CHWiki:Pískoviště/Matematika

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<math>\frac{1}{3v^2}</math>

<math>a+b - c</math>

<math>\lim_{n \to \infty}\frac{1}{n} = 0</math>

<math>{n \choose k} = \frac{n!}{(n-k)!k!}</math>

<math>\left(\begin{array}{cc} 8 & 7 \\ 9 & 8 \\ \end{array}\right)</math>

<math>\left(\begin{array}{cc} 8 & 7 \\ 9 & 6 \\ \end{array}\right)</math>

<latex>\psset{unit=0.5cm} \begin{pspicture}(-4,-0.5)(4,8) \psgrid[subgriddiv=0,griddots=5,

  gridlabels=7pt](-4,-0.5)(4,8)

\psline[linewidth=1pt]{->}(-4,0)(+4,0) \psline[linewidth=1pt]{->}(0,-0.5)(0,8) \psplot[plotstyle=curve,

  linewidth=0.5pt]{-4}{0.9}{10 x exp}

\rput[l](1,7.5){$10^x$} \psplot[plotstyle=curve,linecolor=red,

  linewidth=0.5pt]{-4}{3}{2 x exp}

\rput[l](2.2,7.5){\color{blue}$e^x$} \psplot[plotstyle=curve,linecolor=blue,

  linewidth=0.5pt]{-4}{2.05}{2.7183 x exp}

\rput[l](3.2,7.5){\color{red}$2^x$} \rput(4,8.5){\color{white}change\normalcolor} \rput(-4,-1){\color{white}bounding box\normalcolor} \end{pspicture}</latex>

<latex>\SpecialCoor \begin{pspicture}(-3,-3)(3,3)

  \multido{\i=-2+1}{6}{%
    \psline[linewidth=3pt,linecolor=red]
    (\i,\i)(! \i\space 1 sub \i)}%
    \psaxes[linewidth=0.2mm]{->}(0,0)(-3,-3)(3,3)

\end{pspicture}</latex>

<latex>\psset{xunit=1.7cm} \parametricplot[linewidth=1.2pt,plotstyle=ccurve]% {0}{360}{t sin t 2 mul sin} \psline{<->}(0,-1.2)(0,1.2) \psline{<->}(-1.2,0)(1.2,0)</latex>

<latex>\pscustom[linewidth=2pt,fillstyle=solid,fillcolor=gray]{ \pscurve(0,2)(1,2.5)(2,1.5)(4,3) \pscurve[liftpen=1](4,1)(3,0.5)(2,1)(1,0)(0,.5)}</latex>

<latex>\rput[tl](0,3){\rnode{A}{\psframebox{Node A}}} \rput[br](4,0){\ovalnode{B}{Node B}} \ncangles[angleA=-90,arm=.4cm,linearc=.15]{A}{B}</latex>

<latex>\pspolygon(0,0)(4,2)(4,0) \pcline[offset=12pt]{|-|}(0,0)(4,2) \lput*{:U}{Length}</latex>

<latex>\[ \setlength{\arraycolsep}{1cm} \def\tX{\tilde{\tilde{X}}} \begin{array}{cc} \Rnode{a}{(X-A,N-A)} & \Rnode{b}{(\tX,a)}\\[1.5cm] \Rnode{c}{(X,N)} & \Rnode{d}{\LARGE(\tX,N)}\\[1.5cm] \end{array} \psset{nodesep=5pt,arrows=->} \everypsbox{\scriptstyle} \ncLine{a}{b}\Aput{a} \ncLine{a}{c}\Bput{r} \ncLine[linestyle=dashed]{c}{d}\Bput{b} \ncLine{b}{d}\Bput{s} \]</latex>

<latex>\cnode(.5,.5){.5}{A} \cnode[fillstyle=solid,fillcolor=lightgray](3.5,2.5){.5}{B} \nccoil[coilwidth=.3]{<->}{A}{B}</latex>

<math>\iiint_{\Omega}{f(x,y,z)}dxdydz</math>

<latex>\cnodeput(0,0){A}{X} \cnodeput(3,2){B}{Y} \psset{nodesep=3pt} \ncarc{->}{A}{B} \ncarc{->}{B}{A}</latex>

<latex> \begin{picture}(85,33)(-20,-28) \put(-20,-28){\framebox(85,33){}}

 \gasset{Nadjust=w,Nadjustdist=2,Nh=6,Nmr=1}
 \node[Nmarks=i](A)(0,0){idle}
 \node(B)(50,0){wait}
 \node(C)(50,-20){wait}
 \node[Nmarks=r](D)(0,-20){critical}

 \drawedge(A,B){req1:=true}
 \drawedge(B,C){turn:=2}
 \drawedge[syo=-1,eyo=-1](C,D){turn=1?}
 \drawedge[syo=1,eyo=1,ELside=r](C,D){req2=false?}
 \drawedge(D,A){req1:=false}

\end{picture} </latex>

<latex>\pstree[levelsep=8ex]{\Tcircle{R} }{ \Tcircle{D1} \pstree{ \Tcircle{D2} }{ \Tcircle{D2.1} \Tcircle{D2.2} } \Tcircle{D3} \Tcircle{D4} }</latex>

<latex>\psset{PointSymbol=none} \pstTriangle(-2,-1){A}(1,2){B}(2,-1){C} {% encapsulation de modif param�etres \psset{linestyle=none, PointSymbolB=none, PointNameB=none} \pstMediatorAB{A}{B}{K}{KP} \pstMediatorAB{C}{A}{J}{JP} \pstMediatorAB{B}{C}{I}{IP} }% fin \pstInterLL[PointSymbol=square, PosAngle=-170]{I}{IP}{J}{JP}{O} {% encapsulation de modif param�etres \psset{nodesep=-.8, linecolor=green} \pstLineAB{O}{I}\pstLineAB{O}{J}\pstLineAB{O}{K} }% fin \psdot[dotstyle=square](O) \pstProjection{B}{A}{C} \pstProjection{B}{C}{A} \pstProjection{A}{C}{B} \psset{linecolor=blue}\ncline{A}{A'}\ncline{C}{C'}\ncline{B}{B'} \pstInterLL[PointSymbol=square]{A}{A'}{B}{B'}{H} % le cercle d'Euler (centre au milieu de [OH]) \pstMiddleAB[PointSymbol=o, PointName=\omega]{O}{H}{omega} \pstCircleOA[linecolor=Orange, linestyle=dashed, dash=5mm 1mm]{omega}{B'} \psset{PointName=none} % il passe par le milieu des segments joignant l'orthocentre et les sommets \pstMiddleAB{H}{A}{AH}\pstMiddleAB{H}{B}{BH}\pstMiddleAB{H}{C}{CH} \pstSegmentMark{H}{AH}\pstSegmentMark{AH}{A} \psset{SegmentSymbol=wedge}\pstSegmentMark{H}{BH}\pstSegmentMark{BH}{B} \psset{SegmentSymbol=cup}\pstSegmentMark{H}{CH}\pstSegmentMark{CH}{C}</latex>

<latex> \pstTriangle[PointSymbol=none](4,1){A}(1,3){B}(1.5,-2){C} \pstCircleABC[CodeFig=true, CodeFigColor=blue, linecolor=red, PointSymbol=none]{A}{B}{C}{O}</latex>