This opens. Show full abstract security gaps for steganal-ysis.Figures - uploaded by Alik Palatnik Author content All figure content in this area was uploaded by Alik Palatnik Content may be subject to copyright.
Varignon Theorem Proof Full Abstract SecurityVarignon Theorem Proof Free Public FullDiscover the worlds research 20 million members 135 million publications 700k research projects Join for free Public Full-text 1 Content uploaded by Alik Palatnik Author content All content in this area was uploaded by Alik Palatnik on May 26, 2019 Content may be subject to copyright. The following result may be found, for instance, in 2. Theorem. The V arignon parallelogram of a convex quadrilateral has ar ea half that of the given quadrilateral. Moreover, the perimeter of the V arignon parallelogram equals the sum of the lengths of the diagonals of the given parallelogram. Proof. Let BG GD. C Q D P G E S B R W e thank an anonymous reviewer for pointing out that the proof of the perimeter result generalizes to arbitrary quadrilaterals, whereas the proof of the area result does not. W e invite the reader to supply appropriate diagrams for noncon vex and crossed quadrilaterals (see 1, p. Summary. W e present a visual proof of V airgnons theorem by partitioning the V arignon parallelogram using a midpoint of the quadrilateral diagonal. Serial madhubala hindi wikipediaReferences 1. C. Alsina, R. Nelsen, Charming Proofs: A Journe y into Elegant Mathematics. Mathematical Associa- tion of America, Washington, DC, 2010. H. S. M. Coxeter, S. L. Greitzer, Geometry Revisited. We present and compare various examples of how auxiliary elements can be introduced in various problems and proofs and characterize their auxiliary quality. Some auxiliary elements unite previously unrelated components of the original diagram; others divide a given complex entity into manageable ones. Implications for further educational research and mathematics instruction are proposed. In speaking of the purely aesthetic qualities of theorems and proofs, G. H. Hardy wrote that in beautiful proofs there is a very high degree of unexpectedness, combined with inevitability and economy. Charming Proofs present a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct. By means of a surprising argument or a powerful visual representation, the proofs in this collection will invite readers to enjoy the beauty of mathematics, to share their discoveries with others, and to become involved in the process of creating new proofs. Following a short introduction about proofs and the process of creating proofs, the authors present, in twelve chapters, a wide and varied selection of proofs they consider charming, Topics include the integers, selected real numbers, points in the plane, triangles, squares, and other polygons, curves, inequalities, plane tilings, origami, colorful proofs, three-dimensional geometry, etc. At the end of each chapter are some challenges that will draw the reader into the process of creating charming proofs. Charming Proofs concludes with solutions to all of the challenges, references, and a complete index. As in the authors previous books with the MAA (Math Made Visual and When Less Is More), secondary school and college and university teachers may wish to use some of the charming proofs in their classrooms to introduce their students to mathematical elegance. Some may wish to use the book as a supplement in an introductory course on proofs, mathematical reasoning, or problem solving. View Show abstract Geometry Revisited Book Mar 1967 H. S. M. Coxeter S. L. Greitzer View Jan 1967 51-55 H S M Coxeter S L Greitzer H. S. M. Coxeter, S. MSC: 51M04 Advertisement Recommendations Discover more Project Project-based learning of mathematics (PBLM) Alik Palatnik View project Project CIVIC MATHEMATICS Alik Palatnik View project Project EmbodyMath Alik Palatnik Learning and doing mathematics with your body View project Project Auxiliary lines Alik Palatnik View project Conference Paper HPS: Histogram preserving steganography in spatial domain March 2014 Yinan Wang Weirong Chen Yue Li. Chang-Tsun Li Minimization of perceptual and statistical distortions is one of the main challenges facing steganographic schemes. The most common approach to minimizing perceptual distortion is Least Significant Bit embedding. However, the statistical features (e.g., histogram) of the stego-images may be changed significantly even with selection of the regions of interest in the embedding process.
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