摘要
The purpose of the present work is to derive some solutions for several solid angle cases via a fundamental formula which gives the solid angle for an isosceles triangle. From this formula the solid angle of pyramids is derived but, unlike other presentations, it is shown in a format similar to that of the well-known cone case. Besides the regular polygon cases (straight pyramids), solid angles of some other plane closed curves are calculated. The fundamental formula also leads to some interesting properties showing the not simple behavior of solid angles with the observer point on the curve itself, as it depends on how the observer arrived there. The question of the equi-Ω surfaces is also discussed and calculated in simple cases.
The purpose of the present work is to derive some solutions for several solid angle cases via a fundamental formula which gives the solid angle for an isosceles triangle. From this formula the solid angle of pyramids is derived but, unlike other presentations, it is shown in a format similar to that of the well-known cone case. Besides the regular polygon cases (straight pyramids), solid angles of some other plane closed curves are calculated. The fundamental formula also leads to some interesting properties showing the not simple behavior of solid angles with the observer point on the curve itself, as it depends on how the observer arrived there. The question of the equi-Ω surfaces is also discussed and calculated in simple cases.
