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# SCIENTIFIC AMERICAN February 1999 Volume 280 Number 2

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Through this discussion, the students generate new problems. Notice that 14 is between these numbers. The authors apparently feel that their results are of sufficient importance to scientists and engineers to justify these departures from the more traditional style of writing in mathematics. By the spring of 1988, my checking and rechecking had become all-consuming. Use the pattern to write the next three numbers. 1. 13,21,29,37,, , ,... 2. 7,8, 10, 13,, , ,... 3.165,156,147,138 4.19,33,47,61,, ,, Identify a possible pattern.

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If Kris has 1,056 beads, how many necklaces can she make? Smith, associate professor of electrical and computer engineering at Duke University, led a team that used a circular cloaking device to successfully bend microwaves around a copper disk as if the disk were invisible. The writing is clear, concise, and very readable. Barnsley and Michael Frame, in Notices of the American Mathematical Society, October of 2012. "Benoit Mandelbrot survived Nazi-occupied France to become one of the most creative thinkers of the 20th century. ...

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This pioneering work initiated numerous studies." Furthermore, Bashirov et al. [" Multiplicative calculus and its applications"] illustrated the usefulness of [the geometric] calculus with some interesting applications." - Feng Gu (Hangzhou Normal University in China) and Yeol-Je Cho (Gyeongsang National University in Korea); from their 2015 article [249]. "Bigeometric calculus - a modelling tool" - Mustafa Riza (Eastern Mediterranean University in North Cyprus) and Bugce Eminaga (Girne American University in Cyprus); from their 2014 article "Bigeometric calculus - a modelling tool" [178], which includes a new mathematical model for studying tumor therapy with oncolytic virus. "Bigeometric Runge-Kutta method is, at least for a particular set of initial value problems, superior with respect to accuracy and computation-time to the ordinary Runge-Kutta method." - Mustafa Riza (Eastern Mediterranean University in North Cyprus) and Bugce Eminaga (Girne American University in Cyprus); from their 2015 article "Bigeometric Calculus and Runge Kutta Method" [215], which includes new mathematical models (of the growth of cells, genes, bacteria, and viruses) for studying such things as tumor therapy with oncolytic virus and cell-cycle-specific cancer-chemotherapy. "While one problem can be easily expressed in one calculus, the same problem can not be expressed as easily [in another]." - Emine Misirli and Yusuf Gurefe, both of Ege University in Turkey; from their 2009 lecture [123]. "If non-Newtonian calculus is employed together with classical calculus in the formulations, then many of the complicated phenomena in physics or engineering may be analyzed more easily." - Ahmet Faruk Çakmak (Yıldız Technical University in Turkey) and Feyzi Basar (Fatih University in Turkey); from their 2014 article "Certain spaces of functions over the field of non-Newtonian complex numbers". [161] In this paper, the multiplicative least square method is introduced and is applied to integrals for the finite product representation of the positive functions.

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Surprisingly, their time evolution can be analyzed by employing a non-Newtonian calculus ..." - Wojbor Woyczynski, Case Western Reserve University, USA; from an abstract to his 2013 seminar [146]. "The goal of this paper is chaos examination in multiplicative dynamical systems described with the [bigeometric] derivative." - Dorota Aniszewska and Marek Rybaczuk, both from Wroclaw University of Technology in Poland; from their 2008 article "Lyapunov type stability and Lyapunov exponent for exemplary multiplicative dynamical systems". [131] " ... evolution of fractal characteristics will be examined with the help of dynamical system theory or more precisely in terms of [the bigeometric] calculus."

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The paper is one of Mandelbrot's first publications on the topic of fractals. [25] [26] Mandelbrot emphasized the use of fractals as realistic and useful models for describing many "rough" phenomena in the real world. Pomerance, Acta Arith. 25 (1974), 265–300. Gullberg, Jan, Mathematics: From the Birth of Numbers (New York: W. Liu Hui made major improvements to Chang's influential textbook Nine Chapters, making him among the most important of Chinese mathematicians ever. (He seems to have been a much better mathematician than Chang, but just as Newton might have gotten nowhere without Kepler, Vieta, Huygens, Fermat, Wallis, Cavalieri, etc., so Liu Hui might have achieved little had Chang not preserved the ancient Chinese learnings.) Among Liu's achievements are an emphasis on generalizations and proofs, an early recognition of the notions of infinitesimals and limits, the Gaussian elimination method of solving simultaneous linear equations, calculations of solid volumes (including the use of Cavalieri's Principle), anticipation of Horner's Method, and a new method to calculate square roots.

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Fourier's greatest fame rests on his use of trigonometric series (now called Fourier series) in the solution of differential equations. Of course, biomedical imaging provides physicians and researchers with invaluable noninvasive-methods for examining living tissues. What is the distance in inches between these two cities on the map? 262 Chapter 4 Proportional Relationships C N N E C T I CHAPTER 4 SBSv Paul BunyaH Statues According to legend, Paul Bunyan was a giant lumberjack whose footsteps created Minnesota's ten thousand lakes.

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There exists a simple syntactical translation which translates all classical theorems of arithmetic into theorems which are intuitionistically provable. Programming in higher level mathematical language such as Mathematica: Lists, Functions, Expressions, Recursion, Iteration, graphics, packages. Some of these insights are unexpected, however, and run contrary to accepted wisdom. He found a generalization of Pascal's Mystic Hexagram.

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How many book covers can be made out of 40 ft of book cover material? (Lesson 3- 1 0) Find each percent of change. The authors emphasise that although applications provide motivation they are not trying to supply aids for teaching applied mathematics. The efficiency of these proposed minimization methods is demonstrated by examples, .... Since Gauss did not make known many of his brilliant creations, other mathematicians [such as Lobatchevsky and Bolyai] worked toward and arrived at the same results independently. ...

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A simple algebraic identity appearing in a statistics book led us to create the first NNC, the geometric calculus. Fractal geometry is a field of maths born in the 1970’s and mainly developed by Benoit Mandelbrot. In the beginning we were naively unaware that unconventional ideas, even in science and mathematics, are often ignored, ridiculed, or demeaned by the academic establishment, even in the 20th and 21st centuries. The sigmoidal calculus, as introduced in ...

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Are fractal urban structures just nostalgic remnants of an obsolete pre-modern era? There is something wrong with those cells. The fractal dimension of cancerous material is higher than that of healthy cells. 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. Write and solve an equation to determine the missing angle measure of the pentagon.