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Simultaneous Approximation of Two Real Numbers by Rationals

​
a
1
π
2
3
-1
cos
1
3
+2
-1
cos
1
3
a
2
π
0.135914
2
2
3
1+
5
choose m > 1/ϵ
3
point size
0.02
a
1
≈
3
,
a
2
≈
2
2
3
This Demonstration illustrates the simultaneous approximation of two real numbers by rational numbers, because there is always a small square with at least two points.
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