{"product_id":"2940013018488","title":"The Fourth Dimension Simply Explained","description":"Scanned, proofed and corrected from the original hardcover edition for enjoyable reading. (Worth every penny spent!)\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e***\u003cbr\u003e\u003cbr\u003eAn excerpt from the Introduction:\u003cbr\u003e\u003cbr\u003eWe observe the forms and positions of objects very largely by sight. Now the organs of sight of a being confined to \u003cbr\u003e\u003cbr\u003esome particular space may be supposed suited to the dimensions of his space. The picture formed in the retina of our \u003cbr\u003e\u003cbr\u003eeye is two-dimensional, the retina is a surface. A two-dimensional being, unable to perceive anything outside of his \u003cbr\u003e\u003cbr\u003eplane would have a one-dimensional retina, or at least his picture of an object in his world would be a mere line, \u003cbr\u003e\u003cbr\u003edifferent pictures being distinguished by the lengths, colors, and shading of these lines. The retina of a four-\u003cbr\u003e\u003cbr\u003edimensional being would be three-dimensional if he is to receive separate impressions from all the rays of light \u003cbr\u003e\u003cbr\u003ewithin a given angle of vision. In fact, the boundary of an opaque object, the part which alone he can see, is \u003cbr\u003e\u003cbr\u003ethree-dimensional as is always the boundary of objects in space of four dimensions. \u003cbr\u003e\u003cbr\u003eIt is not easy for us to imagine such pictures, and so we can attempt to get an impression of the shapes of objects \u003cbr\u003e\u003cbr\u003eby supposing that a three-dimensional being, a person like ourselves, could pass through a series of parallel three-\u003cbr\u003e\u003cbr\u003espaces (three-dimensional spaces) and in each three-space examine that portion of the object which lies in this \u003cbr\u003e\u003cbr\u003espace, that section of the object. This is just as we might suppose a two-dimensional being able to pass through a \u003cbr\u003e\u003cbr\u003eseries of planes and in each plane to see the section of an object made by that plane. The section which we should \u003cbr\u003e\u003cbr\u003esee of a four-dimensional object would be a solid whose surface forms a part of the three-dimensional boundary of the \u003cbr\u003e\u003cbr\u003eobject. This way of studying four-dimensional objects is discussed quite fully...\u003cbr\u003e \u003cbr\u003e\u003cbr\u003eThere is another somewhat similar way of studying an object that we may find quite useful. We can imagine ourselves \u003cbr\u003e\u003cbr\u003eturning from one three-space into another perpendicular three-space. That is, by discarding one of the directions in \u003cbr\u003e\u003cbr\u003eour space we can suppose that we take into view the fourth direction, which goes away from our space, and so get its \u003cbr\u003e\u003cbr\u003erelation to two of our directions. We shall describe the section of an object made by any three-space as what we can \u003cbr\u003e\u003cbr\u003esee in that three-space. We shall do this particularly with reference to the different sections of an object obtained \u003cbr\u003e\u003cbr\u003eat any point by taking different perpendicular three-spaces. \u003cbr\u003e\u003cbr\u003eOne of the first things, for example, that we consider in studying Geometry of Four Dimensions is the line \u003cbr\u003e\u003cbr\u003eperpendicular to a three-space; such is the line which goes out from a point in our space in a new fourth direction \u003cbr\u003e\u003cbr\u003eperpendicular to all the lines of our space through that point. If we can let go of one of the dimensions of our \u003cbr\u003e\u003cbr\u003espace, keeping only that part which lies in a certain plane, and take into view the new fourth dimension, we shall \u003cbr\u003e\u003cbr\u003esee a plane and a line going out from it, perpendicular to all the lines of it, something with which we are perfectly \u003cbr\u003e\u003cbr\u003efamiliar. \u003cbr\u003e \u003cbr\u003e***\u003cbr\u003e\u003cbr\u003eComplete list of contributors:\u003cbr\u003e\u003cbr\u003eGRAHAM DENBY FITCH\u003cbr\u003eEDWARD H. CUTLER\u003cbr\u003eCARL A. RICHMOND\u003cbr\u003eCLAUDE BRAGDON\u003cbr\u003eARTHUR HAAS\u003cbr\u003eLEONARD C. GUNNELL\u003cbr\u003eBURTON HOWARD CAMP\u003cbr\u003eELIZABETH BROWN DAVIS\u003cbr\u003eG. M. ACKLOM\u003cbr\u003eLOUIS W. WORRELL\u003cbr\u003eARTHUR R. CRATHORNE\u003cbr\u003ePERCY WILCOX GUMAER\u003cbr\u003eW. S. DAVIDSON\u003cbr\u003eCHARLES JOHNSTON\u003cbr\u003eW. T., HOLLAND\u003cbr\u003eGEORGE GAILEY CHAMBERS\u003cbr\u003eELMER E. BURNS\u003cbr\u003eA. C. SILVERMAN\u003cbr\u003eWILMOT E. ELLIS","brand":"OGB","offers":[{"title":"Default Title","offer_id":47073634156784,"sku":"2940013018488","price":0.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/2940013018488_p0.jpg?v=1763575835","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/2940013018488","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}