Brocard Revelation
Brocard can refer to: * Brocard (law) * Henri Brocard, a nineteenth-century mathematician, and these geometrical entities he discovered: ** Brocard points ** Brocard triangle ** Brocard circle * Saint Brocard Brocard is said to have been one of the first leaders of hermits at Mount Carmel, and was perhaps the leader of the community on the death of Berthold of Calabria around 1195. Various details of his life are legendary. History Brocard (or Burchard ...

Brocard (law)
A brocard is a legal maxim in Latin that is, in a strict sense, derived from traditional legal authorities, even from ancient Rome. The word is a variant of the Latinized name of Burchard of Worms (died AD 1025), Bishop of Worms, Germany, who compiled 20 volumes of ''Ecclesiastical Rules''. History Begun in AD 1008, the materials took Burchard four years to compile. He wrote it while living in a small structure on top of a hill in the forest outside Worms, after his defeat of Duke Otto and while raising his adopted child. The collection, which he called the ''Collectarium Canonum'' or ''Decretum'', became a primary source for canon law. Along with numerous documents from a variety of sources, including the Old Testament and Saint Augustine of Hippo, Burchard included the '' Canon Episcopi'' in this collection, under the belief that it dated from an episcopal "Council of Anquira" in AD 314, but no other evidence of this council exists. Because of this inclusion, Burchard has be ...
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Henri Brocard
Pierre René Jean Baptiste Henri Brocard (12 May 1845 – 16 January 1922) was a French meteorologist and mathematician, in particular a geometer. His best-known achievement is the invention and discovery of the properties of the Brocard points, the Brocard circle, and the Brocard triangle, all bearing his name. Contemporary mathematician Nathan Court wrote that he, along with Émile Lemoine and Joseph Neuberg, was one of the three co-founders of modern triangle geometry. He is listed as an Emeritus at the International Academy of Science, was awarded the Ordre des Palmes Académiques, and was an officer of the Légion d'honneur. He spent most of his life studying meteorology as an officer in the French Navy, but seems to have made no notable original contributions to the subject. Biography Early years Pierre René Jean Baptiste Henri Brocard was born on 12 May 1845, in Vignot (a part of Commercy), Meuse to Elizabeth Auguste Liouville and Jean Sebastien Brocard. He attende ...
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Brocard Points
In geometry, Brocard points are special points within a triangle. They are named after Henri Brocard (1845–1922), a French mathematician. Definition In a triangle ''ABC'' with sides ''a'', ''b'', and ''c'', where the vertices are labeled ''A'', ''B'' and ''C'' in counterclockwise order, there is exactly one point ''P'' such that the line segments ''AP'', ''BP'', and ''CP'' form the same angle, ω, with the respective sides ''c'', ''a'', and ''b'', namely that : \angle PAB = \angle PBC = \angle PCA =\omega.\, Point ''P'' is called the first Brocard point of the triangle ''ABC'', and the angle ''ω'' is called the Brocard angle of the triangle. This angle has the property that :\cot\omega = \cot \alpha + \cot \beta + \cot \gamma, \, where \alpha, \, \beta, \, \gamma are the vertex angles \angle CAB, \, \angle ABC, \, \angle BCA respectively. There is also a second Brocard point, Q, in triangle ''ABC'' such that line segments ''AQ'', ''BQ'', and ''CQ'' form equal angles wit ...
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Brocard Triangle
In geometry, the Brocard triangle of a triangle is a triangle formed by the intersection of lines from a vertex to its corresponding Brocard point and a line from another vertex to its corresponding Brocard point and the other two points constructed using different combinations of vertices and Brocard points. This triangle is also called the first Brocard triangle, as further triangles can be formed by forming the Brocard triangle of the Brocard triangle and continuing this pattern. The Brocard triangle is inscribed in the Brocard circle. It is named for Henri Brocard. See also *Henri Brocard *Brocard points In geometry, Brocard points are special points within a triangle. They are named after Henri Brocard (1845–1922), a French mathematician. Definition In a triangle ''ABC'' with sides ''a'', ''b'', and ''c'', where the vertices are labeled '' ... Notes Triangles {{Elementary-geometry-stub ...
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Brocard Circle
In geometry, the Brocard circle (or seven-point circle) is a circle derived from a given triangle. It passes through the circumcenter and symmedian of the triangle, and is centered at the midpoint of the line segment joining them (so that this segment is a diameter). Equation In terms of the side lengths a, b, and c of the given triangle, and the areal coordinates (x,y,z) for points inside the triangle (where the x-coordinate of a point is the area of the triangle made by that point with the side of length a, etc), the Brocard circle consists of the points satisfying the equation :a^2yz+b^2zx+c^2xy=\frac\left(\frac+\frac+\frac\right). Related points The two Brocard points lie on this circle, as do the vertices of the Brocard triangle. These five points, together with the other two points on the circle (the circumcenter and symmedian), justify the name "seven-point circle". The Brocard circle is concentric with the first Lemoine circle. Special cases If the triangle is equila ...
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