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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> extropy-chat-bounces@lists.extropy.org [mailto:extropy-chat-bounces@lists.extropy.org] <b>On Behalf Of </b>Kelly </span> <span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'><o:p></o:p></span></p><div><div><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:#1F497D'>>>…</span>A hiker walks north 4 km, turns and walks east 3 km. <span style='color:#1F497D'>…</span> assuming the north pole trick, what is the farthest she could end up from the start?<span style='color:#1F497D'> spike</span><o:p></o:p></p></div></div></div></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:#1F497D'>>…</span>The furthest distance I can figure is 4+(6/pi).<span style='color:#1F497D'> –</span>Kelly<span style='color:#1F497D'><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Kelly, that is the solution you get if you allow her to go pi radians around the pole. 4+6/pi = ~ 5.9, but let her go pi/2 radians around the pole, and you get about 6.07 km. But pi/2 is still not the optimal solution.<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>I will settle for a wimpy numerical solution if your calculus is rusty. I managed to derive the function and even take the derivative, but setting it equal to zero and solving turned out to be crazy complicated. The answer is between 115 and 116 degrees. She can end up more than 6.25 km from start.<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>spike<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p></div></div></div></body></html>