Diophantine Approximation on Quadratic Polynomials
Given an integer $a$ which is not a perfect square, I'd like to ask how to perform Diophantine Approximation of $frac{x^2}{y^2}$ to $a$ where $x$ and $y$ are integers. Specifically, integers satisfying $|frac{x^2}{y^2}-a|<epsilon$ are preferred.
number-theory approximation diophantine-approximation
asked Jan 4 at 10:57
Hang WuHang Wu
426210
add a comment |
Given an integer $a$ which is not a perfect square, I'd like to ask how to perform Diophantine Approximation of $frac{x^2}{y^2}$ to $a$ where $x$ and $y$ are integers. Specifically, integers satisfying $|frac{x^2}{y^2}-a|<epsilon$ are preferred.
number-theory approximation diophantine-approximation
asked Jan 4 at 10:57
Hang WuHang Wu
426210
Set $y$ to a power of $10$.
– N74
Jan 4 at 11:08
Just find a rational approximation $frac{x}{y}$ (for example with the continued fraction method) of $sqrt{a}$. This gives a reasonable approximation of the desired form.
– Peter
Jan 4 at 14:35
add a comment |
Given an integer $a$ which is not a perfect square, I'd like to ask how to perform Diophantine Approximation of $frac{x^2}{y^2}$ to $a$ where $x$ and $y$ are integers. Specifically, integers satisfying $|frac{x^2}{y^2}-a|<epsilon$ are preferred.
number-theory approximation diophantine-approximation
asked Jan 4 at 10:57
Hang WuHang Wu
426210
Given an integer $a$ which is not a perfect square, I'd like to ask how to perform Diophantine Approximation of $frac{x^2}{y^2}$ to $a$ where $x$ and $y$ are integers. Specifically, integers satisfying $|frac{x^2}{y^2}-a|<epsilon$ are preferred.
number-theory approximation diophantine-approximation
number-theory approximation diophantine-approximation
asked Jan 4 at 10:57
Hang WuHang Wu
426210
asked Jan 4 at 10:57
Hang WuHang Wu
426210
asked Jan 4 at 10:57
Hang WuHang Wu
426210
asked Jan 4 at 10:57
Hang WuHang Wu
426210
asked Jan 4 at 10:57
Hang WuHang Wu
426210
426210
Set $y$ to a power of $10$.
– N74
Jan 4 at 11:08
Just find a rational approximation $frac{x}{y}$ (for example with the continued fraction method) of $sqrt{a}$. This gives a reasonable approximation of the desired form.
– Peter
Jan 4 at 14:35
add a comment |
Set $y$ to a power of $10$.
– N74
Jan 4 at 11:08
Just find a rational approximation $frac{x}{y}$ (for example with the continued fraction method) of $sqrt{a}$. This gives a reasonable approximation of the desired form.
– Peter
Jan 4 at 14:35
Set $y$ to a power of $10$.
– N74
Jan 4 at 11:08
Set $y$ to a power of $10$.
– N74
Jan 4 at 11:08
Just find a rational approximation $frac{x}{y}$ (for example with the continued fraction method) of $sqrt{a}$. This gives a reasonable approximation of the desired form.
– Peter
Jan 4 at 14:35
Just find a rational approximation $frac{x}{y}$ (for example with the continued fraction method) of $sqrt{a}$. This gives a reasonable approximation of the desired form.
– Peter
Jan 4 at 14:35
add a comment |
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Set $y$ to a power of $10$.
– N74
Jan 4 at 11:08
Just find a rational approximation $frac{x}{y}$ (for example with the continued fraction method) of $sqrt{a}$. This gives a reasonable approximation of the desired form.
– Peter
Jan 4 at 14:35