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The area of a sector at centre of a planar quadric

Three linearly dependent and pairwise linearly independent vectors of an euclidian space uniquely determine a planar quadric with symmetry centre in the origin. A rather simple formula for the area of an arbitrary sector at centre of such a quadric will be shown by classical methods. The formula describes that area in dependence of 1. the lengths of the two straight lines that bound the sector at two sides, 2. the length of an arbitrary straight line from the centre to the quadric arc that bounds the sector at the third side, 3. the two angles in between these three straight lines.

preprint2022arXivOpen access
Helmut Kahl
math.HOmath.MG
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Helmut Kahl

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