Spherical coordinates are a fascinating subject. It turns out that they are used in astronomy and geography with some interesting applications, like measuring orbits: https://en.wikipedia.org/wiki/Spherical_coordinate_system#In_astronomy
aramk-hub
I don't completely understand the analysis of these formulas in the figure. My first question is why is the area of the square not r^2 sin^2(theta)? Each side is rsin(theta) right? I'm wondering what I am missing. I understand the second formula since it is the first just applied and divided by r^2, but I don't quite understand how we found the value of the first formula.
ksaralle
the intuition behind the formula is quite complicated. First of all, there are two variables (two angles, in two directions) that defines the area. After establishing this understanding, the area can be interpreted as the production of a calculated width and height, each of which is deduced with r and trigonometry of angles.
Spherical coordinates are a fascinating subject. It turns out that they are used in astronomy and geography with some interesting applications, like measuring orbits: https://en.wikipedia.org/wiki/Spherical_coordinate_system#In_astronomy
I don't completely understand the analysis of these formulas in the figure. My first question is why is the area of the square not r^2 sin^2(theta)? Each side is rsin(theta) right? I'm wondering what I am missing. I understand the second formula since it is the first just applied and divided by r^2, but I don't quite understand how we found the value of the first formula.
the intuition behind the formula is quite complicated. First of all, there are two variables (two angles, in two directions) that defines the area. After establishing this understanding, the area can be interpreted as the production of a calculated width and height, each of which is deduced with r and trigonometry of angles.