Momwe mungawerengere kuchuluka kwa mipope yachitsulo mumtolo wa hexagonal?

Pamene zitsulo mphero kubala mtanda wamapaipi achitsulo, amawamanga m’mipangidwe ya makona atatu kuti azitha kuyenda ndi kuŵerenga mosavuta. Mtolo uliwonse uli ndi mapaipi asanu ndi limodzi mbali iliyonse. Ndi mapaipi angati mumtolo uliwonse?

Yankho: 3n(n-1)+1, pomwe n ndi chiwerengero cha mapaipi kumbali imodzi ya hexagon yakutali kwambiri. 1) * 6 = mapaipi 6, kuphatikiza chitoliro chimodzi chapakati.
Kutengera fomula:
Mbali iliyonse imakhala ndi mapaipi a n. Wosanjikiza akunja ali (n-1) * 6 mapaipi, wosanjikiza wachiwiri (n-2) * 6 mapaipi, ..., (n-1) th wosanjikiza (n-(n-1)) * 6 = 6 mapaipi, ndipo potsiriza 1 chitoliro pakati. Chiwerengero chonsecho ndi [(n-1) + (n-2) + ... + 1]*6 + 1. Mawu omwe ali mkati mwa mabulaketi amaimira chiwerengero cha masamu a masamu (chiwerengero cha mawu oyambirira ndi otsiriza ogawidwa ndi 2, kenako n-1 kuti apereke n * (n-1)/2).
Izi zimabweretsa 3n*(n-1)+1.