Kodi mungawerengere bwanji chiwerengero cha mapaipi achitsulo mu mtolo wa hexagonal?

Pamene mafakitale achitsulo amapanga gulu lamapaipi achitsulo, amawamanga m'mawonekedwe a hexagonal kuti azinyamula mosavuta komanso kuwerengera. Mtolo uliwonse uli ndi mapaipi asanu ndi limodzi mbali iliyonse. Kodi pali mapaipi angati mu mtolo uliwonse?

Yankho: 3n(n-1)+1, pomwe n ndi chiwerengero cha mapaipi mbali imodzi ya hexagon yakunja. 1) * 6 = mapaipi 6, kuphatikiza chitoliro chimodzi pakati.
Kuchokera kwa fomula:
Mbali iliyonse imakhala ndi mapaipi a n. Gawo lakunja lili ndi mapaipi a (n-1) * 6, gawo lachiwiri (n-2) * 6, ..., gawo la (n-1)th (n-(n-1)) * 6 = mapaipi a 6, ndipo potsiriza chitoliro chimodzi pakati. Chiwerengero chonse ndi [(n-1) + (n-2) + ... + 1]*6 + 1. Mawu omwe ali mkati mwa mabulaketi akuyimira chiwerengero cha masamu (chiwerengero cha mawu oyamba ndi omaliza ogawika ndi 2, kenako kuchulukitsidwa ndi n-1 kuti mupeze n*(n-1)/2).
Izi pamapeto pake zimabweretsa 3n*(n-1)+1.