Visualize hypercheckers and hyperchess in the 4th dimension, rotate a Rubik's hypercube, stack tesseracts together to build a hyperpyramid or a hypercross, view a hypertable with hyperchairs, climb hyperstairs, open the hyperdoor to a hyperhouse, watch hypertelevision, read a hyperbook, arrange glomes in a 4D lattice structure to create hypercrystals, stack hyperfruits at a hypersupermarket, record the position of a hyperstar with hypercelestial coordinates, make a hypermap using hypercompass directions, watch a spinning hyperplanet with tilt revolve around a hypersun, see a sample alphanumeric system for writing and arithmetic in 4D space, line up a shot on a hyperbilliards table, enjoy hyperbowling or hypertennis, and contemplate an object's reflection from a hyperplanar or hyperspherical mirror - all on this colorful journey through the fourth dimension. Each page consists of colorful images of four-dimensional objects with a paragraph caption describing the figures at the bottom.

"What Vesalius was to Galen, what Copernicus was to Ptolemy, that was Lobachevski to Euclid." Lobachevski was the first to publish non-Euclidean geometry. An unabridged printing, to include all figures, from the translation by Halsted.

These full-color illustrations on 8"x10" pages are at once aesthetically captivating and instructive. Each page consists of colorful images of tesseracts (4D hypercubes) or glomes (4D hyperspheres) with a paragraph caption describing the figures at the bottom. Color is used effectively to show how to visualize the features of tesseracts and glomes, how to draw tesseracts in perspective, how a tesseract unfolds, how the features of tesseracts and glomes change as they rotate, how to find the intersection of a tesseract or glome with a hyperplane, how hyperspherical coordinates are defined, how to understand hypercompass directions, and how to draw longitudes, hyperlatitudes, and latitudes. Rectangular hyperboxes and a hyperellipsoid are also shown. Subsequent volumes of this series will build upon these fundamental 4D objects to help you imagine features of a 4D world such as a hyperchair, a hypercross, a hyperpyramid, a hyperhouse, crystal structures, and simple hypermachines.

Bertrand Russell was a prolific writer, revolutionizing philosophy and doing extensive work in the study of logic. This, his first book on mathematics, was originally published in 1897 and later rejected by the author himself because it was unable to support Einstein's work in physics. This evolution makes An Essay on the Foundations of Geometry invaluable in understanding the progression of Russell's philosophical thinking. Despite his rejection of it, Essays continues to be a great work in logic and history, providing readers with an explanation for how Euclidean geometry was replaced by more advanced forms of math. British philosopher and mathematician BERTRAND ARTHUR WILLIAM RUSSELL (1872-1970) won the Nobel Prize for Literature in 1950. Among his many works are Why I Am Not a Christian (1927), Power: A New Social Analysis (1938), and My Philosophical Development (1959).

AUTHOR: Chris McMullen earned his Ph.D. in particle physics from Oklahoma State University. Dr. McMullen currently teaches physics at Northwestern State University of Louisiana. His background on the geometry and physics of a possible fourth dimension of space includes a half-dozen research papers on the prospects of discovering large extra dimensions at the Large Hadron Collider.DESCRIPTION: This book takes you on a visual tour of a fourth dimension of space. It is much more visual and conceptual than algebraic, yet it is detailed and technical, with the intention of satisfying the needs of mathematically-minded readers familiar with the fundamentals of algebra, geometry, and graphing. Here is a sample of what you will find: A fascinating tour of the second and lower dimensions, which will help to understand the fourth dimension by analogy.A chapter dedicated toward imagining what it might be like to live in a hypothetical 4D hyperuniverse. This includes details like 4D wheels with axles, a 4D staircase, and a 4D room.Pictures of flat 4D objects called polytopes, like the tesseract, pentachoron, and icositetrachoron. A unique graph of a hecatonicosachoron has 12 of its 120 bounding dodecahedra highlighted to help visualize its complicated structure.In-depth discussion of the hypercube, including numerical patterns, rotations, cross sections, and perspective. Watch a tesseract unfold.Visual intersections of 15 pairs of perpendicular planes and 6 pairs of orthogonal hyperplanes in 4D space.Unique graphs of curved hypersurfaces in 4D space, like the glome, spherinder, cubinder, and hyperparaboloid.PUZZLES: Several puzzles are included to challenge the reader to contemplate the fourth dimension. Answers are included at the back of the book.AUDIENCE: This book is highly visual and very conceptual such that anyone with an appreciation for geometry may understand it, while at the same time including ample detail to also satisfy readers with a strong background in mathematics.

The secrets of life and the Universe revealed...
Living with Geometry is about how civilization has been using and abusing Geometry and other related scientific subject areas for our finite needs in the physical, material plane for ages gone by, and how we must now turn to the natural world, learn from it and employ the ancient and trusted sciences of a wondrous yesteryear to carry on in future, in order for the human spirit to be freed from its material confines, and how the physical environment can be saved along with us.
It is about what went missing, what went wrong, and what we need to learn about, in order to deal with the problem. The project became literally, "A Survey for the Truth."

An Unabridged Printing, To Include All Exercises: Foundations - Elementary Theorems On Order - The Affine Group In The Plane - Euclidean Plane Geometry - Ordinal And Metric Properties Of Conics - Inversion Geometry And Related Topics - Comprehensive Index

This is the definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and for elementary Euclidean geometry, essentially according to Hilbert. Appropriate for liberal arts students, prospective high school teachers, math. majors, and even bright high school students. The first eight chapters are mostly accessible to any educated reader; the last two chapters and the two appendices contain more advanced material, such as the classification of motions, hyperbolic trigonometry, hyperbolic constructions, classification of Hilbert planes and an introduction to Riemannian geometry.

"Lobachevsky believed that another form of geometry existed, a non-Euclidean geometry, and this 1840 treatise is his argument on its behalf. Line by line in this classic work he carefully presents a new and revolutionary theory of parallels, one that allows for all of Euclids axioms, except for the last. This 1891 translation includes a bibliography and translator George B. Halsteds essay on elliptic geometry. Russian mathematician NICHOLAS LOBACHEVSKY (17921856) is best remembered as the founder (along with Janos Bolyai) of non-Euclidean geometry. He is also the author of New Foundations of Geometry (18351838) and Pangeometry (1855)."

A fascinating memoir from the man who revitalized visual geometry, and whose ideas about fractals have changed how we look at both the natural world and the financial world.
Benoit Mandelbrot, the creator of fractal geometry, has significantly improved our understanding of, among other things, financial variability and erratic physical phenomena. In "The Fractalist, " Mandelbrot recounts the high points of his life with exuberance and an eloquent fluency, deepening our understanding of the evolution of his extraordinary mind. We begin with his early years: born in Warsaw in 1924 to a Lithuanian Jewish family, Mandelbrot moved with his family to Paris in the 1930s, where he was mentored by an eminent mathematician uncle. During World War II, as he stayed barely one step ahead of the Nazis until France was liberated, he studied geometry on his own and dreamed of using it to solve fresh, real-world problems. We observe his unusually broad education in Europe, and later at Caltech, Princeton, and MIT. We learn about his thirty-five-year affiliation with IBM's Thomas J. Watson Research Center and his association with Harvard and Yale. An outsider to mainstream scientific research, he managed to do what others had thought impossible: develop a new geometry that combines revelatory beauty with a radical way of unfolding formerly hidden laws governing utter roughness, turbulence, and chaos.
With full-color inserts and black-and-white photographs throughout.

The name non-Euclidean was used by Gauss to describe a system of geometry which differs from Euclid's in its properties of parallelism. Such a system was developed independently by Bolyai in Hungary and Lobatschewsky in Russia, about 120 years ago. Another system, differing more radically from Euclid's, was suggested later by Riemann in Germany and Cayley in England. The subject was unified in 1871 by Klein, who gave the names of parabolic, hyperbolic, and elliptic to the respective systems of Euclid-Bolyai-Lobatschewsky, and Riemann-Cayley. Since then, a vast literature has accumulated. The Fifth edition adds a new chapter, which includes a description of the two families of 'mid-lines' between two given lines, an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, a computation of the Gaussian curvature of the elliptic and hyperbolic planes, and a proof of Schlafli's remarkable formula for the differential of the volume of a tetrahedron.