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php -r '$bestdiff = 1000; $bestz = 0; $bestz = 0; $pp = PI() * PI(); for ($z = 1; $z <= 100; $z++) {
for ($n = 1; $n <= 100; $n++) {
$p = $z / $n; $diff = abs($pp - $p); if ($diff < 0.1) { print "$z / $n = $p; diff $diff\n"; } if ($diff < $bestdiff) { $bestdiff = $diff; $bestz = $z; $bestn = $n; }}} print "$bestz / $bestn = $pp mit +- $bestdiff\n";'
49 / 5 = 9.8; diff 0.069604401089357
59 / 6 = 9.8333333333333; diff 0.036271067756024
69 / 7 = 9.8571428571429; diff 0.0124615439465
79 / 8 = 9.875; diff 0.005395598910642
88 / 9 = 9.7777777777778; diff 0.091826623311579
89 / 9 = 9.8888888888889; diff 0.019284487799531
98 / 10 = 9.8; diff 0.069604401089357
99 / 10 = 9.9; diff 0.030395598910642
79 / 8 = 9.8696044010894 mit +- 0.005395598910642
Fazit: auf 98/10 hatte ich auch so kommen koennen :-).
Ich merke mir die 49/5, und dass man zu Zaehler und Nenner "n" addieren kann, um einen fuers Kuerzen passenderen Bruch zu bekommen.