Items related to Method of Exhaustion: Method of exhaustion, Area, Shape,...

Method of Exhaustion: Method of exhaustion, Area, Shape, Inscribed figure, Polygon, Eudoxus of Cnidus, Grégoire de Saint-Vincent, Proof by contradiction, Reductio ad absurdum, Calculus - Softcover

 
9786130701741: Method of Exhaustion: Method of exhaustion, Area, Shape, Inscribed figure, Polygon, Eudoxus of Cnidus, Grégoire de Saint-Vincent, Proof by contradiction, Reductio ad absurdum, Calculus
Softcover
ISBN 10: 6130701748 ISBN 13: 9786130701741
Publisher: OmniScriptum, 2010

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the n-th polygon and the containing shape will become arbitrarily small as n becomes large. As this difference becomes arbitrarily small, the possible values for the area of the shape are systematically "exhausted" by the lower bound areas successively established by the sequence members. The idea originated with Antiphon, although it is not entirely clear how well he understood it.The theory was made rigorous by Eudoxus. The first use of the term was in 1647 by Grégoire de Saint-Vincent in Opus geometricum guadraturae circuli et sectionum coni.The method of exhaustion typically required a form of proof by contradiction, known as reductio ad absurdum. This amounts to finding an area of a region by first comparing it to the area of a second region.

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Reseña del editor

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the n-th polygon and the containing shape will become arbitrarily small as n becomes large. As this difference becomes arbitrarily small, the possible values for the area of the shape are systematically "exhausted" by the lower bound areas successively established by the sequence members. The idea originated with Antiphon, although it is not entirely clear how well he understood it.The theory was made rigorous by Eudoxus. The first use of the term was in 1647 by Grégoire de Saint-Vincent in Opus geometricum guadraturae circuli et sectionum coni.The method of exhaustion typically required a form of proof by contradiction, known as reductio ad absurdum. This amounts to finding an area of a region by first comparing it to the area of a second region.

"About this title" may belong to another edition of this title.

Publisher
OmniScriptum
Publication date
2010
Language
English
ISBN 10 
6130701748
ISBN 13 
9786130701741
Binding
Tapa blanda
Number of pages
92
Editor
Miller Frederic P., Vandome Agnes F., McBrewster John