From 179d06fd1e5b7455d986d12e7a7ccb59c8224ba6 Mon Sep 17 00:00:00 2001 From: Mark Date: Sat, 9 Dec 2023 18:19:12 -0800 Subject: [PATCH] Moved Proof techniques --- {Advanced => Misc}/Proof Techniques/main.tex | 0 .../Proof Techniques/parts/0 intro.tex | 0 .../parts/1 contradiction.tex | 0 .../Proof Techniques/parts/2 induction.tex | 0 Misc/Warm-Ups/snake.tex | 232 ++++++++++++++++++ 5 files changed, 232 insertions(+) rename {Advanced => Misc}/Proof Techniques/main.tex (100%) rename {Advanced => Misc}/Proof Techniques/parts/0 intro.tex (100%) rename {Advanced => Misc}/Proof Techniques/parts/1 contradiction.tex (100%) rename {Advanced => Misc}/Proof Techniques/parts/2 induction.tex (100%) create mode 100755 Misc/Warm-Ups/snake.tex diff --git a/Advanced/Proof Techniques/main.tex b/Misc/Proof Techniques/main.tex similarity index 100% rename from Advanced/Proof Techniques/main.tex rename to Misc/Proof Techniques/main.tex diff --git a/Advanced/Proof Techniques/parts/0 intro.tex b/Misc/Proof Techniques/parts/0 intro.tex similarity index 100% rename from Advanced/Proof Techniques/parts/0 intro.tex rename to Misc/Proof Techniques/parts/0 intro.tex diff --git a/Advanced/Proof Techniques/parts/1 contradiction.tex b/Misc/Proof Techniques/parts/1 contradiction.tex similarity index 100% rename from Advanced/Proof Techniques/parts/1 contradiction.tex rename to Misc/Proof Techniques/parts/1 contradiction.tex diff --git a/Advanced/Proof Techniques/parts/2 induction.tex b/Misc/Proof Techniques/parts/2 induction.tex similarity index 100% rename from Advanced/Proof Techniques/parts/2 induction.tex rename to Misc/Proof Techniques/parts/2 induction.tex diff --git a/Misc/Warm-Ups/snake.tex b/Misc/Warm-Ups/snake.tex new file mode 100755 index 0000000..50e812e --- /dev/null +++ b/Misc/Warm-Ups/snake.tex @@ -0,0 +1,232 @@ +\documentclass[ + solutions, + singlenumbering, + nopagenumber +]{../../resources/ormc_handout} +\usepackage{../../resources/macros} + +\usepackage{ifthen} + +\usetikzlibrary{arrows.meta} +\usetikzlibrary{shapes.geometric} +\usetikzlibrary{patterns} + +% We put nodes in a separate layer, so we can +% slightly overlap with paths for a perfect fit +\pgfdeclarelayer{nodes} +\pgfdeclarelayer{path} +\pgfsetlayers{main,nodes} + +% Layer settings +\tikzset{ + % Layer hack, lets us write + % later = * in scopes. + layer/.style = { + execute at begin scope={\pgfonlayer{#1}}, + execute at end scope={\endpgfonlayer} + }, + % + % Arrowhead tweak + >={Latex[ width=2mm, length=2mm ]}, + % + % Labels inside edges + label/.style = { + rectangle, + % For automatic red background in solutions + fill = \ORMCbgcolor, + draw = none, + rounded corners = 0mm + }, + % + % Nodes + main/.style = { + draw, + circle, + fill = white, + line width = 0.4mm, + text width = 5mm, + align = center + }, + accept/.style = { + draw, + circle, + fill = white, + double, + double distance = 0.5mm, + line width = 0.4mm, + text width = 5mm, + align = center + }, +} + + + +\title{Warm-Up: Snakes} +\subtitle{Prepared by \githref{Mark} on \today} + +\begin{document} + + \maketitle + \newcounter{mycounter} + \setcounter{mycounter}{0} + \newif\iftmp + + \begin{center} + \begin{tikzpicture}[scale = 0.6] + \begin{scope}[layer = nodes] + \foreach \r in {1,3,5,7,9} { + \foreach \i in {1,...,10} { + \pgfmathparse{Mod(\i-1,10)} + \let\x\pgfmathresult + \pgfmathparse{div(\i-1,10) + \r} + \let\y\pgfmathresult + \pgfmathparse{(\r-1)*10+\i} + \let\z\pgfmathresult + + \tmpfalse + \pgfmathapproxequalto{\z}{4} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{5} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{19} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{21} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{28} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{31} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{35} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{44} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{47} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{52} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{53} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{59} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{70} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{76} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{81} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{88} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{98} + \ifpgfmathcomparison\tmptrue + \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi + + \stepcounter{mycounter} + \iftmp + \node[accept] (\arabic{mycounter}) at (2*\x, 2*\y) { + $\pgfmathprintnumber{\z}$ + }; + \else + \node[main] (\arabic{mycounter}) at (2*\x, 2*\y) { + $\pgfmathprintnumber{\z}$ + }; + \fi + } + + \foreach \i in {1,...,10} { + \pgfmathparse{9 - Mod(\i-1,10)} + \let\x\pgfmathresult + \pgfmathparse{div(\i-1,10) + \r + 1} + \let\y\pgfmathresult + \pgfmathparse{\r*10+\i} + \let\z\pgfmathresult + + \tmpfalse + \pgfmathapproxequalto{\z}{4} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{5} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{19} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{21} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{28} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{31} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{35} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{44} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{47} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{52} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{53} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{59} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{70} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{76} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{81} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{88} + \ifpgfmathcomparison\tmptrue + \else\pgfmathapproxequalto{\z}{98} + \ifpgfmathcomparison\tmptrue + \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi + + \stepcounter{mycounter} + + \iftmp + \node[accept] (\arabic{mycounter}) at (2*\x, 2*\y) { + $\pgfmathprintnumber{\z}$ + }; + \else + \node[main] (\arabic{mycounter}) at (2*\x, 2*\y) { + $\pgfmathprintnumber{\z}$ + }; + \fi + } + } + \end{scope} + + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (4) -- +(1,0) -- +(1, 13) -- +(3, 13) -> (75); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (5) -- +(0,-1) -- +(1,-1) -- +(1,1) -- (15); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (19) -- +(1, 0) -- +(1, 5) -- + (-1, 5) -- (41); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (21) -- +(1, 0) -- +(1,-5) -- +(3, -5) -- (3); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (28) -- +(1,0) -- +(1,3) -- +(3,3) -- (50); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (31) -- +(1,0) -- +(1,-7) -- +(-3, -7) -- (8); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (35) -- +(-1,0) -- +(-1,11) -- (96); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (44) -- +(-1,0) -- +(-1,7) -- +(-3,7) -- (82); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (47) -- +(1,0) -- +(1,-3) -- +(5,-3) -- (30); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (52) -- +(-1, 0) -- +(-1, -1) -- +(-5,-1) -- +(-5,-5) -- +(-11,-5) -- (23); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (53) -- +(-1,0) -- +(-1,7) -- (94); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (59) -- +(-1, 0) -- +(-1,1) -- +(-3,1) -- +(-3,9) -- +(7, 9) -- (95); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (70) -- +(-1, 0) -- +(-1, 5) -- (91); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (76) -- +(-1, 0) -- +(-1,-1) -- +(-5,-1) -- +(-5,-5) -- +(-7,-5) -- (41); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (81) -- +(0, -1) -- +(3, -1) -- +(3, -3) -- (62); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (88) -- +(1, 0) -- +(1, -3) -- +(-1,-3) -- (67); + \draw[->, line width = 0.6mm, rounded corners = 2mm] + (98) -- +(0, 1.5) -- +(15.5, 1.5) -- +(15.5,-15) -- +(13, -15) -- (12); + \end{tikzpicture} + \end{center} + +\end{document} \ No newline at end of file