diff --git a/infographics/math/pdf/semicerchi.pdf b/infographics/math/pdf/semicerchi.pdf new file mode 100644 index 0000000..c483e11 Binary files /dev/null and b/infographics/math/pdf/semicerchi.pdf differ diff --git a/infographics/math/semicerchi.tex b/infographics/math/semicerchi.tex new file mode 100755 index 0000000..8e7e147 --- /dev/null +++ b/infographics/math/semicerchi.tex @@ -0,0 +1,126 @@ +\documentclass{standalone} +% +\usepackage{tikz} +% +\usepackage{tkz-euclide} +\usetkzobj{all} +% +\usepackage{dsfont} +% +\usepackage{xcolor} +% +\definecolor{space}{HTML}{0A2543} +\definecolor{earth}{HTML}{0089FA} +\definecolor{dida}{HTML}{FFDE00} +\definecolor{title}{HTML}{FBA706} +% +\usepackage{amsmath} +% +\usepackage{fontspec} +\setmainfont{Open Dyslexic} +% +\title{Un fatto curioso sui semicerchi} +\begin{document} + \begin{tikzpicture} + \draw [use as bounding box,color=white] (-0.2,15.2) -| (30.2,15.2) |- (30.2,-60) -| (-0.2,-60); + %title + \draw [black,ultra thick,fill=title] (0,7) rectangle (30,15); + \node (example-textwidth-2) [right, align=center, text width=30cm, color=black, font=\fontsize{90pt}{91pt}\selectfont] at (0,11) {Un fatto curioso sui semicerchi}; + \def\a{5} + \def\b{9} + \begin{scope}[shift={(0,4)}] + \tkzDefPoint(15,0){C1} + \tkzDefShiftPoint[C1](\a,0){A} + \tkzDefShiftPoint[C1](-\a,0){A1} + \tkzDefShiftPoint[C1](0,-\a-\b){C2} + \tkzDefShiftPoint[C2](\b,0){B} + \tkzDefShiftPoint[C2](-\b,0){B1} + % + \tkzDrawSector[rotate,ultra thick,fill=earth](C1,A)(-180) + \tkzDrawSector[rotate,ultra thick,fill=earth](C2,B)(180) + % + \tkzCircumCenter(A,A1,B) + \tkzGetPoint{O} + \tkzDrawCircle(O,A1) + % + \tkzDefLine[perpendicular=through A1,K=-1](A1,C1) + \tkzGetPoint{x} + \tkzInterLL(A1,x)(C2,B) + \tkzGetPoint{H} + \tkzInterLC(A1,H)(O,A1) + \tkzGetPoints{A2}{r} + \tkzDrawSegments(A1,A2) + + \tkzMarkRightAngle(C1,A1,A2) + \tkzDrawPoints(C1,C2) + \tkzLabelPoints[font=\fontsize{18pt}{19pt}](H,B) + \tkzLabelPoints[above,font=\fontsize{18pt}{19pt}](A1) + \tkzLabelPoints[below,font=\fontsize{18pt}{19pt}](B1,A2) + % + \tkzLabelSegment[font=\fontsize{18pt}{19pt}\selectfont](C1,A1){\emph{a}} + \tkzLabelSegment[font=\fontsize{18pt}{19pt}\selectfont](C1,A){\emph{a}} + \tkzLabelSegment[font=\fontsize{18pt}{19pt}\selectfont](C2,B){\emph{b}} + \tkzLabelSegment[font=\fontsize{18pt}{19pt}\selectfont](C2,H){\emph{a}} + \tkzLabelSegment[right,font=\fontsize{18pt}{19pt}\selectfont](A1,H){\emph{a + b}} + \tkzLabelSegment[font=\fontsize{18pt}{19pt}\selectfont](H,B1){\emph{b - a}} + \tkzLabelSegment[left,font=\fontsize{18pt}{19pt}\selectfont](H,A2){\emph{x}} + \end{scope} + % + \begin{scope}[shift={(0,-17)}] + \draw [fill=space, thick] (3.5,0) rectangle (23,-6); + \draw [fill=dida, thick] (1.8,0.5) rectangle (11.2,-0.5); + \node [right, align=left, color=black, font=\fontsize{23pt}{24pt}\selectfont] at (2,0) {Teorema delle corde}; + \node [right, align=left, color=white, font=\fontsize{23pt}{24pt}\selectfont] at (4,-2) {$A_1H : HB = B_1H : HA2$}; + \node [right, align=left, color=white, font=\fontsize{23pt}{24pt}\selectfont] at (4,-4) {$A_1H = a+b = HB \Rightarrow b-a = B_1H = HA_2 = x$}; + \end{scope} + % + \begin{scope}[shift={(0,-26)}] + \tkzDefPoint(15,0){C1} + \tkzDefShiftPoint[C1](\a,0){A} + \tkzDefShiftPoint[C1](-\a,0){A1} + \tkzDefShiftPoint[C1](0,-\a-\b){C2} + \tkzDefShiftPoint[C2](\b,0){B} + \tkzDefShiftPoint[C2](-\b,0){B1} + % + \tkzDrawSector[rotate,ultra thick,fill=earth](C1,A)(-180) + \tkzDrawSector[rotate,ultra thick,fill=earth](C2,B)(180) + % + \tkzCircumCenter(A,A1,B) + \tkzGetPoint{O} + \tkzDrawCircle(O,A1) + % + \tkzDefLine[perpendicular=through A1,K=-1](A1,C1) + \tkzGetPoint{x} + \tkzInterLL(A1,x)(C2,B) + \tkzGetPoint{H} + \tkzInterLC(A1,H)(O,A1) + \tkzGetPoints{A2}{r} + \tkzDrawSegments(A1,A2 A2,A) + + \tkzMarkRightAngle(C1,A1,A2) + \tkzLabelPoints[above,font=\fontsize{18pt}{19pt}](A1,A) + \tkzLabelPoints[below,font=\fontsize{18pt}{19pt}](A2) + % + \tkzLabelSegment[font=\fontsize{18pt}{19pt}\selectfont](A1,A){2\emph{a}} + \tkzLabelSegment[right,font=\fontsize{18pt}{19pt}\selectfont](A1,A2){2\emph{b}} + \tkzLabelSegment[right,font=\fontsize{18pt}{19pt}\selectfont](A2,A){2\emph{r}} + \tkzDrawPoint(O) + \end{scope} + % + \begin{scope}[shift={(0,-47)}] + \draw [fill=space, thick] (3.5,0) rectangle (23,-10); + \draw [fill=dida, thick] (1.8,0.6) rectangle (11.2,-0.5); + \node [right, align=left, color=black, font=\fontsize{23pt}{24pt}\selectfont] at (2,0) {Teorema di Pitagora}; + \node [right, align=left, color=white, font=\fontsize{23pt}{24pt}\selectfont] at (4,-2) {$(2a)^2 + (2b)^2 = (2r)^2 \Rightarrow a^2 + b^2 = r^2$}; + \node [right, align=left, color=white, font=\fontsize{23pt}{24pt}\selectfont] at (4,-4) {$A_a = \frac{1}{2} \pi a^2, \qquad A_b = \frac{1}{2} \pi b^2$}; + \node [right, align=left, color=white, font=\fontsize{23pt}{24pt}\selectfont] at (4,-6) {$A_c = \frac{1}{2} \pi r^2$}; + \node [right, align=left, color=white, font=\fontsize{23pt}{24pt}\selectfont] at (4,-8) {$A_a + A_b = \frac{1}{2} \pi (a^2 + b^2) = \frac{1}{2} \pi r^2 = \frac{1}{2} A_c, \, \forall a, b \in \mathds{R}$}; + \end{scope} + % + \begin{scope}[shift={(0,-59)}] + \node at (27,0) () {\includegraphics[width=3.7cm]{licenza}}; + \node at (18,-0.1) {\textcolor{black}{\fontsize{14}{15}\selectfont Testo e illustrazioni: @ulaulaman - Gianluigi Filippelli}}; + \end{scope} + \end{tikzpicture} +% +\end{document} \ No newline at end of file