Coordinate chart for a circle

[dyn]

Main Question or Discussion Point

Hi. I have been looking at the coordinate charts for the unit circle x^2 + y^2 = 1. In the notes I have the circle is split into 4 coordinate charts the first being -

$U_1$ : x>0 , $A_1$ = y (PS without the symbols tab I have used A for the letter phi )

There are 3 more similar charts. My question is - do the 4 charts on their own show that they are referring to a unit circle ? I can't see that they do without providing extra information

 

[Evo]

Hi. I have been looking at the coordinate charts for the unit circle x^2 + y^2 = 1. In the notes I have the circle is split into 4 coordinate charts the first being -

$U_1$ : x>0 , $A_1$ = y (PS without the symbols tab I have used A for the letter phi )

There are 3 more similar charts. My question is - do the 4 charts on their own show that they are referring to a unit circle ? I can't see that they do without providing extra information

Is there anything else that you can add that could help get you an answer?

 

[lavinia]

Hi. I have been looking at the coordinate charts for the unit circle x^2 + y^2 = 1. In the notes I have the circle is split into 4 coordinate charts the first being -

$U_1$ : x>0 , $A_1$ = y (PS without the symbols tab I have used A for the letter phi )

There are 3 more similar charts. My question is - do the 4 charts on their own show that they are referring to a unit circle ? I can't see that they do without providing extra information

Dont understand what A = y means. Can you explain that?


The circle can be covered by four charts which intersect in connected segments. If one keeps track of the intersections then one can show that one has a circle. But four charts could intersect in a different way on a different manifold. Also you can cover the circle with four charts in more than one way.

Hope that helps.

 

[dyn]

φ₁ = y is how it should read. What I don't understand is how or if the 4 coordinate charts alone specifically refer only to the unit circle. It seems to me the function or inverse function needs to be specified as well