Non-Euclidean Geometries

Geometric Formulas (Quickstudy: Academic)

Format: Pamphlet Language: English Format: PDF / Kindle / ePub Size: 5.69 MB Downloadable formats: PDF There were two ways to contradict the postulate: space could have 1) no parallel lines (straight lines in a plane will always meet if extended far enough), or 2) multiple straight lines through a given point parallel to a given line in the plane. We think that [the geometric calculus] can especially be useful as a mathematical tool for economics and finance ... We must underscore that to discover that there was a non-Newtonian way to look to differential equations has been a great surprise for us. [...]

Projective Geometry - Volume II

Format: Paperback Language: English Format: PDF / Kindle / ePub Size: 6.46 MB Downloadable formats: PDF One of the most exciting areas of NNC application is fractal geometry, a subject created in the 1970s by Benoit Mandelbrot, a brilliant maverick mathematician/scientist whose work was, like ours, at first dismissed as pointless. I strongly recommend they be used in that manner by students, although it's not necessary. A preferential attachment network model is a sequence of random graphs that is built according to a simple dynamic rule. On the Internet, each of the books can be read and downloaded, free of charge, at HathiTrust, Google Books, and the Digital Public Library of America. [...]

The algebra of logic

Format: Paperback Language: English Format: PDF / Kindle / ePub Size: 12.70 MB Downloadable formats: PDF Cambridge. 1999. 0521459303 Lastly, there is a reprint of a 1945 classic on special and general relativity by Lillian Lieber with illustrations by her husband Hugh. In fact there are infinitely many possible inequivalent Riemannian metrics and each gives a different geometry to the manifold. Hilbert was warmly regarded by his colleagues and students, and contributed to the careers of several great mathematicians and physicists including Georg Cantor, Hermann Minkowski, Hermann Weyl, John von Neumann, Emmy Noether, Alonzo Church, and Albert Einstein. [...]

How to draw a straight line ; a lecture on linkages

Format: Paperback Language: English Format: PDF / Kindle / ePub Size: 14.62 MB Downloadable formats: PDF Cantor's creation of transfinite set theory was an achievement of major consequence in the history of mathematics." - Joseph Dauben, from his book Georg Cantor: His Mathematics and Philosophy of the Infinite, pages 1 and 6 (1990). "Resistance to irrationals [i.e., irrational numbers] continued for thousands of years. For our orthogonal coord systems, side lengths may be simply read off from the metric as the square root of the coordinate differentials. [Footnote: The volume element in spherical coordinates is not equal to the product of the dx dy dz differentials of the transform equations (TE3). [...]

Einstein's Legacy: The Unity of Space and Time

Format: Print Length Language: English Format: PDF / Kindle / ePub Size: 14.42 MB Downloadable formats: PDF In the beginning we were naively unaware that new and unusual ideas, even in science and mathematics, are often ignored, ridiculed, or demeaned by the academic establishment, even in the 20th and 21st centuries. This new operator, the multiplicative gradient, ... is developed using non-Newtonian calculus." - Romulus Terebes (Technical University of Cluj-Napoca [TUCN], Romania), Monica Borda (TUCN, Romania), Christian Germain (IMS Laboratory, Bordeaux, France), Raul Malutan (TUCN, Romania), and Ioana Iles (TUCN, Romania); from their 2015 article "A multiplicative gradient-based anisotropic diffusion approach for speckle noise removal". [268] "This work presents a new operator of non-Newtonian type which [has] shown [to] be more efficient in contour detection [in images with multiplicative noise] than the traditional operators. ... [...]

Mary Reed Missionary to the Lepers

Format: Hardcover Language: English Format: PDF / Kindle / ePub Size: 7.51 MB Downloadable formats: PDF This pioneering work initiated numerous studies." - Agamirza E. Riemann's new idea of space proved crucial in Einstein's general relativity theory and Riemannian geometry, which considers very general spaces in which the notion of length is defined, is a mainstay of modern geometry. [edit]Symmetry The theme of symmetry in geometry is nearly as old as the science of geometry itself. Nevertheless, some authors have used the name "multiplicative calculus" for the geometric calculus, while others have used the same name for the bigeometric calculus. [...]

365 Multiplication Worksheets with 4-Digit Multiplicands,

Format: Print Length Language: English Format: PDF / Kindle / ePub Size: 6.42 MB Downloadable formats: PDF The theory of Lebesgue integration, Lebesgue measure, sequences of functions, absolute continuity, properties of LP-spaces. The author develops the axioms to include Euclidean, elliptic, and hyperbolic geometry, showing how geometry has real and far-reaching implications. Unseen University's mad but Good with Numbers Bursar has posited that there is an extra number between three and four, which he calls 'umpt' (as in, 'umpteen' minus ten). [...]

Lectures on Vector Bundles over Riemann Surfaces. (MN-6)

Format: Paperback Language: English Format: PDF / Kindle / ePub Size: 12.63 MB Downloadable formats: PDF Given distinct points A and B, they determine a unique ray with initial point A. A shortest curve between any pair of points on such a curved surface is called a minimal geodesic. The dissertation is entitled "Multiplicative calculus and its applications". [191] Non-Newtonian calculus and some of its applications are the topics of the 2011 doctoral dissertation of Ugur Kadak at Gazi University in Turkey. Englehardt and Ruochen Li. "The discrete Weibull distribution: an alternative for correlated counts with confirmation for microbial counts in water", Risk Analysis, Volume 31, Issue 3, Pages 370–381, DOI: 10.1111/j.1539-6924.2010.01520.x, Wiley, 2011. [86] David Baqaee. "Intertemporal choice: a Nash bargaining approach", Reserve Bank of New Zealand, Research: Discussion Paper Series, ISSN 1177-7567, DP2010/08, September 2010. [87] Agamirza E. [...]

Selected Questions of Mathematical Physics and Analysis

Format: Paperback Language: English Format: PDF / Kindle / ePub Size: 9.39 MB Downloadable formats: PDF The 20th century Developments in algebraic geometry included the study of curves and surfaces over finite fields as demonstrated by the works of among others André Weil, Alexander Grothendieck, and Jean-Pierre Serre as well as over the real or complex numbers. Because history shows that the deeper your idea cuts into the heart of a field, the more your peers are likely to challenge you. Classification of all locally Cn or Dn geometries.- 12.6. Euler's polyhedron formula — Take any polyhedron, add the number of vertices and the number of faces, and then subtract the number of edges. [...]

Euclidean And Non-Euclidean Geometry::Development and

Format: Paperback Language: Format: PDF / Kindle / ePub Size: 5.22 MB Downloadable formats: PDF We knew that the bigeometric calculus like the geometric calculus and maybe many other non-Newtonian calculi would be useful. You may want to demonstrate the following model of Poincaré's disk. This attitude persisted into the current century, when fractals had been around for at least twenty-five years and chaos for forty. I predict that non-Newtonian calculus will come to be recognized as the most important mathematical discovery of the Twentieth Century." - James R. [...]