Qhov tseeb hexagon: nthuav li cas nws yog thiab yuav ua li cas los ua nws

Puas muaj ib lub cwj mem nyob ib ncig ntawm koj? Saib ntawm nws seem - nws yog ib txwm hexagon los yog, raws li nws tseem hu ua, ib tug hex. Daim ntawv no kuj muaj ib tug txiv-section, ib tug hexagonal teb ntawm chess, tus siv lead ua ntxaij ntoo ntawm ib co complex molecules ntawm carbon (e.g., graphite) flake, honeycombs thiab lwm yam khoom. Giant kev hexagon twb nyuam qhuav raug kuaj tau hauv Saturn huab cua. Puas yog nws zoo li coj txawv txawv los siv heev npaum li cas ntawm daim ntawv no rau nws tsim? Cia saib no daim duab nyob rau hauv kom meej.

Ib qho kev sibtham hauv lub cev yog ib tug polygon uas muaj rau sab zoo tib yam thiab cov vaj huam sib luag. Los ntawm tsev kawm ntawv chav kawm peb paub tias nws muaj cov khoom nram qab no:

• Qhov ntev ntawm nws lub cim sib raug mus rau lub vojvoog ntawm lub voj voos circumscribed. Ntawm tag nrho cov geometric duab , cov cuab yeej no yog ib tug ib txwm hexagon.
• Cov duab sib npaug sib npaug, thiab tus nqi ntawm txhua tus yog 120 °.
• Tus ntsuas ntawm qhov hexagon tuaj yeem nrhiav tau los ntawm formula P = 6 * R, yog tias lub vojvoog ntawm lub voj voos circumscribed paub, los yog P = 4 * √ (3) * r, yog lub voj voog sau rau hauv nws. R thiab r yog cov kev cai ntawm lub circumscribed thiab inscribed lub voj voog.
• Lub cheeb tsam nyob ntawm cov kev hexagon yog txhais raws li nram no: S = (3 * √ (3) * R ²⁾ / 2. Yog hais tias lub vojvoog tsis paub, nws qhov ntev ntawm ib sab - raws li paub, nws sib raug mus rau qhov ntev ntawm lub voj voog ntawm qhov circumscribed vajvoog.

Ib txwm hexagon muaj ib qho nthuav feature, ua tsaug uas nws tau txais zoo li no ib qho dav faib nyob rau hauv - nws yog peev xwm sau tej nplaim ntawm lub dav hlau tsis muaj overlaps thiab tej qhov chaw. Muaj qee tus Lemma Pala, raws li tus cai hexagon, nws sab yog 1 / √ (3), yog lub log tsheb thoob plaws, uas yog, nws tuaj yeem npog tej txheej nrog ib txoj kab uas hla ntawm ib chav tsev.

Tam sim no xav txog kev tsim kho ntawm ib txwm hexagon. Muaj ob peb txoj kev, qhov nyuaj tshaj plaws uas siv txoj kev siv lub compass, ib qho xaum thiab ib tus kav. Ua ntej, kos ib lub voj voog uas muaj lub vaj huam sib luag, tom qab ntawd qhov chaw nyob ntawm lub voj voog no ua ib qho chaw. Yog tias tsis hloov qhov kev daws teeb meem ntawm lub koob taw qhia, muab qhov point ntawm qhov point, kos tus cim ntxiv rau ntawm lub voj voog, mus txog thaum peb tau tag nrho 6 ntsiab lus. Tam sim no nws tshua tsuas yog mus txuas lawv nrog txhua txoj kab ncaj nraim, thiab qhov xav tau yuav tau txais.

Hauv kev xyaum, muaj qee lub sij hawm thaum koj xav kos ib tug loj hexagon. Piv txwv, nyob rau ob-theem gipsokartonnom qab nthab, nyob ib ncig ntawm daim ntawm lub hauv paus chandelier, koj yuav tsum tau nruab rau hauv qis theem ntawm rau me me teeb. Lub compasses ntawm xws li ntau thiab tsawg yuav heev, heev nyuaj nrhiav. Kuv yuav ua li cas rau qhov no? Kuv kos lub voj voog loj npaum li cas? Nws yooj yim heev. Nws yog ib qho tsim nyog yuav tsum tau siv ib txoj hlua ntawm qhov tsim nyog ntev thiab khi ib qho ntawm nws cov hnub tsis txawv ntawm tus cwj mem. Tam sim no nws tseem tshua tsuas yog nrhiav tau tus pab tus neeg uas xav nias ob kawg ntawm cov xov mus rau lub qab nthab ntawm qhov xav tau. Ntawm chav kawm, qhov no, me yuam kev yuav ua tau, tab sis lawv tsis pom zoo rau ib tus neeg sab nrauv.