>>12854509
Is there a way to simplify irrational expressions by using a complementary form, similar to a complex conjugate. In Phi below, it is not a more simplified expression but recognizing the description is of a form [length] from some [point], we can pick any other point to start from and generate a new distance.
The reason I am thinking about this is for other numbers, suppose it wasn't phi, but instead it is continued below in some generalized format. Is there a proof showing this format is the simplest expression, or that is a bit undefined. Is there a proof that given some k, A, and p that there isn't another expression where k = 1 but p and A are anything else. In this way we get a constructor of "[distance] from [1/2]"
I was thinking about reducing this format to a complimentary form by inverting everything.
If p could be any real number, then its root could also be any real number, and this just becomes a function. There are many kinds of functions which can define a target point. I am just building an intuition about the relationships of irrational numbers. Ultimately, I want to work toward transforming some irrational in this form to any other form.
Is there a way to simplify irrational expressions by using a complementary form, similar to a complex conjugate. In Phi below, it is not a more simplified expression but recognizing the description is of a form [length] from some [point], we can pick any other point to start from and generate a new distance.
The reason I am thinking about this is for other numbers, suppose it wasn't phi, but instead it is continued below in some generalized format. Is there a proof showing this format is the simplest expression, or that is a bit undefined. Is there a proof that given some k, A, and p that there isn't another expression where k = 1 but p and A are anything else. In this way we get a constructor of "[distance] from [1/2]"
I was thinking about reducing this format to a complimentary form by inverting everything.
If p could be any real number, then its root could also be any real number, and this just becomes a function. There are many kinds of functions which can define a target point. I am just building an intuition about the relationships of irrational numbers. Ultimately, I want to work toward transforming some irrational in this form to any other form.
