蜂房结构的秘密

󰕕󰭮󰺟󰤵󱈐󰎔󰔫󰬡󱇎󰵃󰨢󰘷󰧰󰚍󰬡󰘥六󱢰󰝮󰤱󱇎󰢪󰢬󰸴󰙽󰛖󰚫󰤱󰎖說󰵓󰘥󱒔󰔫󱞚󰎔󰞢󰔫󰬡󱇎󰢪󰨢󰔫󰬡󰗐󰘥六󱢰󰝮󰩡󰢍󰤱六稜󰨪󱧯󰎖不󱈘󰎔󰗱󰱨󰕕󰭮󰺟不󰤵󱈐󰎔󰟷󰠄󱇎󰢪󰠀不󰨢󰔫󰶺󱌥󱈐󰎔󰗱󰗐󰘷󱇎󰵃󰤱󰔫󱢰󰎔󰔫󰤴󰺏󰢓󰛟󰗼󰔫󱢰󰤱󰎖󰚇󰺍󰠄󱇎󰢪󰤱󰕭󱁴󰎔󱍫󱇎󱄎󰧬󰺗󰔫󰴙󰏈󱛥󰏉󰎔󰴲兩󱢰󰖉󱈶󱁲󰎔󰵕󰛖󰚫󰩡󱇎󰢪󰤱󰢍󰺝󰎖說󰕈󰠡󰢡󰎔󰺍󰴙󱛥󰙍不󰨢󰔫󱃇󰘓󰫿󰎔󰛖󰨢󰚓󱉝󱉹󰔫󰕭󰤱󱉹󰝮󰱳󰎔󰘷󰔿󰬡󰙤󰿛󰤱菱󰝮󰸴󰙽󰛖󰚫󰎖󰀩󰩡了󰖱便󱨠󱊘󰎔󱉹󰔫󰕭󱇎󰢪󰤱󰝮狀󰨢󰬙󱠏󰾽󰤱󰎔󰢍󰺝󰙻󰕂󰎖󰀪

󱉹󰔫

󰺍󰬡菱󰝮󰽘󱆖󰖧󰲦󱈘󰪝󱖂󰭮󰤱󱘋󱔊󰎖󱖕󱈉󰎔󰔫󰛯󰙼󰗻󰳍拉󱋿󰫭󰀩󰁈󰁪󰁢󰁤󰁰󰁮󰁰󰀡󰁇󰁪󰁭󰁪󰁱󰁱󰁰󰁎󰁢󰁳󰁢󰁭󰁥󰁪󰀼󰀡󰀲󰀷󰀷󰀶󰀮󰀲󰀸󰀳󰀺󰀪󰀡󰤱󰤄󰴏󰔳󰎔量度󱈘󰺍󰬡菱󰝮󰎔󰠀󰿇󰷼󰺍菱󰝮󰤱󱁬󰟡󰿛󰣍

109D28'󰎖󰴂󱠲󰨢󰎚󰩡󰩷󱏖󱍫󱇎󱄎󰚕󰚼󰻛󱦟󰺍󰬡󰟡󰎔󰴲󰟄󰬚󰤱󱇎󰢪󰹻󰫠󰚫󰺍󰬡󱑌󰕗󰡋󰁀

󰗼󰔫󰛯󰤄󰴏󰪝󱖂󰭮雷󱃋󰛏󱋿󰀩󰁓󰁦󰁯󰁦󰀮󰁂󰁯󰁵󰁰󰁪󰁯󰁦󰀡󰁇󰁦󰁳󰁤󰁩󰁢󰁶󰁭󰁵󰀡󰁥󰁦󰀡󰁓󰁦󰁢󰁶󰁮󰁶󰁳󰀼󰀡󰀲󰀷󰀹󰀴󰀮󰀲󰀸󰀶󰀸󰀪󰼼󰗠了󰔫󰬡󰷲󱃣󰎔󰗔󱎁󰩡󰘴了󰺍󱑌󰤱󰟡度󰎔󰼉󰗱󰗐󰘴󰻈󰖟󰤱󰞗料來󰧬󰺗󰨴󰙵󰭲󱗨󰤱󱇎󰢪󰎖󰽄句󱇩說󰎔󰚇󱧯󱗨󰡐󰡳󰤱󰵣󰤉󰕀󰎔󰺍󱑌󰤱󱇎󰢪󰎔󱜔󰥤󰫿󱗨󱄎󰻈󰕛󰎖󰠃󱊔󰕂󰎔雷󱃋󰛏󱋿󰤱󰷲󱃣󰨢󰘥󱒔󰤱󰎔󰝺󰬚󰗱󰗐󰺏󱈘󰗐󰕀󰤱󰫠󱌩來󱢞󰣔󰎖

󱉹󰔲

󰚇󱉹󰔲󰕭󰾽󰗠了󰔫󰬡󰗐󰘥六󱢰󰝮󰁂󰁃󰁄󰁅󰁆󰁇󰩡󰢍󰤱六稜󰨪󱧯󰎔󰁐󰩡󰘥六󱢰󰝮󰤱󰕭󰖨󱞚󰎖󰹻󰁂󰁃󰀾󰀲󰎖連󰿨󰁐󰁃󰡉󰁂󰁄󰎔󰠀󱌠󰙌󱞚󰩡󰁑󰎖󰝺󰬚󰗱󰗐利󰘴󰗐󰕀󰖱󰤄來󰧬󰺗󰗠󱇎󰢪󰢍󰺝󰤱菱󰝮󰀻󰙣󰚇󰁃󰗐󰕀󰤱󰛯󱆜󱙇󰔫󱞚󰁈󰎔󰠀󰹻󰁃󰁈󰀾󰁩󰎔󰾥󰧵󰤎󱀑󰔿󰟡󰁂󰁄󰁈󰤱󱢰󰩺󰴲󱙗󱧯󰁂󰁃󰁄󰁈切󰗠󰎔󰠀󰴲󰘌󰖘󱠏󰣋󰚇󰔿󰟡󰁐󰁂󰁄󰕰󰕂󰎔󰜛󰴲∆OAC󰡉∆BAC󰫹󰙽󰚇󰔫󰲦󰎖󰺍󰮴󰎔󰬺󱙗󱧯󰤱󰺷󱞚󰁈󰼉󱄎󰛯󰣍󰀱󰕰󰕂󰎔󰠀󱌠󱇠󰛯󱆜󰩡󰁒󰎖󰚕󰚼󰎔󰚇󰁂󰁄󰤱󱢰󰕂󰼉󱄎󰗠󰷼󰔫󰬡菱󰝮󰁂󰁈󰁄󰁒了󰎖類󰛿󰚆󰎔󰝺󰬚󰗱󰗐󰖉󰜑󰚇󰁅󰎕󰁇󰗐󰕀󰁩󰬡󰻢󰛯󰤱󰛯󱆜󰡳󰗠󰁉󰀩󰘢󰚶󰾽󰗠󰀪󰎕󰁌兩󱞚󰎔󰵕󰛖󰺗󰗠󰗼󰘆󰤱兩󰬡菱󰝮󰎖󰥺󰵄󰣔󱧩󰎔󱆖󱈘切󰻊󰧵󰤱立󱧯󱧯󱗨󰎔󰡉󰙣󰦛󰤱六稜󰨪󱧯󰤱󱧯󱗨󰨢󰔫󱑌󰤱󰎔󰛟󰣍󰘌󰤱󱜔󰥤󰫿󱗨󰎔󰼉󱏁󰫞󰔫󰾾󰫠󱌩了󰎖

󰘷󵡒󰢐󰖆󰚤󰀩󰁄󰁰󰁴󰁪󰁯󰁦󰀡󰁇󰁰󰁳󰁮󰁶󰁭󰁢󰀪󰎔󰗱󰤵󰀡AC2=12+12−2⋅1⋅1⋅cos120D=3󰀼󰔾󰚂󰩡

∠ABP=60D󰎔OB⊥AC󰎔󰢬󰗐PB=

11󰎖󰘷󰚼󰵓󰀡PG=h2+󰎖24󰘷󱉹󰔲󰗱󰤵󰎔󱆖切󰻊󰧵󰎔∆ABG󰎕∆CBG󰡉菱󰝮󰁐󰁂󰁃󰁄󱄎󰯣󰘈󰎔󰜛󱖞󰬡立󱧯󱄎󰾇

1113󰕛󰫿󱗨󰀻2⋅⋅3⋅+2⋅⋅1⋅h=h+󰎖󰗼󰘆󰎔立󱧯󱏺󰗣了菱󰝮󰕩󰁂󰁈󰁄󰁒󰎔󰙍󰜛󱏺

2222󰗣了󰫿󱗨󰀻2⋅S=3h2+1211h+.3=3h2+󰎖󰘷󰚼󰗱󰤵立󱧯󰫿󱗨󱧢󰖏󰩡24413了󰎖󰀩󰣹󱃠󰀻󰝺󰪚󱊙󰁂󰁈󰁄󰁒󰺝󰖉󱁞行󰫠󱌩󰎔󰠡󵡒兩󰬡菱󰝮󰺝−h−

42

󰖉󰤱󰿨󰣠󱚨󱇠󰨴󰙵󰎔󰨚󰚼不󰘘󰫹󱓤󰫠󱌩󰎖󰀪

󰠩󰺍裡󰎔󰝺󰬚󰼉󱏁󰫞󰞣󰀡󰁩󰀡󰬖󰎔󰠌󰁔󱈒󰛟󰻈󰕛󰎖󰝺󱄎󰕿󰸯兩󰬡不󰙵󰤱󰖱󰤄來󰞣󰵓󰺍󰬡󰁩󰬖󰎖󰬈󰙣󰎔󰻈󰤴󰵷了󱅝󰤱󰖱󰤄󰎔󱅝󰾥󰨢󰠌󰘴󰏈󱃞󲱽󰖉󰏉󰤱󰞣󱖄󰤄󰎖令󰀡

dS

=3dh

hh2+1414−1=0

󰦞󰀡3h=h2+󱇞󰕰󰵓󰀡h=󰜛󱅝󰀡h=

181󰀡󰮴󰎔󱇎󰢪󰤱󱜔󰥤󰫿󱗨󱄎󱈒󰛟󰻈󰕛󰎖󰚕󰣠󰕕󰭮不󱎁識󰔾󰢨󰥃不󰻛󱦟8󰞣󱖄󰤄󰎔󰝺󰬚󰙍󰗱󰗐󰬗󰜗󰔲󰚻󰖱󰿓󰤱󰜒󰜑󰚤󰤄來󰞣󰗠󰚶󱣂數󰬖󰎖󰙣󰶍󰗰

S=3h2+131󱌩󰚤󰕭󰤱󰵄數󰺝󰖉󰎔󰵓󰀡y=3h2+−h−h−

424󰸝󱂈󰖗󰯣󰗰󰯅󱇆󰵓󰀡y2+2hy+h2=3h2+

34

3

󰜛󰀡2h2−2yh+(−y2)=0

4

󰘷󰣍󰀡󰁩󰀡󰘘󰡳󰨢󰔫󰬡󱊔數󰎔󰢬󰗐󰗐󰕂󰤱󰔲󰚻󰖱󰿓󰘘󰡳󰚶󱊔數󱇞󰎔󰨚3

∆=4y2−4⋅2⋅(−y2)≥0

44y2−6+8y2≥0y2≥

12

1了󰎖󰗖󰔵󰕂󰫿󰤱2󰘷󰣍󰝺󰬚󱃣󰗌󱈒󰠩󰻈󰕛󰬖󰎔󰢬󰗐󰁺󰼉󱚨󱇠󰿛󰣍󰖱󰿓󰵓󰀡2h2−2h+󰙵󱑌󰗱󰗐󰵓󰠩h=

11=0󰀡󰀭󰀡2(h−)=048183󰎖󰻈󰧵󱚨󰘴󵡒󰢐󰖆󰚤82󱚨󰘴󰖍󰥈󰡳理󰣍∆ABG󰕂󰗱󰗐󰤵󱈐AG=

2⎛3⎞⎛3⎞2⎜⎟+⎜⎟−(3)18⎠⎝8⎠󰣍∆AGC󰎔󰵓󰀡cos∠AGC=⎝=−

3⎛3⎞⎛3⎞2⎜⎟⎜⎟⎝8⎠⎝8⎠󰜛󱅝∆AGC󰿛󰣍󰟡109D28'󰮴󰎔󱇎󰢪󰤱󱜔󰥤󰫿󱗨󱄎󱈒󰠩󰻈󰕛󰎔󰘷󰚼󱢞󱔄了雷󱃋󰛏󱋿󰤱󰷲󱃣󰎖

󱣂󰣍雷󱃋󰛏󱋿󰤱󰷲󱃣󰙍󰽘󱆖󰿇󰘳󱈘󰔫󰬡󰔼󰖉󰚶󱔊󰤱󰨚󰠃󰎖󱅝雷󱃋󰛏󱋿󰼼󰗠󰗔󰤱󰷲󱃣󰧵󰎔󱅗󰕓數󱖂󰭮󰨲󰘍󰝦󰀩󰁋󰁰󰁩󰁢󰁯󰁯󰀡󰁔󰁢󰁮󰁶󰁦󰁭󰀡󰁌󰁰󰁦󰁯󰁪󰁨󰀡󰀼󰀲󰀸󰀲󰀳󰀮󰀲󰀸󰀶󰀸󰀪立󰠥󰿯󰗠了󱢞󰣔󰎔󰜀󰗔󰫠󱌩󰗠󰤱󰿨󰣠󰨢󰎔菱󰝮󱁬󰟡󰿛󰣍󰀲󰀱󰀺󰎖󰀳󰀷󰀨󰎖󰲦󰥣󰔳󰬚󰗐󰩡󱍫󱇎󰨢󰚕󰚼󰸲󰕛󰤱󰣒󱟽󰎔󰗔󰬚󱍹󰺗󰗠來󰤱󰟡度󰡉󰔳類󰫠󱌩󰗠來󰤱󰟡度󰗠󰷼󱎄󰮁󰎔不󰟩󰩡󰡛󰎔󰛶󰤉󱎄󰮁󰙍󰪚不󱈘󰨢2'󰎔󰎔󰗱見󱍫󱇎󰕢󱆖󰴜󰏈󱜣󰣔󰏉了󰎖󱓴󰤵󱈘了󰼓年󰧵󰎔󱤕󰯑蘭數󱖂󰭮󰳍󰜌勞林󰀩󰁄󰁰󰁭󰁪󰁯󰀡󰁎󰁢󰁤󰁭󰁢󰁶󰁳󰁪󰁯󰀼󰀡󰀲󰀷󰀺󰀹󰀮󰀲󰀸󰀵󰀷󰀪󰼼󰗠了󰗼󰔫󰬡󱢞󰣔󰎔󰠀󰵓109D28'󰀡󰤱󰿨󰣠󰺍󰮴󰔳󰬚󰕩󰿇󰷼󰎔󰨲󰘍󰝦󰚇󰫠󱌩󰮴󰢬󰠌󰘴󰤱󱊙數󰥤󰠀不󰘥󱒔󰎔󰚂󰛖󰞣󰵓󰔫󰬡󱙑󱎄󰤱󰿨󰣠󰎖󰬺來󰎔󱍫󱇎󰧬󰺗󱇎󰢪󰤱󰫠󱌩󰕩󰨢󰘥󱒔󰤱󰎔󰪚󰨢󰔳類󰫠󱙑數󱒽了󰀢