diff --git a/notes/images/2-gamma-area.png b/notes/images/2-gamma-area.png deleted file mode 100644 index 7f01fa5..0000000 Binary files a/notes/images/2-gamma-area.png and /dev/null differ diff --git a/notes/sections/2.md b/notes/sections/2.md index b902da3..6f7deb1 100644 --- a/notes/sections/2.md +++ b/notes/sections/2.md @@ -24,9 +24,37 @@ known methods involve sums, subtractions or products of very big or small numbers, packed in series, partial sums or infinite products. Thus, the efficiency of the methods lies on how quickly they converge to their limit. -![The area of the blue region converges to the Euler–Mascheroni -constant.](images/2-gamma-area.png){#fig:gamma width=7cm} - +\begin{figure} +\hypertarget{fig:gamma}{% +\centering +\begin{tikzpicture}[yscale=3] + \definecolor{brick}{RGB}{160, 54, 35} + % Series + \draw [fill=brick, brick] (1,0) rectangle (2,1); + \draw [fill=brick, brick] (2,0) rectangle (3,0.5); + \draw [fill=brick, brick] (3,0) rectangle (4,0.333); + \draw [fill=brick, brick] (4,0) rectangle (5,0.25); + \draw [fill=brick, brick] (5,0) rectangle (6,0.2); + \draw [fill=brick, brick] (6,0) rectangle (7,0.167); + \draw [fill=brick, brick] (7,0) rectangle (7.5,0.143); + % Logarithm + \filldraw [brick!40!white, domain=1:7.5, variable=\x] + (1,0) -- plot({\x},{1/\x}) -- (7.5,0) -- cycle; + % Axis + \draw [thick, ->] (1,0) -- (1,1.2); + \draw [thick, ->] (0.5,0) -- (7.5,0); + \draw (1.0,-0.05) -- (1.0,0.05); \node [below, scale=0.7] at (1.0,-0.05) {1}; + \draw (2.0,-0.05) -- (2.0,0.05); \node [below, scale=0.7] at (2.0,-0.05) {2}; + \draw (3.0,-0.05) -- (3.0,0.05); \node [below, scale=0.7] at (3.0,-0.05) {3}; + \draw (4.0,-0.05) -- (4.0,0.05); \node [below, scale=0.7] at (4.0,-0.05) {4}; + \draw (5.0,-0.05) -- (5.0,0.05); \node [below, scale=0.7] at (5.0,-0.05) {5}; + \draw (6.0,-0.05) -- (6.0,0.05); \node [below, scale=0.7] at (6.0,-0.05) {6}; + \draw (7.0,-0.05) -- (7.0,0.05); \node [below, scale=0.7] at (7.0,-0.05) {7}; +\end{tikzpicture} +\caption{The area of the red region converges to the Euler–Mascheroni + constant..}\label{fig:gamma} +} +\end{figure} ## Computing the constant