数学在太空战中的应用（高手讨论
<p> 有一天我突法奇想，想到一个问题，如下</p><p> 假如台球的桌面是一个三角形，看作一个三角形．我在一个边上把台球打向邻边，然后反弹到下一个邻边，最后回到出发点．请给出运动轨迹，探讨出发点的适用范围。（此题为３边的，我已经作出，与大家讨论讨论）</p><p> 如果是n边的，情况会怎样？</p><p> 在太空无重力的情况下，人的运动就如台球的运动，需要反弹前进。（参考科幻书 ＥＮＤ’ＧＡＭＥ）</p><p> 有兴趣的朋友探讨以下ＱＱ 405757408</p><p> </p> <p>可否将你的关于三边的详细证明发上来？让大家讨论看看有没有办法做归纳！谢谢！</p> <strong>关于3边的证明</strong><div twffan="done" style="PADDING-RIGHT: 0px; MARGIN-TOP: 10px; FONT-SIZE: 9pt; OVERFLOW-X: hidden; WIDTH: 97%; WORD-BREAK: break-all; TEXT-INDENT: 24px; LINE-HEIGHT: normal; HEIGHT: 200px; WORD-WRAP: break-word;"><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">求解</span><span twffan="done" style="COLOR: blue;"><font face="Times New Roman"> </font></span><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">如下</span><span lang="EN-US" twffan="done" style="COLOR: blue;"> <p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><shapetype id="_x0000_t202" path="m0,0l0,21600,21600,21600,21600,0xe" ospt="202" coordsize="21600,21600"></shapetype><stroke joinstyle="miter"></stroke><stroke></stroke><path gradientshapeok="t"></path><path></path><shapetype></shapetype><shape id="_x0000_s1040" stroked="f" fillcolor="#0c9" filled="f" type="#_x0000_t202" style="MARGIN-TOP: -12.35pt; Z-INDEX: 15; LEFT: 0px; MARGIN-LEFT: 364.75pt; WIDTH: 29.15pt; POSITION: absolute; HEIGHT: 36pt; TEXT-ALIGN: left; mso-wrap-style: none; v-text-anchor: top-baseline;"></shape><textbox style="mso-fit-shape-to-text: t;"></textbox><textbox></textbox><shape></shape><span twffan="done" style="Z-INDEX: 15; LEFT: 0pt; POSITION: absolute;"><table cellspacing="0" cellpadding="0" width="100%"><tbody><tr><td style="BORDER-LEFT-COLOR: #ece9d8; BORDER-BOTTOM-COLOR: #ece9d8; BORDER-TOP-COLOR: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-RIGHT-COLOR: #ece9d8;"><div class="shape" twffan="done" vshape="_x0000_s1040" style="PADDING-RIGHT: 7.2pt; PADDING-LEFT: 7.2pt; PADDING-BOTTOM: 3.6pt; PADDING-TOP: 3.6pt;"><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none;"><span lang="EN-US" twffan="done" style="FONT-SIZE: 24pt; COLOR: black;"><font face="Times New Roman">E <p></p></font></span></p><p></p><p></p></div></td></tr></tbody></table></span><shape id="_x0000_s1039" stroked="f" fillcolor="#0c9" filled="f" type="#_x0000_t202" style="MARGIN-TOP: 29.65pt; Z-INDEX: 14; LEFT: 0px; MARGIN-LEFT: 160.75pt; WIDTH: 31.9pt; POSITION: absolute; HEIGHT: 36pt; TEXT-ALIGN: left; mso-wrap-style: none; v-text-anchor: top-baseline;"></shape><textbox style="mso-fit-shape-to-text: t;"></textbox><font face="Times New Roman"></font><textbox></textbox><shape></shape><span twffan="done" style="Z-INDEX: 14; LEFT: 0pt; POSITION: absolute;"><table cellspacing="0" cellpadding="0" width="100%"><tbody><tr><td style="BORDER-LEFT-COLOR: #ece9d8; BORDER-BOTTOM-COLOR: #ece9d8; BORDER-TOP-COLOR: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-RIGHT-COLOR: #ece9d8;"><div class="shape" twffan="done" vshape="_x0000_s1039" style="PADDING-RIGHT: 7.2pt; PADDING-LEFT: 7.2pt; PADDING-BOTTOM: 3.6pt; PADDING-TOP: 3.6pt;"><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none;"><span lang="EN-US" twffan="done" style="FONT-SIZE: 24pt; COLOR: black;"><font face="Times New Roman">D <p></p></font></span></p><p></p><p></p></div></td></tr></tbody></table></span><line id="_x0000_s1038" to="282pt,116.4pt" from="258pt,32.4pt" style="Z-INDEX: 13; LEFT: 0px; POSITION: absolute; TEXT-ALIGN: left; flip: x;"></line><stroke endarrow="block"></stroke><font face="Times New Roman"></font><stroke></stroke><line></line><line id="_x0000_s1037" to="258pt,116.4pt" from="252pt,44.4pt" style="Z-INDEX: 12; LEFT: 0px; POSITION: absolute; TEXT-ALIGN: left; flip: x y;"></line><font face="Times New Roman"></font><line></line><shape id="_x0000_s1036" stroked="f" fillcolor="#0c9" filled="f" type="#_x0000_t202" style="MARGIN-TOP: 5.65pt; Z-INDEX: 11; LEFT: 0px; MARGIN-LEFT: 274.75pt; WIDTH: 30.5pt; POSITION: absolute; HEIGHT: 36pt; TEXT-ALIGN: left; mso-wrap-style: none; v-text-anchor: top-baseline;"></shape><textbox style="mso-fit-shape-to-text: t;"></textbox><font face="Times New Roman"></font><textbox></textbox><shape></shape><span twffan="done" style="Z-INDEX: 11; LEFT: 0pt; POSITION: absolute;"><table cellspacing="0" cellpadding="0" width="100%"><tbody><tr><td style="BORDER-LEFT-COLOR: #ece9d8; BORDER-BOTTOM-COLOR: #ece9d8; BORDER-TOP-COLOR: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-RIGHT-COLOR: #ece9d8;"><div class="shape" twffan="done" vshape="_x0000_s1036" style="PADDING-RIGHT: 7.2pt; PADDING-LEFT: 7.2pt; PADDING-BOTTOM: 3.6pt; PADDING-TOP: 3.6pt;"><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none;"><span lang="EN-US" twffan="done" style="FONT-SIZE: 24pt; COLOR: black;"><font face="Times New Roman">C <p></p></font></span></p><p></p><p></p></div></td></tr></tbody></table></span><shape id="_x0000_s1035" stroked="f" fillcolor="#0c9" filled="f" type="#_x0000_t202" style="MARGIN-TOP: 20.4pt; Z-INDEX: 10; LEFT: 0px; MARGIN-LEFT: 228pt; WIDTH: 30pt; POSITION: absolute; HEIGHT: 36pt; TEXT-ALIGN: left;"></shape><textbox style="mso-fit-shape-to-text: t;"></textbox><font face="Times New Roman"></font><textbox></textbox><shape></shape><span twffan="done" style="Z-INDEX: 10; LEFT: 0pt; POSITION: absolute;"><table cellspacing="0" cellpadding="0" width="100%"><tbody><tr><td style="BORDER-LEFT-COLOR: #ece9d8; BORDER-BOTTOM-COLOR: #ece9d8; BORDER-TOP-COLOR: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-RIGHT-COLOR: #ece9d8;"><div class="shape" twffan="done" vshape="_x0000_s1035" style="PADDING-RIGHT: 7.2pt; PADDING-LEFT: 7.2pt; PADDING-BOTTOM: 3.6pt; PADDING-TOP: 3.6pt;"><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none;"><span lang="EN-US" twffan="done" style="FONT-SIZE: 24pt; COLOR: black;"><font face="Times New Roman">B <p></p></font></span></p><p></p><p></p></div></td></tr></tbody></table></span><shape id="_x0000_s1034" stroked="f" fillcolor="#0c9" filled="f" type="#_x0000_t202" style="MARGIN-TOP: 134.4pt; Z-INDEX: 9; LEFT: 0px; MARGIN-LEFT: 240pt; WIDTH: 30pt; POSITION: absolute; HEIGHT: 36pt; TEXT-ALIGN: left;"></shape><textbox style="mso-fit-shape-to-text: t;"></textbox><font face="Times New Roman"></font><textbox></textbox><shape></shape><span twffan="done" style="Z-INDEX: 9; LEFT: 0pt; POSITION: absolute;"><table cellspacing="0" cellpadding="0" width="100%"><tbody><tr><td style="BORDER-LEFT-COLOR: #ece9d8; BORDER-BOTTOM-COLOR: #ece9d8; BORDER-TOP-COLOR: #ece9d8; BACKGROUND-COLOR: transparent; BORDER-RIGHT-COLOR: #ece9d8;"><div class="shape" twffan="done" vshape="_x0000_s1034" style="PADDING-RIGHT: 7.2pt; PADDING-LEFT: 7.2pt; PADDING-BOTTOM: 3.6pt; PADDING-TOP: 3.6pt;"><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none;"><span lang="EN-US" twffan="done" style="FONT-SIZE: 24pt; COLOR: black;"><font face="Times New Roman">A <p></p></font></span></p><p></p><p></p></div></td></tr></tbody></table></span><line id="_x0000_s1033" to="366pt,56.4pt" from="174pt,14.4pt" style="Z-INDEX: 8; LEFT: 0px; POSITION: absolute; TEXT-ALIGN: left; flip: y;"></line><font face="Times New Roman"></font><line></line><line id="_x0000_s1032" to="366pt,116.4pt" from="258pt,14.4pt" style="Z-INDEX: 7; LEFT: 0px; POSITION: absolute; TEXT-ALIGN: left; flip: y;"></line><font face="Times New Roman"></font><line></line><line id="_x0000_s1031" to="210pt,86.4pt" from="174pt,56.4pt" style="Z-INDEX: 6; LEFT: 0px; POSITION: absolute; TEXT-ALIGN: left; flip: x y;"></line><font face="Times New Roman"></font><line></line><line id="_x0000_s1030" to="258pt,122.4pt" from="210pt,86.4pt" style="Z-INDEX: 5; LEFT: 0px; POSITION: absolute; TEXT-ALIGN: left;"></line><font face="Times New Roman"></font><line></line><shapetype id="_x0000_t120" path="m10800,0qx0,10800,10800,21600,21600,10800,10800,0xe" ospt="120" coordsize="21600,21600"></shapetype><path gradientshapeok="t" textboxrect="3163,3163,18437,18437"></path><path></path><shapetype></shapetype><shape id="_x0000_s1029" fillcolor="#0c9" type="#_x0000_t120" style="MARGIN-TOP: 116.4pt; Z-INDEX: 4; LEFT: 0px; MARGIN-LEFT: 252pt; WIDTH: 6pt; POSITION: absolute; HEIGHT: 6pt; TEXT-ALIGN: left; mso-wrap-style: none; v-text-anchor: middle;"></shape><font face="Times New Roman"></font><shape></shape><line id="_x0000_s1028" to="384pt,116.4pt" from="270pt,20.4pt" style="Z-INDEX: 3; LEFT: 0px; POSITION: absolute; TEXT-ALIGN: left;"></line><font face="Times New Roman"></font><line></line><line id="_x0000_s1027" to="378pt,122.4pt" from="180pt,116.4pt" style="Z-INDEX: 2; LEFT: 0px; POSITION: absolute; TEXT-ALIGN: left; flip: y;"></line><font face="Times New Roman"></font><line></line><line id="_x0000_s1026" to="276pt,116.4pt" from="186pt,14.4pt" style="Z-INDEX: 1; LEFT: 0px; POSITION: absolute; TEXT-ALIGN: left; flip: x;"></line><font face="Times New Roman"></font><line></line><span lang="EN-US" twffan="done" style="COLOR: blue;"><span twffan="done" style="mso-spacerun: yes;"><font face="Times New Roman"> </font></span></span><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">如图</span><span lang="EN-US" twffan="done" style="COLOR: blue;"> <p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">假如小球从</span><span lang="EN-US" twffan="done" style="COLOR: blue;"><font face="Times New Roman">A</font></span><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">点出发</span><span lang="EN-US" twffan="done" style="COLOR: blue;"><font face="Times New Roman">, <p></p></font></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">做</span><span lang="EN-US" twffan="done" style="COLOR: blue;"><font face="Times New Roman">A</font></span><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的对称点</span><span lang="EN-US" twffan="done" style="COLOR: blue;"><font face="Times New Roman">D,</font></span><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">再做</span><span lang="EN-US" twffan="done" style="COLOR: blue;"><font face="Times New Roman">A</font></span><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的另一边</span><span lang="EN-US" twffan="done" style="COLOR: blue;"> <p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的对称点</span><span lang="EN-US" twffan="done" style="COLOR: blue;"><font face="Times New Roman">E <p></p></font></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">联结</span><span lang="EN-US" twffan="done" style="COLOR: blue;"><font face="Times New Roman">DE </font></span><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">交点</span><span lang="EN-US" twffan="done" style="COLOR: blue;"><font face="Times New Roman">BC <p></p></font></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">则三角形</span><span lang="EN-US" twffan="done" style="COLOR: blue;"><font face="Times New Roman">ABC</font></span><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">就是运动轨迹。</span><span lang="EN-US" twffan="done" style="COLOR: blue;"> <p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">经过严、验证</span><span lang="EN-US" twffan="done" style="COLOR: blue;"><font face="Times New Roman"> A</font></span><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">—</span><span lang="EN-US" twffan="done" style="COLOR: blue;"><font face="Times New Roman">>B</font></span><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">—</span><span lang="EN-US" twffan="done" style="COLOR: blue;"><font face="Times New Roman">>C</font></span><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的过程遵守</span><span lang="EN-US" twffan="done" style="COLOR: blue;"> <p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">反射定律</span><span lang="EN-US" twffan="done" style="COLOR: blue;"> <p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">由于</span><span lang="EN-US" twffan="done" style="COLOR: blue;"><font face="Times New Roman">DE</font></span><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">不能超过上面的顶点</span><span lang="EN-US" twffan="done" style="COLOR: blue;"> <p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span twffan="done" style="COLOR: blue; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">由此范围可以得到</span><span lang="EN-US" twffan="done" style="COLOR: blue;"> <p></p></span></p><p></p></div> <p>好想法，顶</p> <p>不错</p>
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