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...s” [19], Florentin Smarandache proposed a number of ways in which we could explore “new math concepts and theories, especially if they run counter to the classical ones.” In a manner consistent with his unique point of view, he defined several types of geometry that are purposefully not Euclidean and that focus on structures that the rest of us can use to enhance our under...

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... American Research Press Rehoboth, NM 2002 2 The picture on the cover is a representation of an s-manifold illustr... ...e picture on the cover is a representation of an s-manifold illustrating some of the behavior of lines in an s-manifold. This book has been pee... ...o.com/group/smarandachegeometries/ Paper abstracts can be submitted online to the First International Conference on Smarandache Geometries, that w... ...nference on Smarandache Geometries, that will be held between 3-5 May, 2003, at the Griffith University, Gold Coast Campus, Queensland, Australia, o... .../fabz54. ISBN: 1-931233-44-6 Standard Address Number: 297-5092 Printed in the United States of America 3 Table of Contents Introduction ... ...an geometry, as is the angle sum of a quadrilateral. It is not an invariant for polygons in general, however, since the angle sum for polygons with ... ... A closely related quantity, the sum of the turning angles, is an invariant for polygons. In Figures 14 and 15, the turning angles are indicated out... ...rse them in a counter-clockwise direction. Walking along the perimeter of these polygons, 18 the turning angle is the angle required to change fr... ... from one edge to start the next. The sum of the turning angles is 360º for any polygon in Euclidean geometry. The turning angle can be interprete...

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...The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs...

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... reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical metho...

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...Collected Eclectic Ideas - preface by the author.............................3 Contents....................................................6 ASTRONOMY..................................14 1. First Lunar Space Base, project proposal, by V. Christianto, Florentin...

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...The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs...

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... reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical metho...

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...Collected Eclectic Ideas - preface by the author.............................3 Contents....................................................6 ASTRONOMY..................................14 1. First Lunar Space Base, project proposal, by V. Christianto, Florentin...

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...There have been some significant changes in this edition. A new Geography section has replaced the former Land and Water sections. Entries in the new section include area (total and land), comparative area, land boundaries, coastline, maritime claims, boundary disputes, climate, terrain, land use, environment, and sp...

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...INOIS LIBRARY AT URBANACHAMPAIGN BOOKSTACKS Central Intelligence Agency The World Factbook 1987 CP/1S WF 87-001 US Government officials should o... ...ctbook 1987 CP/1S WF 87-001 US Government officials should obtain copies of The World Factbook directly from their own organization or through liaiso... ...ctbook directly from their own organization or through liaison channels from the Central Intelligence Agency. Requesters in the Department of Defense ... ...ngton, D.C. 20340-3344 Tel: (202) 373-3869 or Autovon 243-3869 Requesters in the Department of State may obtain copies from: Department of State INR/I... ...646 New State Washington, D.C. 20520 Tel: (202) 647-9673. Requesters outside the US Government may purchase copies from: Superintendent of Documents U... ...100 nm (defined by geographic coordinates) Extended economic zone: irregular polygon varying in breadth from about 35 nm to more than 300 nm Territori... ...g in breadth from about 35 nm to more than 300 nm Territorial sea: irregular polygon vary- ing in breadth from less than 3 nm to about 55 nm Climate: ... ... of exploita- tion Extended economic zone: 200 nm Territorial sea: irregular polygon up to 285 nm in breadth Boundary disputes: none; involved in comp...

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...This book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers and functions; and Some irrationality results. Chapter 1 deals essentially with geo...

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...************ AB/AC=(MB/MC)(sin u / sin v) 1/z + 1/y = 1/z Z(n) is the smallest integer m such that 1+2+…+m is divisible by n *************... ... ISBN: 1-931233-51-9 Standard Address Number 297-5092 Printed in the United States of America "...It is just this, which gives the highe... ...is, which gives the higher arithmetic that magical charm which has made it the favourite science of the greatest mathematicians, not to mention its in... ...icles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric the- orems; Diophantin... ...ality results. Chapter 1 deals essentially with geometric inequalities for the remarkable elements of triangles or tetrahedrons. Other themes have an ... ...Mat. A (Bucure sti), 8(1987), No.4, 186-191. 286 2. J. S andor, Regular polygons and irrational numbers (Hungarian), Mat. Lapok 1/1993, 6-8. 3. J. ...

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...Introduction: Recently I set myself to put down what I believe. I did this with no idea of making a book, but at the suggestion of a friend and to interest a number of friends with whom I was associated. We were all, we found, extremely uncertain in our outlook upon life, about our religious feelings and in our ideas of right and wrong....

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...: A Confession of Faith and Rule of Life by H.G. Wells is a publication of the Pennsylvania State University. This Portable Document file is furnished... ...e, for any purpose, and in any way does so at his or her own risk. Neither the Pennsylvania State University nor Jim Manis, Faculty Editor, nor anyone... ...State University nor Jim Manis, Faculty Editor, nor anyone associated with the Pennsylvania State University assumes any responsibility for the materi... ...te University assumes any responsibility for the material contained within the document or for the file as an electronic transmission, in any way. Fir... ...rst and Last Things: A Confession of Faith and Rule of Life by H.G. Wells, the Pennsyl- vania State University, Electronic Classics Series, Jim Manis,... ...loy them as the mathematician studies the circle by sup- posing it to be a polygon of a very great number of sides. We must make use of terms and some...

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...Introduction: On February the first 1887, the Lady Vain was lost by collision with a derelict when about the latitude 1' S. and longitude 107' W. On January the Fifth, 1888--that is eleven months and four days after--my uncle, Edward Prendick, a priva...

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...of Dr. Moreau by H. G. Wells A Penn State Electronic Classics Series Page The Island of Dr. Moreau by H. G. Wells is a publication of the Pennsylvani... ...e, for any purpose, and in any way does so at his or her own risk. Neither the Pennsylvania State University nor Jim Manis, Faculty Editor, nor anyone... ...State University nor Jim Manis, Faculty Editor, nor anyone associated with the Pennsylvania State Uni- versity assumes any responsibility for the mate... ... Uni- versity assumes any responsibility for the material contained within the document or for the file as an electronic transmission, in any way. The... ...ctronic transmission, in any way. The Island of Dr. Moreau by H. G. Wells, the Pennsylvania State University, Electronic Classics Series, Jim Manis, F... ...heavy tread of the Horse-rhinoceros upon my right. Then suddenly through a polygon of green, in the half darkness under the luxuriant growth, I saw th...

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...Excerpt: Towards the middle of the month of May, in the year 1660, at nine o?clock in the morning, when the sun, already high in the heavens, was fast absorbing the dew from the ramparts of the castle of Blois a little cavalcade, composed of ...

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... ... ...te University. This Portable Document file is furnished free and without any charge of any kind. Any person using this document file, for any purpose... ...kind. Any person using this document file, for any purpose, and in any way does so at his or her own risk. Neither the Pennsylvania State University n... ...r own risk. Neither the Pennsylvania State University nor Jim Manis, Faculty Editor, nor anyone associated with the Pennsylvania State University assu... ...iated with the Pennsylvania State University assumes any responsibility for the material contained within the document or for the file as an electroni... ...dy had occasion to speak: — 488 Ten Years Later – V ol. 1 “Instead of making use of the square or rectangle, as has been done to this time, you will ... ... which you will determine the length in proportion to the dimensions taken upon the place, will be divided into two parts and upon the middle point yo... ...ded into two parts and upon the middle point you will elevate a perpendicular towards the center of the polygon, which will equal in length the sixth ...

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...ics Series Publication Roderick Hudson by Henry James is a publication of the Pennsylvania State University. This Portable Document file is furnished... ...e, for any purpose, and in any way does so at his or her own risk. Neither the Pennsylvania State University nor Jim Manis, Faculty Editor, nor anyone... ...State University nor Jim Manis, Faculty Editor, nor anyone associated with the Pennsylvania State University assumes any responsibility for the materi... ...te University assumes any responsibility for the material contained within the document or for the file as an electronic transmission, in any way. Rod... ...as an electronic transmission, in any way. Roderick Hudson by Henry James, the Pennsylvania State University, Electronic Classics Series, Jim Manis, F... ...ously cool, but the gray streets were stifling, and the great, dove-tailed polygons of pavement as hot to the tread as molten lava. Rowland, who suffe...

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Excerpt: The Pickwick Papers, Volume Two by Charles Dickens.

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...es Dickens Volume Two A Penn State Electronic Classics Series Publication The Pickwick Papers, Volume Two by Charles Dickens is a publication of t... ..., for any purpose, and in any way does so at his or her own risk . Neither the Pennsylvania State University nor Jim Manis, Faculty Editor, nor anyone... ...State University nor Jim Manis, Faculty Editor, nor anyone associated with the Pennsylva nia State University assumes any responsibility for the mate... ...te University assumes any responsibility for the material contained within the document or for the file as an electronic transmission, in any way. The... ...ission, in any way. The Pickwick Papers, Volume T wo by Charles Dickens , the Pennsylvania State University, Electronic Clas sics Series, Jim Manis... ...an tell you,’ replied Lowten. ‘It went the half hour as I came through the Polygon. I’m here before him, though, so I don’t mind.’ Comforting himself ...

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...Excerpt: I lay ill through several weeks, and the usual tenor of my life became like an old remembrance. But this was not the effect of time so much as of the change in all my habits made by the helplessness and inaction of a sick-room. Before I had been confined to it m...

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...s Thirty five through Sixty seven by Charles Dickens is a publication of the Pennsylvania State University. This Portable Document file is furnished... ..., for any purpose, and in any way does so at his or her own risk . Neither the Pennsylvania State University nor Jim Manis, Faculty Editor, nor anyone... ...State University nor Jim Manis, Faculty Editor, nor anyone associated with the Pennsylvania State University assumes any responsibility for the materi... ...te University assumes any responsibility for the material contained within the document or for the file as an electronic transmission, in any way. Ble... ... Containing Chapters Thirty five through Sixty seven by Charles Dickens , the Pennsylvania State University, Electronic Classics Series , Jim Manis,... ...presented ourselves at Mr. Skimpole’s door. He lived in a place called the Polygon, in Somers Town, where there were at that time a number of poor Spa...

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...Excerpt: CHAPTER 1; Under certain circumstances there are few hours in life more agreeable than the hour dedicated to the ceremony known as afternoon tea. There are circumstances in which, whether you partake of the tea or not--some people of course never do--the situation is in itself delightful. Those that I have in m...

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...U nder certain circumstances there are few hours in life more agreeable than the hour dedicated to the ceremony known as afternoon tea. There are circ... ...as afternoon tea. There are circum stances in which, whether you partake of the tea or not—some people of course never do—the situation is in itself ... ...old this simple history offered an admirable setting to an innocent pastime. The implements of the little feast had been disposed upon the lawn of an ... ...isposed upon the lawn of an old English country house, in what I should call the perfect middle of a splendid summer afternoon. Part of the afternoon ... ...f the afternoon had waned, but much of it was left, and what was left was of the finest and rarest quality. Real dusk would not arrive for many hours; ... ... “If one’s two sided it’s enough,” said Isabel. “You’re the most charming of polygons!” her companion broke out. At a glance from his companion, howev...

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Excerpt: The Portrait of a Lady by Henry James.

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...nry James A PENN S TAT E ELE C T R O N IC CLAS SIC S SERIES PUBLICA TIO N The Portrait of a Lady by Henry James is a publication of the Pennsylvania ... ...e, for any purpose, and in any way does so at his or her own risk. Neither the Pennsylvania State University nor Jim Manis, Faculty Editor, nor anyone... ...State University nor Jim Manis, Faculty Editor, nor anyone associated with the Pennsylvania State University assumes any responsibility for the materi... ...te University assumes any responsibility for the material contained within the document or for the file as an electronic transmission, in any way. The... ...lectronic transmission, in any way. The Portrait of a Lady by Henry James, the Pennsylvania State University, Electronic Classics Series, Jim Manis, F... ...If one’s two-sided it’s enough,” said Isabel. “You’re the most charming of polygons!” her compan- ion broke out. At a glance from his companion, howev...

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...Preface: A Chancery judge once had the kindness to inform me, as one of a company of some hundred and fifty men and women not laboring under any suspicions of lunacy, that the Court of Chancery, though the shining subject of much popular prejudice (at which po...

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...s Series Publication Bleak House by Charles Dickens is a publication of the Pennsylvania State University. This Portable Document file is furnished... ..., for any purpose, and in any way does so at his or her own risk . Neither the Pennsylvania State University nor Jim Manis, Faculty Editor, nor anyone... ...State University nor Jim Manis, Faculty Editor, nor anyone associated with the Pennsylvania State University assumes any responsibility for the materi... ...te University assumes any responsibility for the material contained within the document or for the file as an electronic transmission, in any way. Ble... ... an electronic transmission, in any way. Bleak House by Charles Dickens , the Pennsylvania State University, Electronic Classics Series , Jim Manis,... ...presented ourselves at Mr. Skimpole’s door. He lived in a place called the Polygon, in Somers Town, where there were at that time a number of poor Spa...

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...Excerpt: PART I. Chapter One. We were in class when the head-master came in, followed by a ?new fellow,? not wearing the school uniform, and a school servant carrying a large desk. Those who had been asleep woke up, and every one rose as if just surprised at his work. The head...

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...Madame Bovary by Gustave Flaubert Translated from the French Translated from the French Translated from the French Translated... ...ench Translated from the French Translated from the French Translated from the French Translated from the French by by by by by Eleanor Marx-Aveling E... ...ovary by Gustave Flaubert, trans. Eleanor Marx-Aveling is a publication of the Pennsylvania State University. This Portable Document file is furnishe... ...e, for any purpose, and in any way does so at his or her own risk. Neither the Pennsylvania State University nor Jim Manis, Faculty Editor, nor anyone... ...State University nor Jim Manis, Faculty Editor, nor anyone associated with the Pennsylvania State University assumes any responsibility for the materi... ...eparated by a red band; after that a sort of bag that ended in a cardboard polygon covered with complicated braiding, from which hung, at the end of a...