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Following the life and work of famous mathematicians from antiquity to the present, Stewart traces mathematics' developing handling of the concept of symmetry.One of the first takeaways, established in the preface of this book, is that it dispels the idea of the origins of symmetry in geometry, as is often the first context in which the term is introduced.
The type of symmetry is determined by the way the pieces are organized, or by the type of transformation: An object has reflectional symmetry (line or mirror symmetry) if there is a line (or in 3D a plane) going through it which divides it into two pieces that are mirror images of each other. [6]
For example, mathematical beauty arises in a Math Circle activity on symmetry designed for 2nd and 3rd graders, where students create their own snowflakes by folding a square piece of paper and cutting out designs of their choice along the edges of the folded paper. When the paper is unfolded, a symmetrical design reveals itself.
Facial symmetry is one specific measure of bodily symmetry. Along with traits such as averageness and youthfulness, it influences judgments of aesthetic traits of physical attractiveness and beauty. [1] For instance, in mate selection, people have been shown to have a preference for symmetry. [2] [3]
A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other.. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). [1]
Excluding the 10% most and 10% least beautiful women, women's attractiveness does not change between 18 and 40. If extremes are included, however, "there's no doubt that younger [women] are more physically attractive – indeed in many ways beauty and youth are inextricable. That's why most of the models you see in magazines are teenagers". [58]
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For the person interested in tilings and patterns, Visions of Symmetry provides many beautiful examples (which illustrate the theory expounded in Grünbaum and Shepard's Tilings and patterns [1987])." [8] J. Kevin Colligan reviewing the book for The Mathematics Teacher wrote: "This book sits on the boundary between mathematics and art, as did ...