极坐标简介及其与直角坐标的比较
2013-07-22 09:36
本GeoGebra范例旨在介绍极坐标系的基本概念，并直观演示极坐标与直角坐标之间的转换与比较。通过动态交互，用户可观察点在两种坐标系下的表示，包括极径、极角及直角坐标分量。范例利用圆弧、线段和向量等元素展示象限特征，是学习解析几何的绝佳工具。
所属专题
坐标几何（中一）GeoGebra互动教材
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<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<startPoint x="-0.5" y="-10" z="1"/>
</element>
<element type="numeric" label="lang">
<value val="2"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="5"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="button" label="button0">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="5"/>
<labelOffset x="920" y="39"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[lang,If[lang==1,2,1]]
RunClickScript[buttonLang]
"/>
<caption val="中文"/>
</element>
<element type="button" label="buttonLang">
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="5"/>
<labelOffset x="879" y="39"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetCaption[button0,If[lang==1,"ENG","中文"]]
SetCaption[showPolar,If[lang==1,"顯示極坐標平面"," "]]
SetCaption[showRect,If[lang==1,"顯示直角坐標平面"," "]]
SetCaption[showPolarCo,If[lang==1,"顯示極坐標"," "]]
SetCaption[showRectCo,If[lang==1,"顯示直角坐標"," "]]
SetCaption[fixPolar,If[lang==1,"局限點在極坐標平面格線"," "]]
SetCaption[showQ,If[lang==1,"顯示兩點"," "]]
SetCaption[listAngle,If[lang==1,"間隔 =","interval ="]]
SetCaption[button1,If[lang==1,"動畫","Animate"]]"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
</element>
<expression label="text5" exp=""Cartesian plane""/>
<element type="text" label="text5">
<show object="true" label="false" ev="43"/>
<condition showObject="lang ≠ 1"/>
<objColor r="127" g="0" b="255" alpha="0"/>
<layer val="5"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="0.85" size="-3" style="0"/>
<absoluteScreenLocation x="43" y="59"/>
</element>
<expression label="text6" exp=""Polar plane""/>
<element type="text" label="text6">
<show object="true" label="false" ev="43"/>
<condition showObject="lang ≠ 1"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="5"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="0.85" size="-3" style="0"/>
<absoluteScreenLocation x="43" y="27"/>
</element>
<expression label="text7" exp=""Cartesian coordinates""/>
<element type="text" label="text7">
<show object="true" label="false" ev="43"/>
<condition showObject="lang ≠ 1 ∧ showRect"/>
<objColor r="127" g="0" b="255" alpha="0"/>
<layer val="5"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="0.85" size="-3" style="0"/>
<absoluteScreenLocation x="419" y="59"/>
</element>
<expression label="text8" exp=""Polar coordinates""/>
<element type="text" label="text8">
<show object="true" label="false" ev="43"/>
<condition showObject="lang ≠ 1 ∧ showPolar"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="5"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="0.85" size="-3" style="0"/>
<absoluteScreenLocation x="419" y="28"/>
</element>
<expression label="text9" exp=""restrict points on polar grid lines""/>
<element type="text" label="text9">
<show object="true" label="false" ev="43"/>
<condition showObject="lang ≠ 1 ∧ showPolar"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="5"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="0.85" size="-3" style="0"/>
<absoluteScreenLocation x="701" y="29"/>
</element>
<expression label="text10" exp=""show two points""/>
<element type="text" label="text10">
<show object="true" label="false" ev="43"/>
<condition showObject="lang ≠ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="5"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="0.85" size="-3" style="0"/>
<absoluteScreenLocation x="700" y="59"/>
</element>
<expression label="textPolar" exp=""" + (LaTeX[If[fixPolar, "P(" + (Length[P_{pol}]) + ", " + (Angle[P_{pol}]) + ")", "P(" + (Length[P_{rec}]) + ", " + (Angle[P_{rec}]) + ")"]]) + "\\n" + (LaTeX[If[showQ, If[fixPolar, "Q(" + (Length[Q_{pol}]) + ", " + (Angle[Q_{pol}]) + ")", "Q(" + (Length[Q_{rec}]) + ", " + (Angle[Q_{rec}]) + ")"], ""]]) + """ />
<element type="text" label="textPolar">
<show object="true" label="false" ev="8"/>
<condition showObject="showPolarCo"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="1.6" size="12" style="0"/>
<absoluteScreenLocation x="23" y="59"/>
</element>
<command name="Segment">
<input a0="(0, 0)" a1="(Distance[P_{pol}, (0, 0)], 0)"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="5"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="2" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="CircleArc">
<input a0="(0, 0)" a1="(Distance[P_{pol}, (0, 0)], 0)" a2="P_{pol}"/>
<output a0="c"/>
</command>
<element type="conicpart" label="c">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="5"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-4" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="numeric" label="t">
<value val="1"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="5"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="200" x="32" y="355" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.001" speed="5" type="3" playing="false"/>
</element>
<command name="Point">
<input a0="{f, c}" a1="t"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="false" ev="4"/>
<condition showObject="fixPolar"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<coords x="1.0000000000000002" y="-1.7320508075688772" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Angle">
<input a0="(Distance[P_{pol}, (0, 0)], 0)" a1="(0, 0)" a2="A"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<angleStyle val="0"/>
<emphasizeRightAngle val="false"/>
<value val="5.235987755982989"/>
<show object="true" label="false" ev="5"/>
<condition showObject="showPolar ∧ fixPolar"/>
<objColor r="127" g="0" b="255" alpha="0.5"/>
<layer val="8"/>
<labelMode val="1"/>
<decoration type="6"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="70"/>
<selectionAllowed val="false"/>
</element>
<element type="button" label="button1">
<show object="true" label="true" ev="3"/>
<condition showObject="showPolar ∧ fixPolar"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="153" b="153" alpha="255"/>
<layer val="8"/>
<labelOffset x="568" y="8"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetVisibleInView(g,1,true)
SetVisibleInView(α,1,true)
SetValue(t,0)
StartAnimation(t)"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="Animate"/>
</element>
<command name="Segment">
<input a0="(0, 0)" a1="A"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="false" ev="5"/>
<condition showObject="showPolar ∧ fixPolar"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="8"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="1.7320508075688772" y="1.0000000000000002" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
</geogebra>