- #1

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- Homework Statement
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- Relevant Equations
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> Let ##C## be the disk with radius 1 with center at the origin in ##R^2##.

> Consider the following linear transformation: ##T: (x,y) \to (\frac{5x+3y}{4},\frac{3x+5y}{4})##

>

> What is the lowest number such that ##T^{n}(C)## contains at lest ##2019## points ##(a,b)##, with a and b integers.

So we have ##x²+y² = 1##,

##T: (x,y)\to ( x + y + \frac{x-y}{4}, x + y - \frac{x-y}{4})##

##T²: (x',y') \to ( x + y + \frac{3(x-y)}{8}, x + y - \frac{3(x-y)}{8})##

To be pretty honest, i couldn't see any pattern that simplify the solution of this problem...

> Consider the following linear transformation: ##T: (x,y) \to (\frac{5x+3y}{4},\frac{3x+5y}{4})##

>

> What is the lowest number such that ##T^{n}(C)## contains at lest ##2019## points ##(a,b)##, with a and b integers.

So we have ##x²+y² = 1##,

##T: (x,y)\to ( x + y + \frac{x-y}{4}, x + y - \frac{x-y}{4})##

##T²: (x',y') \to ( x + y + \frac{3(x-y)}{8}, x + y - \frac{3(x-y)}{8})##

To be pretty honest, i couldn't see any pattern that simplify the solution of this problem...