数学基础知识综合演示:角、函数与立体几何
2019-04-01 13:04
本 GeoGebra 范例综合展示数学基础概念,涵盖角的构造与度量、正切函数与对数函数的图像绘制、黎曼和(上和与下和)的可视化演示,以及棱锥与棱柱等立体几何对象的构建。通过点、线段、直线与交点等基本几何命令,结合函数 f、g、h 的图像分析,帮助学习者直观理解角、三角函数、对数函数、积分近似与圆锥曲线等核心数学知识。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.533.0" app="classic" platform="w" id="08BF8191-1A9D-4B14-B212-FEFEC3E8E970" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="700" height="500" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.4" orientation="1" />
</panes>
<views>
<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="500" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="200" window="100,100,250,400" />
<view id="4" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1,1,1" size="400" window="100,100,700,550" />
<view id="512" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
</views>
<toolbar show="false" items="0 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="698" height="498"/>
<coordSystem xZero="348.99999999999994" yZero="222.5" scale="49.999999999999986" yscale="49.99999999999998"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="3" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="A">
<show object="true" label="true"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-1.4" y="2.93" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="true" label="true"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-3.98" y="-1.73" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="C">
<show object="true" label="true"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0.6" y="-1.63" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="text1" exp=""图1-1""/>
<element type="text" label="text1">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<startPoint x="-0.3" y="-3.1500000000000012" z="1"/>
</element>
<element type="polyhedron" label="Archimedean">
<lineStyle thickness="5" type="0" typeHidden="1"/>
<show object="true" label="true"/>
<objColor r="211" g="47" b="47" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="polyhedron" label="Pyramid">
<lineStyle thickness="5" type="0" typeHidden="1"/>
<show object="true" label="true"/>
<objColor r="219" g="97" b="20" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="polyhedron" label="Prism">
<lineStyle thickness="5" type="0" typeHidden="1"/>
<show object="true" label="true"/>
<objColor r="216" g="27" b="96" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Line">
<input a0="A" a1="B"/>
<output a0="f"/>
</command>
<element type="line" label="f">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.66" y="-2.58" z="14.083400000000001"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Line">
<input a0="B" a1="C"/>
<output a0="g"/>
</command>
<element type="line" label="g">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.10000000000000009" y="4.58" z="7.525399999999999"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Line">
<input a0="C" a1="A"/>
<output a0="h"/>
</command>
<element type="line" label="h">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-4.5600000000000005" y="-2" z="-0.5239999999999996"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Point">
<input a0="g"/>
<output a0="A'"/>
</command>
<element type="point" label="A'">
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="3.004967026264629" y="-1.5774898029199862" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="f"/>
<output a0="C'"/>
</command>
<element type="point" label="C'">
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-2.7210996757366415" y="0.5438277174679267" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Line">
<input a0="A'" a1="C'"/>
<output a0="i"/>
</command>
<element type="line" label="i">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.1213175203879127" y="-5.726066702001271" z="-2.6583226322435562"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="h" a1="i"/>
<output a0="B'"/>
</command>
<element type="point" label="B'">
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.316186312638449" y="-11.010380822347352" z="21.868229120349973"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="text2" exp=""\frac{BA'}{A'C}·\frac{CB'}{B'A}·\frac{AC'}{C'B} = \frac{" + (LaTeX[Distance[B, A']]) + "}{" + (LaTeX[Distance[A', C]]) + "}·\frac{" + (LaTeX[Distance[C, B']]) + "}{" + (LaTeX[Distance[B', A]]) + "}·\frac{" + (LaTeX[Distance[A, C']]) + "}{" + (LaTeX[Distance[C', B]]) + "} =" + (LaTeX[((Distance[B, A'] * Distance[C, B']) * Distance[A, C'] / Distance[A', C] / Distance[B', A] / Distance[C', B])]) + """ />
<element type="text" label="text2">
<show object="true" label="false" ev="8"/>
<objColor r="0" g="51" b="204" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="-0.31999999999999873" y="2.3300000000000014" z="1"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.66" y="-2.58" z="14.083400000000001"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="C"/>
<output a0="k"/>
</command>
<element type="segment" label="k">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.10000000000000009" y="4.58" z="7.525399999999999"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="A"/>
<output a0="l"/>
</command>
<element type="segment" label="l">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-4.5600000000000005" y="-2" z="-0.5239999999999996"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="A'"/>
<output a0="m"/>
</command>
<element type="segment" label="m">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.0525101970800137" y="2.4049670262646288" z="3.9516023710593533"/>
<lineStyle thickness="5" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="B'"/>
<output a0="n"/>
</command>
<element type="segment" label="n">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.1265124628175127" y="-0.49408441351645294" z="-0.1294501163413106"/>
<lineStyle thickness="5" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="C'"/>
<output a0="p"/>
</command>
<element type="segment" label="p">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.2738277174679267" y="1.2589003242633585" z="-6.871936754546738"/>
<lineStyle thickness="5" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
</geogebra>