/sci/ - Science & Math

with triple intergrals, how to know which coordinates system to change to, sometimes its obvious like if im given a hemisphere but the question is in cartesian coordinates obviously id change to spherical coordinates but im just doing that with some vague intuition, I dont understand what im doing, is there some rule or something?

>>11835122
You're missing the fucking point. Whenever you have a well-defined mathematical object you can encode the definition to numbers. I can encode the definition "let x be the smallest natural number such that x has more than 300 distinct divisors". I can translate every character into a number and that way faithfully represent this number as an array of numbers, each of whose entry represents a character of my definition.
The point that I'm making is that while this is used to implement computations with a lot of mathematical objects, the fact that you can do it in no way implies that the mathematical object itself is merely the numerical representation that your implementation uses. Implicit in this implementation is the very numerous assumptions that you hold in your head of what the numers in your implementations actually represent. The numbers just by themselves are meaningless. As I've demonstrated in the previous example >>11835096
>>11835106
>>11835107
>>11835111
, you can write down an array of numbers that can represent a vast multitude of completely different mathematical objects. Just by looking at the array of numbers it is IMPOSSIBLE to tell what mathematical object it is. This means that mathematical objects such as vectors, triangles, tensors are NOT just arrays of numbers. They can be represented and implemented BY arrays of numbers just like literally everything else in maths but that IN NO WAY implies that arrays of numbers is all that they are. The most important part of the object is not the array of numbers but the implicit meaning you hold in your head of what those numbers represent.