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In geometry, the Brocard circle (or seven-point circle) is a circle derived from a given triangle. It passes through the circumcenter and symmedian point of the triangle, and is centered at the midpoint of the line segment joining them (so that this segment is a diameter ).
The Zodiac is an ancient circle of stars [11] where some stars are symbolically combined into 12 star signs also known as constellations. The etymology of the term Zodiac comes from the Latin zōdiacus, from the Greek ζῳδιακός [κύκλος], meaning "[circle] of animals", derived from ζῴδιον, the diminutive of ζῷον "animal".
Brocard's most well-known contributions to mathematics are the Brocard points, the Brocard circle, and the Brocard triangle. The positive Brocard point (sometimes known as the first Brocard point) of a Euclidean plane triangle is the interior point of the triangle for which the three angles formed by two of the vertices and the point are equal.
A serpent or dragon consuming its own tail, it is a symbol of infinity, unity, and the cycle of death and rebirth. Pentacle: Mesopotamia: An ancient symbol of a unicursal five-pointed star circumscribed by a circle with many meanings, including but not limited to, the five wounds of Christ and the five elements (earth, fire, water, air, and soul).
The Brocard points are an example of a bicentric pair of points, but they are not triangle centers because neither Brocard point is invariant under similarity transformations: reflecting a scalene triangle, a special case of a similarity, turns one Brocard point into the other.
When choosing an engagement ring, understanding the symbolism of each diamond shape will help shoppers find the one that best represents them. Here is what the most popular diamond shapes for ...
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, first of the priors of the Carmelite Order according to oral tradition
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