P 2k #Gcapm% *zW$HjDI4D̜P ;Copyright 1996 - Michael D. Huberty, Ko Hayashi & Chia VangngiH iÌiYPipGV[Mb@ ; MDt lh@f }$f fCC MR2@ ; MDt lh@f }$f fCC  JOM"change radius"CCH  AZ>M@M F MM FCwC CmPH]PTN]0HHFN]0N(TClearly, the circumference of circle is greater than the perimeter of the hexagon. gon. perimeter of the hexagon. umference of circle is greater than the perimeter of the hexa\b/;;0/;;+V|Clearly, the perimeter of the twelve-sided polygon provides an improved approximation for the circumference and thus for pi.i.i.hexagon./`4;0;;plGlPsELEstimation of PiPi`O jM IM JMMCwCCC?. m334ِ / E44p4 /fYO/<N4  m {S:AB} = @ N $(B@ radius =  @$$($ #`p(((@/|e2LD(D +  sc!3   | P& P!! "(e @[2L6  5 "t!x $ D($ P556+'D P QB7h4e"f@ MD H ;fL0tffCCB?5%F?5%F 0A7h4e"f@ MD H ;fL0tffCCB?5%F?5%F Q m4Tu@F E4*TuTv0 F   T Circumference A = @ N $(B@circumference of circle = @$$($ #`p(((@/|e2LD(D +  sc!3   | P& P!! "(e @[2L6  5 "t!x $ D($ P556+'D P hm> k@ ; MDt lh@oK@ }$oI oC̬C "'!g 6@ ; MDt lh@f }$f fC-CNf ١''bfO,`UP DbHO,@O,UPOOC̬CCC?rc7N _F DbNpN _pFNC̬CB?5%F?5%F'GkM @F DbHMM0 FMMC-CNfCC? N  m36PZ Calculatorrr@0ZLr  .{D:(circumference of circle)}{2{!:*}radius} = @ N $(B@%(circumference of circle)/diameter = @$$($ #`p(((@/|e2LD(D +  sc!3   | P& P!! "(e @[2L6  5 "t!x $ D($ P556+'D P # e@ ; MDt lh@oK@ }$oI oC3OC&   N1`i@ ; MDt lh@oK@ }$oI oCC3  RlWqNa@ ; MDt lh@f }$f fCC 9x>}# 1@ ; MDt lh@f }$f fCұBm  ' boOd{`UP DbHOdOe {@UP 08<O>CCCC?g bgO3pUP DbHO3PO3UPOOC3OC&C̬C?Qmq wN<` @F DbN<@N< @FNC̬CCC?g vN8 DF DbN8N8 D`FNCC3C̬C?c8N% W0F DbN%N&@ WFN&0 WNCCB?5%F?5%F%c4Mp F DbMPM FMCұBmB?5%F?5%F8!}  lM 0F DbHMM@ FMMCұBmC-CNf?@E# g@ ; MDtoC4C   ' bhUPO8`CrpC͚CCe?5'  ak FNN 0N0NNCf CaCC?N'c@ ; MDt lh@oK@ }$oI oC6C M03@ ; MDt lh@f }$f fCC+1  9#>(M4@ ; MDt lf }$f fCRBm6 Q?q bpOktPUP DbHOkOl0t0UPOOC4CCC?O? d@ ; MDt lh@oK@ }$oI oCC  O> j@ ; MDt lh@oK@ }$oI oCC4"  beOp yF DbOPO yFNC6CCC3?"lqN` f@ ; MDtoC3C7 ! R@WE# m@ ; MDt lh@oK@ }$oI oCC ! Qk xN@ =F DbN@N@p <FNC6CCC?";Uc9N* RF DbN*pN* RpFNC6CB?5%F?5%F"8w  oN |PF DbNN |0FMCұBmCC+1?#8">}  nM F DbMM` FMCRBm6CұBm?$0Oc6M pF DbMM PFMCC+1B?5%F?5%F#{c5M F DbMM` FMCRBm6B?5%F?5%F$?q bqOs`lUP DbOs@OslUP 08<O>C3C7C4C?)k bnO_@UP DbO_O`@ UPOC3OC&C3C7?) bmO\0UP DbO\O\UPOCCC3OC&?& blOWPUP DbOW0OWUPOC6CCC?&"  bkORpUP DbORPORUPOCC4"CC3?'g bjONUP DbONOO`UPOCC4"C̬C?' biOCpUP DbOCPOCUPOCC4"CC?&'QmE atN F DbNN` FNCCC̬C?*Q?Wq asNP F DbN0Nՠ FNCCCC?*ۋI'' am ӀFN0C kCCCZ?+Q?q alN F DbHNNP FNNC3C7CC?*)w|N 7@ ; MDt lh@f }$f fCICNF / M5@ ; MDt lh@f }$f fCz C 0 ; p3Ti F DbFTiTipFTipT?HCC+1CICNFC-CNfCz CCRBm6CұBm#<=$N h@ ; MDt lh@oK@ }$oI oCC3L : hmN b x lh@oK@ }$oI oC)C̴ :   ajN F DbN`N FNNCC+1Cz C?=#8"|  aiN F Dbe NN `F@p@NCRBm6CICNF?<$'  rN pF DbN N p oFNC-CNfCz C?=!|  qN ` sF DbN @N sFNCICNFC-CNf?<v pN wF DbNN w`FMCC+1CICNF?<#8(  mMP F DbM0M FMCz CCRBm6?$=P m7FLFP0F@F0F Perimeter p3 = ce of circle)}{2{!:*}radius} = @ N $(B@!perimeter of inscribed hexagon = r = @$$($ #`p(((@/|e2LD(D +  sc!3   | P& P!! "(e @[2L6  5 "t!x $ D($ P556+'D P>T  p4T}0F DbT}T~@FT ?C6CCCC3OC&C3C7C4CCC3LCC3CC4"C̬CCCCCC)C̴"&)?'*@E brOw iUP DbOwOwphUPOC4CCC3L?? awNP F DbN0N FNCC3CC3L??Qkm arNѐ F DbNpN pFNCCC)C̴?@g aqN F DbNNP FNC)C̴C6C?"@g anN ̠F DbHN`N ̀FNNCC3LC)C̴?@?N  m34g2 Calculator00g2L0  !{D:Perimeter p3}{2{!:*}radius} = :*}radius} = @ N $(B@,(perimeter of inscribed hexagon)/diameter = @$$($ #`p(((@/|e2LD(D +  sc!3   | P& P!! "(e @[2L6  5 "t!x $ D($ P556+'D PG O m6T0F E4TT@FT Perimeter p4 = }{2{!:*}radius} = :*}radius} = @ N $(B@#perimeter of inscribed dodecagon = ameter = @$$($ #`p(((@/|e2LD(D +  sc!3   | P& P!! "(e @[2L6  5 "t!x $ D($ P556+'D PHO  m35 ; Calculator55 ;L5  !{D:Perimeter p4}{2{!:*}radius} = :*}radius} = @ N $(B@.(perimeter of inscribed dodecagon)/diameter = @$$($ #`p(((@/|e2LD(D +  sc!3   | P& P!! "(e @[2L6  5 "t!x $ D($ P556+'D PO