: 2kt6.capm  MlMFaphics Apps html Documents M & M Files MATH 5337  .Rectifying A Circle Using Hippias' Quadratrix x ` Tasks t@oserControl Panels t l havef c$HjDI4D̜P ;Copyright 1996 - Michael D. Huberty, Ko Hayashi & Chia VangngiH iÌiYPipGl| J$JJpͤDt Z LHH$J Y KPO OOXOdFOOODTCuOyLHOBC RW% AXPѐNx *HXPXQ pNxXXCCN dwYdcFaphics Apps html Documents M & M Files MATH 5337  1cMove point "drag" until it reachs point O. Then the rectangle and circle will have the same area. ls t co`0cqc[c[clc[c`0}B4$ 6BXOаNxO:O;HOXOO:XRЀNCCN N N #2  ^PXJPXR0NxXR0XCCN@F Tp m6Tp`Tp j`Tp T BA = gI 6@g e$(B@Distance(B to A) = f @k$($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+ɱN " 4 c\xnQWѠNC CNDCN?p =qN Z" 5 c\ynĴO8 0 n anCCC@?Q?S  OCGnCN Q  xJXLOJPOOOOUUCGnCNCCN? KTRZ c20XpXX c|XCGnCNC?5%F?5%F ( m2OPOp E4O0OOpO OA = gI 6@g e$(B@Distance(O to A) = f @k$($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+ X m24X| 4X BXxB CKXBú5VC*~únMú OA = gI 6@g e$(B@ radius = O to A) = f @k$($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+ LUPY Ser  p4k Stickies Shut Dwn H$?5%F?5%FCGnCNDGnCN c4JmID hBCC?5%F?5%F W\   DDGnCN Dwile  m18 Apps Math Apps etwork Apps User TempAppl  Area p4 = I 6@g e$(B@Area of Circle = = f @k$($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+'  PJ IT O COCM Q\  r cX `XX TNDGnCNCCN?@ m10_'`Nx E4_'`_'@Nx_ AD = p4 = I 6@g e$(B@Distance(A to D) = f @k$($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+x;IIH m31II H@Y0J ${D:(Area of Circle)}{radius{u:2}} = @g e$(B@(Area of Circle)/radius^2 = f @k$($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+J  re 5 `6D BCCOCM?ޛzo ?/l "drag"ل2``**`CCN '  u NxY+p Y$O; O<OY+pO:Y,YCGnCGnCGnBH? ' aaHHO$ICO(CPCOC?C'Wile  zcs Apps Math Apps etwork Apps User TempAppl BC\IBdC᣷?' s User Temp AppleCD Audo PlayerAutomated Tasks CalC@CC? ! m5f33ff33ff  A"drag" = f Circle)}{radius{u:2}} = @g e$(B@Distance(A to "drag") = 2 = f @k$($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+IN  PCGnBH $ m1O3O|0O}pOxO  "drag"O = f Circle)}{radius{u:2}} = @g e$(B@Distance("drag" to O) = 2 = f @k$($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+ F6 m23 r = g"O = f Circle)}{radius{u:2}} = @g e$(B@width = radius = o O) = 2 = f @k$($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+HH  at$KJCGnBHCGnCN? F` Re m3cscsNI{| {D:L'O}{OA}{!:*}90 = radius{u:2}} = @g e$(B@(Distance(L' to O)/Distance(O to A)*90 = @k$($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+Z!I1Re m7cscsNI{| {D:AL'}{BA} = *}90 = radius{u:2}} = @g e$(B@%Distance(A to L')/Distance(B to A) = = @k$($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+ PA m4O@`Q WWXOX -L'O{!:*}tan{(:90 {(:{D:L'O}{OA}{!:*}90}} = @g e$(B@FDistance(L' to O)*tan[90 (Distance(L' to O)/Distance(O to A)*90)] = k$($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+1Z!$GRe m8cscsNI{| 5{D:L'O{!:*}tan{(:90 {(:{D:L'O}{OA}{!:*}90}}}{BA} = @g e$(B@Y(Distance(L' to O)*tan[90 (Distance(L' to O)/Distance(O to A)*90)])/Distance(B to A) = ($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+&  ;L=,2`99`CC|y'%  ab[arctan[-abs[sqrt[ln[log[round[nCCNCC|y?(@  m15 @S@p@HH48  L"drag" = }tan{(:90 {(:{D:L'O}{OA}{!:*}90}}}{BA} = @g e$(B@Distance(L to "drag") = 0 (Distance(L' to O)/Distance(O to A)*90)])/Distance(B to A) = ($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+(tMa ('̙ ?JY0 Nx (0YY Nx 08<Y>((!$&%'(  tCGnCNCC|y?( 8  c5dRHHO BCB?5%F?5%F)AMO| m16<ff33ff  ({D:AD{!:*}AD}{2{!:*}{(:Q'L' (drag)}} = }90}}}{BA} = @g e$(B@height = (AD^2)/(2*"drag"L) = istance(L' to O)/Distance(O to A)*90)])/Distance(B to A) = ($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+ *%Gj m19ssss uuu u      {D:AD}{Q'L' (drag)} = Q'L' (drag)}} = }90}}}{BA} = @g e$(B@AD/("drag"L) = /(2*"drag"L) = istance(L' to O)/Distance(O to A)*90)])/Distance(B to A) = ($  0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+*,j m27ssss uuu u     ={D:AD{!:*}AD}{2{!:*}{(:Q'L' (drag)}{!:*}{(:Q'L' (drag)}} = @g e$(B@^Distance(A to D)*Distance(A to D)/(2*Distance(Q' to L' (drag))*Distance(Q' to L' (drag))) =   0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+ *6K;PH  T$HHBC>= -KP &T$HHBY›w 10' aoGx  VxgdUWtdC J›A6V›` ?2JP  arXHGW g VxVXUUBY›wBC?2 XHI  4CO;›R 3J  aqaphics Apps Math Apps Network Apps User TemppCO;›RBY›w?25H  asH$GXCOCMCO;›R?5M  p6W,UUUUdXHHf?CO;›RBY›wBCCOCM52*w m28G    I   Area POTX = {2{!:*}{(:Q'L' (drag)}{!:*}{(:Q'L' (drag)}} = @g e$(B@Area of Rectangle = tance(A to D)/(2*Distance(Q' to L' (drag))*Distance(Q' to L' (drag))) =   0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+8ZI m303333aD333a4a$ '{D:(Area of Rectangle)}{radius{u:2}} = *}{(:Q'L' (drag)}} = @g e$(B@(Area of Rectangle)/radius^2 = D)/(2*Distance(Q' to L' (drag))*Distance(Q' to L' (drag))) =   0f0(((@/|@>!e2LfDHD h@fgRfLX lgf 3>!=tzhT3 f g |gmghThTg"He @[2L6 g`5n P ng$ g D($g55+9