87 research outputs found
Spherical Trigonometry of the Projected Baseline Angle
The basic geometry of a stellar interferometer with two telescopes consists
of a baseline vector and a direction to a star. Two derived vectors are the
delay vector, and the projected baseline vector in the plane of the wavefronts
of the stellar light. The manuscript deals with the trigonometry of projecting
the baseline further outwards onto the celestial sphere. The position angle of
the projected baseline is defined, measured in a plane tangential to the
celestial sphere, tangent point at the position of the star. This angle
represents two orthogonal directions on the sky, differential star positions
which are aligned with or orthogonal to the gradient of the delay recorded in
the u-v plane. The North Celestial Pole is chosen as the reference direction of
the projected baseline angle, adapted to the common definition of the
"parallactic" angle.Comment: Corrected eq. (6) and definition of N after eq. (11
Tile Count in the Interior of Regular 2n-gons Dissected by Diagonals Parallel to Sides
The regular 2n-gon (square, hexagon, octagon, ...) is subdivided into smaller
polygons (tiles) by the subset of diagonals which run parallel to any of the 2n
sides. The manuscript reports on the number of tiles up to the 78-gon.Comment: 21 pages, 12 figures, one C++ progra
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