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