From 8e131d3c3126e6166fa38f69ec76d14b2676f02a Mon Sep 17 00:00:00 2001 From: Mark Date: Sun, 30 Apr 2023 21:08:34 -0700 Subject: [PATCH] Added tikz orchard --- Advanced/Lattices/main.tex | 2 + Advanced/Lattices/orchard.png | Bin 118289 -> 0 bytes Advanced/Lattices/parts/2 orchard.tex | 83 +++++++++++++++++++++++++- 3 files changed, 82 insertions(+), 3 deletions(-) delete mode 100644 Advanced/Lattices/orchard.png diff --git a/Advanced/Lattices/main.tex b/Advanced/Lattices/main.tex index d3b6ff4..2b50fa9 100755 --- a/Advanced/Lattices/main.tex +++ b/Advanced/Lattices/main.tex @@ -5,6 +5,8 @@ singlenumbering ]{../../resources/ormc_handout} +\usepackage{ifthen} + %\usepackage{lua-visual-debug} \renewcommand{\arraystretch}{1.2} \begin{document} diff --git a/Advanced/Lattices/orchard.png b/Advanced/Lattices/orchard.png deleted file mode 100644 index 97f8e1930a67c3ec843022fb5b9b700cfa073ac2..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 118289 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zZr=wWe}RB#h%KSFK<;?3LVtg&w1mXD(=?7wY(n|nU4Ciz@ACG;qBxfjZrkPSyhihLJQl%!sf9g4HR8Qxs14o=VojE|2x-N zG)U@aus*#VoWuwlK%BI3DVT@YgM5HR>3l=wC|5_8wZso)hS1#Ub+MyIgQ^pTr{GUw z!tST;&JwY32mDr{6l zgPV{^0d7YK`D6gFRZ$4?Dm{HO+M{7iD^>kc;xcwsUlUotbv^j#o`9 zZ&aQ1@qek-I6D5f_B4IE|IbYVYP+xf@kf}ZWdF}-3CUVh?8kElahqG&!Czh6m5 g|Gzcn)4hI3^7cQam0)CA0tvi~^h|XtwH>hkA7gretpET3 diff --git a/Advanced/Lattices/parts/2 orchard.tex b/Advanced/Lattices/parts/2 orchard.tex index ecc3949..afe8af5 100644 --- a/Advanced/Lattices/parts/2 orchard.tex +++ b/Advanced/Lattices/parts/2 orchard.tex @@ -2,10 +2,87 @@ You are standing in the center of a circular orchard of integer radius R. A tree was planted each integer lattice point, and each has grown to the same radius $r$. If the radius is small enough, you will have a clear line of sight through the orchard in certain directions. If the radius is too large, there is no line of sight through the orchard in any direction. See the figure below: -\begin{center} - \includegraphics[width=0.5\linewidth]{orchard.png} -\end{center} +\begin{center} + \hfill + \begin{tikzpicture}[scale=0.4] + \draw[color=black, very thick] (0,0) circle (5); + + \draw[fill=black] (0,0) circle (0.2); + \draw [->, very thick](0,0) -- (0.7, 0.7); + \draw [->, very thick](0,0) -- (-0.7, 0.7); + + \foreach \x in {-4, ..., 4} { + \foreach \y in {-4, ..., 4} { + \ifthenelse{ + % Remove center + \( \x=0 \AND \y=0 \) \OR + % + % Remove corners + \( \x=4 \AND \y=-4 \) \OR + \( \x=4 \AND \y=4 \) \OR + \( \x=-4 \AND \y=4 \) \OR + \( \x=-4 \AND \y=-4 \) \OR + % + % Remove corner corners + \( \x=4 \AND \y=-3 \) \OR + \( \x=4 \AND \y=3 \) \OR + \( \x=-4 \AND \y=3 \) \OR + \( \x=-4 \AND \y=-3 \) \OR + \( \x=3 \AND \y=-4 \) \OR + \( \x=3 \AND \y=4 \) \OR + \( \x=-3 \AND \y=4 \) \OR + \( \x=-3 \AND \y=-4 \) + }{}{ + \draw[fill=cyan!60!green] (\x,\y) circle (0.4); + }}} + + \draw[fill=cyan!60!green] (0, 5) circle (0.4); + \draw[fill=cyan!60!green] (5, 0) circle (0.4); + \draw[fill=cyan!60!green] (0, -5) circle (0.4); + \draw[fill=cyan!60!green] (-5, 0) circle (0.4); + \end{tikzpicture} + \hfill + \begin{tikzpicture}[scale=0.4] + \draw[color=black, very thick] (0,0) circle (5); + + \draw[fill=black] (0,0) circle (0.2); + + \draw [->, very thick](0,0) -- (-5,3.7); + \draw [->, very thick](0,0) -- (5, 3.7); + + \foreach \x in {-4, ..., 4} { + \foreach \y in {-4, ..., 4} { + \ifthenelse{ + % Remove center + \( \x=0 \AND \y=0 \) \OR + % + % Remove corners + \( \x=4 \AND \y=-4 \) \OR + \( \x=4 \AND \y=4 \) \OR + \( \x=-4 \AND \y=4 \) \OR + \( \x=-4 \AND \y=-4 \) \OR + % + % Remove corner corners + \( \x=4 \AND \y=-3 \) \OR + \( \x=4 \AND \y=3 \) \OR + \( \x=-4 \AND \y=3 \) \OR + \( \x=-4 \AND \y=-3 \) \OR + \( \x=3 \AND \y=-4 \) \OR + \( \x=3 \AND \y=4 \) \OR + \( \x=-3 \AND \y=4 \) \OR + \( \x=-3 \AND \y=-4 \) + }{}{ + \draw[fill=cyan!60!green] (\x,\y) circle (0.2); + }}} + + \draw[fill=cyan!60!green] (0, 5) circle (0.2); + \draw[fill=cyan!60!green] (5, 0) circle (0.2); + \draw[fill=cyan!60!green] (0, -5) circle (0.2); + \draw[fill=cyan!60!green] (-5, 0) circle (0.2); + \end{tikzpicture} + \hfill ~ +\end{center} \problem{} Show that if $r < \frac{1}{\sqrt{R^2 + 1}}$, you have at least one directon with a clear line of sight. \\