discriminating.
I also want students to have some insight into why symmetry is attractive and aesthetically appealing to us. Using the verse from the Bhagavad-Gita as a guide, symmetry can be learned in a unifying way that students seem to enjoy.
Then we examine some finite designs from the artwork of different cultures and revise our notions of symmetry based on the fact that these designs should come under our definition of symmetry.
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