Smarandache Sequences, Stereograms and Series, by C. Ashbacher PDF Download
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Author: Charles Ashbacher
Publisher: Infinite Study
ISBN: 1931233233
Category : Numbers, Natural
Languages : en
Pages : 135
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Book Description
Florentin Smarandache is truly a Renaissance man, having produced quality work in art, mathematics and literature. This is my fifth book where I expand on some of his mathematical ideas and there seems to be no end in sight. In chapter 1, several sequences created by concatenating all of the natural numbers are examined. By expressing the numbers in bases other than 10, a single type of concatenation can generate several different sequences. Upon examination, it can be seen that there are some significant differences between the sequences. Subsets of the natural numbers can be concatenated to create additional sequences and several are examined in chapter 2. The successive odd numbers and the successive even numbers are concatenated to form two of the sequences that are considered in detail. A stereogram is a two-dimensional image that contains a three-dimensional image. By looking at it long enough, the eyes lose focus in just the right way and the image appears. Simple Smarandache stereograms can be constructed using only characters and many different images are presented in chapter 3. The Smarandache functions can be used in combination with other mathematical operations to create many different infinite series. Many such series are examined in chapter four and conclusions whether they converge or diverge are reached.
Author: Charles Ashbacher
Publisher: Infinite Study
ISBN: 1931233233
Category : Numbers, Natural
Languages : en
Pages : 135
Get Book Here
Book Description
Florentin Smarandache is truly a Renaissance man, having produced quality work in art, mathematics and literature. This is my fifth book where I expand on some of his mathematical ideas and there seems to be no end in sight. In chapter 1, several sequences created by concatenating all of the natural numbers are examined. By expressing the numbers in bases other than 10, a single type of concatenation can generate several different sequences. Upon examination, it can be seen that there are some significant differences between the sequences. Subsets of the natural numbers can be concatenated to create additional sequences and several are examined in chapter 2. The successive odd numbers and the successive even numbers are concatenated to form two of the sequences that are considered in detail. A stereogram is a two-dimensional image that contains a three-dimensional image. By looking at it long enough, the eyes lose focus in just the right way and the image appears. Simple Smarandache stereograms can be constructed using only characters and many different images are presented in chapter 3. The Smarandache functions can be used in combination with other mathematical operations to create many different infinite series. Many such series are examined in chapter four and conclusions whether they converge or diverge are reached.
Author: Marius Coman
Publisher: Infinite Study
ISBN: 1599732521
Category :
Languages : en
Pages : 136
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Book Description
About the works of Florentin Smarandache have been written a lot of books (he himself wrote dozens of books and articles regarding math, physics, literature, philosophy). Being a globally recognized personality in both mathematics (there are countless functions and concepts that bear his name) and literature, it is natural that the volume of writings about his research is huge. What we try to do with this encyclopedia is to gather together as much as we can both from Smarandache’s mathematical work and the works of many mathematicians around the world inspired by the Smarandache notions. We structured this book using numbered Definitions, Theorems, Conjectures, Notes and Comments, in order to facilitate an easier reading but also to facilitate references to a specific paragraph. We divided the Bibliography in two parts, Writings by Florentin Smarandache (indexed by the name of books and articles) and Writings on Smarandache notions (indexed by the name of authors). We treated, in this book, about 130 Smarandache type sequences, about 50 Smarandache type functions and many solved or open problems of number theory. We also have, at the end of this book, a proposal for a new Smarandache type notion, id est the concept of “a set of Smarandache-Coman divisors of order k of a composite positive integer n with m prime factors”, notion that seems to have promising applications, at a first glance at least in the study of absolute and relative Fermat pseudoprimes, Carmichael numbers and Poulet numbers. This encyclopedia is both for researchers that will have on hand a tool that will help them “navigate” in the universe of Smarandache type notions and for young math enthusiasts: many of them will be attached by this wonderful branch of mathematics, number theory, reading the works of Florentin Smarandache.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 796
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Book Description
Author: Gene Levine
Publisher: Sterling Publishing Company, Inc.
ISBN: 1402751451
Category : Computer graphics
Languages : en
Pages : 147
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Book Description
A stereogram is a two-dimensional image that, when viewed properly, creates a stunning, almost magical impression of depth. Objects seem to float or to pop out of patterns. And these complex and sophisticated designs, produced by two of the most famous stereogram creators in the world, are state of the art.
Author: Gary W. Priester
Publisher:
ISBN: 9781841932682
Category : Computer art
Languages : en
Pages : 260
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Book Description
Seeing isn't always believing! This incredible collection of visual illusions and stereogram images proves it. In Eye Tricks, there are shapes to beguile and confuse, colours in which to lose yourself and patterns to marvel at - while they scramble your mind. A great visual experience for anyone with a good visual sense and/or a love for clever visual illusions.
Author: Richard H. Groshong
Publisher: Springer Science & Business Media
ISBN: 354031055X
Category : Science
Languages : en
Pages : 411
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Book Description
The book includes new material, in particular examples of 3-D models and techniques for using kinematic models to predict fault and ramp-anticline geometry. The book is geared toward the professional user concerned about the accuracy of an interpretation and the speed with which it can be obtained from incomplete data. Numerous analytical solutions are given that can be easily implemented with a pocket calculator or a spreadsheet.
Author: Daniel Sillescu
Publisher: Sybex
ISBN: 9780782116625
Category : Computers
Languages : en
Pages : 72
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Book Description
Stereogram books and posters have been selling like hot cakes. On the surface, the images appear as static or some repeating pattern. But if you refocus on the image correctly, a 3D image seems to rise from the page. This book features numerous high quality images, plus instructions on how to create stereograms, and software to let users generate their own sterograms.
Author: Ian P. Howard
Publisher: Oxford University Press, USA
ISBN: 9780195084764
Category : Medical
Languages : en
Pages : 756
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Book Description
This book is a survey of knowledge about binocular vision, with an emphasis on its role in the perception of a three-dimensional world. The primary interest is biological vision. In each chapter, physiological, behavioral, and computational approaches are reviewed in some detail, discussed, and interrelated. The authors describe experiments required to answer specific questions and relates them to new terminologies and current theoretical schemes.
Author: Gene Levine
Publisher: National Geographic Books
ISBN: 1936140667
Category : Games & Activities
Languages : en
Pages : 0
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Book Description
There’s something really magical about a stereogram; in fact, these stunning designs practically come alive with movement. As they tease and surprise our brains, they teach us to look at things differently and make us aware of how our eyes play tricks on us. And, of course, they are simply beautiful to see. Through the power of illusion and the illustrator’s skill, meaningless patterns and hidden objects on a 2-D page take shape and pop out in full, glorious, clearly defined 3-D. Images that were flat gain amazing dimension. These incredible, colorful, artistic creations offer unbelievable motion and depth.
Author: Ross Honsberger
Publisher: Cambridge University Press
ISBN: 9780883853146
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Presents problems from probability, number theory, combinatorics, and geometry, and provides ingenious solutions and/or intriguing results.
