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Henry P.Manning

The Fourth Dimension Simply Explained

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To remove the contents of an egg without puncturing its shell or to drink the liquor in a bottle without removing the cork is clearly unthinkable — or is it? Understanding the world of Einstein and curved space requires a logical conception of the fourth dimension.This readable, informative volume provides an excellent introduction to that world, with 22 essays that employ a minimum of mathematics. Originally written for a contest sponsored by Scientific American, these essays are so well reasoned and lucidly written that they were judged to merit publication in book form. Their easily understood explanations cover such topics as how the fourth dimension may be studied, the relationship of non-Euclidean geometry to the fourth dimension, analogues to three-dimensional space, some four-dimensional absurdities and curiosities, possible measurements and forms in the fourth dimension, and extensive considerations of four-dimensional space's simpler properties.Since each essay is independently conceived, all of the writers offer fresh viewpoints and original examples. Because of this, some of the most important principles relating to the fourth dimension are viewed from several different angles at once — an invaluable aid to visualizing these abstruse but fascinating ideas. New Introduction by Thomas F. Banchoff, Brown University. 82 figures.
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353 Druckseiten
Jahr der Veröffentlichung
2012
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  • Mily Sietehat Zitat gemachtvor 3 Jahren
    Almost all of the essayists explored analogies for constructing a four-dimensional geometry that extended our understanding of ordinary three-dimensional space, and almost all of them debunked the spiritist claims. Manning explains that there is a great deal of repetition in the essays, although there are differences in emphasis that justify their selection.

    The Dimensional Analogy
    For several years after his graduation from Brown University in 1883, Manning taught in secondary schools, so he was aware of the importance of the dimensional analogy in the curriculum. He starts his introduction “The geometry studied in the schools is divided into two parts, Plane Geometry, or Geometry of Two Dimensions, and Solid Geometry, or Geometry of Three Dimensions, and the study of these geometries suggests an extension to geometry of four or more dimensions.” Unfortunately a good deal of solid geometry has disappeared from the secondary-school curriculum, so the power of the dimensional analogy is no longer so strong. This may be one of the most important reasons to republish these essays, reflecting as they do a common appreciation of the geometrical background of the average reader of Scientific American nearly a century ago.
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