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On the Pentacardioid: Abstract of a Dissertation Submitted to the Board of University Studies of the Johns Hopkins University in Conformity With the ... of Doctor of Philosophy (Classic Reprint) - Softcover
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Excerpt from On the Pentacardioid: Abstract of a Dissertation Submitted to the Board of University Studies of the Johns Hopkins University in Conformity With the Requirements for the Degree of Doctor of Philosophy
An equation in complex variables is said to be self-conjugate when it is identical with the equation obtained by replacing each quantity by its conjugate, or differs from this equation merely by some factor; such an equation corre sponde to an equation in real variables with real coefficients. The roots of a self-conjugate equation in t are either turns or pairs of inverse points as to the base circle, and these latter bear to the self-conjugate equation in t the same relation that pairs of conjugate imaginary roots bear to the equation with real coefficients in one real variable.
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On the Pentacardioid (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book explores the Pentacardioid, the first significant curve in a series examined by Professor Morley. It begins by establishing the general symbol for an Ennacardioid as Cn, then using the corresponding symbol C5 for the Pentacardioid. The author employs a coordinate system and analysis methods established by Professor Morley to lay the groundwork for further exploration. In establishing a parameter, the author highlights the existence of three independent complex arbitrary constants which are dependent on six conditions. This allows the shape of the C5 to be determined by only two absolute conditions. The author explains construction methods for the C5, demonstrating how to build up the curve from two fundamental epicycloids which are easily constructed with simple mechanical means. The author also provides instructions on how to alter the relative sizes of the fundamental curves, and how to alter the amplitude of the determining coefficient of the resulting curve. The book delves into the singularities of the C5, which are shown to include six simple double points, three cusps, and six double tangents, for a total of 21 double points. It is also shown that the C5 is of class five and order eight. The cusps are further examined, with a self-conjugate cubic equation used to determine cusp parameters. Conditions for a node on a curve are discussed, and the author establishes the general condition which the parameters of a node must satisfy. The author provides instructions on how to calculate the twelve parameters of the six double tangents. Finally, the author examines the complete system of C5s, considering sets of C5s which are connected together by special properties or common singularities. The author restricts the determining coefficient to a third portion of the plane bounded by a pair of straight lines or rays through the origin, then considers the behavior of the three cusps when one of the cusp parameters is fixed. A graphical method is presented for determining the reality of the singularities of the C5, and a table of regions is provided which lists the number of simple singularities possessed by a given C5 based on the region in which the coefficient s1 of the given C5 happens to lie. This book provides a comprehensive examination of the Pentacardioid, exploring its equation, construction, singularities, and complete system, offering valuable insights into the mathematical properties of this fascinating curve. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781332173068_0
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On the Pentacardioid Abstract of a Dissertation Submitted to the Board of University Studies of the Johns Hopkins University in Conformity With the of Doctor of Philosophy Classic Reprint
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PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781332173068
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On the Pentacardioid Abstract of a Dissertation Submitted to the Board of University Studies of the Johns Hopkins University in Conformity With the of Doctor of Philosophy Classic Reprint
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PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781332173068
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On the Pentacardioid : Abstract of a Dissertation Submitted to the Board of University Studies of the Johns Hopkins University in Conformity With the Requirements for the Degree of Doctor of Philosophy (Classic Reprint)
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Zustand: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | Keine Beschreibung verfügbar. Bestandsnummer des Verkäufers 26067400/2
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