Koła wpisane w koło

[wodzu77]

Witam.
Mam w koło o promieniu 48 mm wpisać jak najwięcej okręgów o promieniu 4,7 mm oraz w drugie koło o promieniu 48 mm jak najwięcej okręgów o promieniu 6,3 mm.

[SlotaWoj]

Tylko metoda „prób i błędów”.
Wewnątrz okręgu o promieniu 48 można umieścić 80 okręgów o promieniu 4,7.

Edit:

Uprzednio wpisałem złą wartość (40 dla półkola). Poprawiłem.

[Longines]

Można umieścić 41 okręgów o promieniu 6.3
O promieniu 4.7 możesz policzyć sam.

[norwimaj]

Uprzednio wpisałem złą wartość (40 dla półkola). Poprawiłem.

Jeśli w półkole można ich wpisać aż \(\displaystyle{ 40,}\) to dlaczego w całe koło tylko \(\displaystyle{ 80}\)? Nie zostawiasz za dużo wolnego miejsca przy średnicy okręgu?

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[SlotaWoj]

@Norwimaj

Próbowałem równobocznego ułożenia, ale zbyt wcześnie uznałem je za mniej efektywnego od innego (kółeczka „zewnętrzne” są stycznie wewnętrznie do dużego) i zrezygnowałem.

[norwimaj]

A co z drugim zadaniem? \(\displaystyle{ 43}\) koła o promieniu \(\displaystyle{ 6{,}3\;\mathrm{mm}}\) zmieszczą się bez problemu, ale może uda się zmieścić więcej?

[SlotaWoj]

44 koła o promieniu 6,3 mm.



Trzeba to jeszcze sprawdzić anaitcznie, bo może braknąć do tysięcznej części milimetra.