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  3. Episodes in Nineteenth and Twentieth Century Euclidean Geometry (New Mathematical Library), CK 61
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ISBN Professor Honsberger has succeeded in 'finding' and 'extricating' unexpected and little known proper He has laid the foundations for his proofs with almost entirely synthetic methods easily accessible to students of Euclidean geometry early on. While in most of his other books Honsberger presents each of his gems, morsels, and plums, as self contained tidbits, in this volume he connects chapters with some deductive treads.

He includes exercises and gives their solutions at the end of the book. Why not share!

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Views Total views. Actions Shares. Their common value is the Brocard angle of. The second or negative Brocard point of is the interior point for which. Their common value is again.

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ebooksbuy4 - Episodes in nineteenth and twentieth century Euclidean geometry download pdf ebook

The Brocard angle satisfies. The two Brocard points are isogonal conjugates cf. Isogonal ; they coincide if is equilateral, in which case. The Brocard configuration for an extensive account see [a6] , named after H. Brocard who first published about it around , belongs to triangle geometry, a subbranch of Euclidean geometry that thrived in the last quarter of the nineteenth century to fade away again in the first quarter of the twentieth century. A brief historical account is given in [a5].

Episodes in Nineteenth and Twentieth Century Euclidean Geometry (New Mathematical Library), CK 61

Although his name is generally associated with the points and , Brocard was not the first person to investigate their properties; in , long before Brocard wrote about them, they were mentioned by A. Crelle in [a4] see also [a8] and [a11]. Information on Brocard's life can be found in [a7]. The Brocard points and Brocard angle have many remarkable properties.

Some characteristics of the Brocard configuration are given below.

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Let be an arbitrary plane triangle with vertices , , and angles , ,. If denotes the circle that is tangent to the line at and passes through the vertices and , then also passes through. Similarly for the circles and. So the three circles , , intersect in the first Brocard point. Analogously, the circle that passes through and and is tangent to the line at , meets the circles and in the second Brocard point. Further, the circumcentre of and the two Brocard points are vertices of a isosceles triangle for which.

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The lengths of the sides of this triangle can be expressed in terms of the radius of the circumcircle of , and the Brocard angle :.