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In all the many, many years I ve been learning and performing technical analysis, there is no set of studies which has interested me more than those of Fibonacci. In both JavaCharts and ProphetCharts, there are four kinds of Fibonacci studies available: retracements, fans, time zones, and arcs. In this chapter we will explore each of these, as always, with actual examples from the recent past. But rst, let us learn a little about the namesake of these studies.

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P. Dyson, A. Longshaw: Architecting Enterprise Solutions: Patterns for High-Capability Internet-Based Systems, John Wiley & Sons, 2004 B. Elsinga, A. Hofman: Controlled Access Patterns, in Proceedings of EuroPLoP, 2002,

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Leonardo of Pisa lived from 1170 to 1250, and he is regarded as perhaps the greatest mathematician of the Middle Ages. His father William had the nickname Bonaccio, which means good-natured, so Leonardo was subsequently known by the nickname of Fibonacci (short for lius Bonacci, or the son of Bonaccio). William worked in North Africa at a trading post, and even though his home country of Italy had used the Roman numeral system for centuries, he came into contact with traders who instead used the Arabic method of numbers (which is what we use today 1, 2, 3, 4, and so forth, as opposed to numbers such as XI and MMC). Leonardo helped his father with his work, and in the course of doing so, he became acquainted with and enamored by the Arabic style of numbering, which seemed far more sensible and ef cient than the Roman style. The world owes Leonardo a debt of gratitude for help347

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J. Epstein: Architecture and Concepts of the ARGuE Guard, in Proceedings of the 15th Annual Computer Security Applications Conference, pp. 45 54, Phoenix, Arizona, December 1999 W. Essmayr, G. Pernul, A. Min Tjoa: Access Controls by Object-Oriented Concepts, in Proceedings of IFIP WG 11.3 Eleventh International Conference on Database Security, August 1997 European Union: Directive 95/46/EC of the European Parliament and of the Council of 24 October 1995 on the Protection of Individuals with Regard to the Processing of Personal Data and on the Free Movement of Such

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ing to popularize this system of numbers, since it s doubtful anyone today would appreciate having to use Roman numerals in everyday life. Another great contribution Leonardo made was with respect to his writings related to what we today call Fibonacci numbers. This is a sequence of numbers which begins like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1,597. Each number is the sum of the two preceding numbers. These numbers have a variety of interesting properties, including the fact that, as the sequence progresses, each number divided by its preceding number approaches the mathematical gure phi (approximately 1.618033989), known as the golden ratio, which has a wide variety of expressions in nature. In the world of stock charts, the concepts put forth by Fibonacci are manifested in drawn objects retracements, time zones, arcs, and fans. We will explore each of these. There are entire volumes written on the golden ratio and Fibonacci numbers, including their relationship to nature. We will focus on how these mathematical insights can help make us better, more pro table traders.

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Data, Official Journal of the European Communities, No. L 281, 23rd November 1995, pp. 31 50 [EU02] European Union: Directive 2002/58/EC of the European Parliament and of the Council of 12 July 2002 Concerning the Processing of Personal Data and the Protection of Privacy in the Electronic Communications Sector (Directive on privacy and Electronic Communications), Official Journal of the European Communities, No. L 201, 31 July 2002, pp. 37 47 M. Evered, S. B geholz: A Case Study in Access Control Requirements for a Health Information System, presented at Australasian Information Security Workshop 2004 (AISW 2004), Dunedin, New Zealand, 2004 Evidian: Product Description and White Papers:

2.21 In Playback mode, Scroll Display reduces the size of the images for faster loading and review when the Control dial is turned quickly.

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