From a7540c29d4e973860d7cd50b4eede1eb6abb6cb7 Mon Sep 17 00:00:00 2001 From: Neeldhara Misra Date: Fri, 27 Mar 2026 11:17:09 +0000 Subject: [PATCH] Update on Overleaf. --- Fonts/Anek/AnekOdia-Bold.ttf | Bin 0 -> 170796 bytes Fonts/Anek/AnekOdia-Medium.ttf | Bin 0 -> 170080 bytes Fonts/Anek/AnekOdia-Regular.ttf | Bin 0 -> 170380 bytes Fonts/Anek/AnekOdia-SemiBold.ttf | Bin 0 -> 170404 bytes Fonts/Libre/LibreBaskerville-Bold.ttf | Bin 0 -> 112372 bytes Fonts/Libre/LibreBaskerville-BoldItalic.ttf | Bin 0 -> 121656 bytes Fonts/Libre/LibreBaskerville-Italic.ttf | Bin 0 -> 121392 bytes Fonts/Libre/LibreBaskerville-Medium.ttf | Bin 0 -> 112484 bytes Fonts/Libre/LibreBaskerville-MediumItalic.ttf | Bin 0 -> 121700 bytes Fonts/Libre/LibreBaskerville-Regular.ttf | Bin 0 -> 112336 bytes Fonts/NotoSans/NotoSans-Bold.ttf | Bin 0 -> 630964 bytes Fonts/NotoSans/NotoSans-BoldItalic.ttf | Bin 0 -> 644340 bytes Fonts/NotoSans/NotoSans-Italic.ttf | Bin 0 -> 642344 bytes Fonts/NotoSans/NotoSans-Medium.ttf | Bin 0 -> 631052 bytes Fonts/NotoSans/NotoSans-Regular.ttf | Bin 0 -> 629024 bytes Fonts/NotoSans/NotoSans-SemiBold.ttf | Bin 0 -> 631364 bytes Fonts/NotoSans/NotoSansMath-Regular.otf | Bin 0 -> 498408 bytes Fonts/NotoSans/NotoSansOriya-Bold.ttf | Bin 0 -> 155216 bytes Fonts/NotoSans/NotoSansOriya-Medium.ttf | Bin 0 -> 155148 bytes Fonts/NotoSans/NotoSansOriya-Regular.ttf | Bin 0 -> 154960 bytes Fonts/NotoSans/NotoSansOriya-SemiBold.ttf | Bin 0 -> 155176 bytes .../dejavu-sans-mono/DejaVuSansMono-Bold.ttf | Bin 0 -> 318392 bytes .../DejaVuSansMono-BoldOblique.ttf | Bin 0 -> 239876 bytes .../DejaVuSansMono-Oblique.ttf | Bin 0 -> 245948 bytes Fonts/dejavu-sans-mono/DejaVuSansMono.ttf | Bin 0 -> 335068 bytes cartography/cartography_lv_1_1.tex | 476 ++++++++++++++ cartography/grid_Orthographic.pdf | Bin 0 -> 8690 bytes cartography/rhumb_lines_PlateCarree.pdf | Bin 0 -> 28054 bytes cartography/world_map_Orthographic.pdf | Bin 0 -> 36025 bytes cartography/world_map_PlateCarree.pdf | Bin 0 -> 57407 bytes latex_instructions.txt | 10 + leelavati.cls | 61 ++ leelavati_defs.sty | 591 ++++++++++++++++++ rook/rooks-fighting.pdf | Bin 0 -> 37433 bytes rook/rooks-fighting.tex | 50 ++ 35 files changed, 1188 insertions(+) create mode 100644 Fonts/Anek/AnekOdia-Bold.ttf create mode 100644 Fonts/Anek/AnekOdia-Medium.ttf create mode 100644 Fonts/Anek/AnekOdia-Regular.ttf create mode 100644 Fonts/Anek/AnekOdia-SemiBold.ttf create mode 100644 Fonts/Libre/LibreBaskerville-Bold.ttf create mode 100644 Fonts/Libre/LibreBaskerville-BoldItalic.ttf create mode 100644 Fonts/Libre/LibreBaskerville-Italic.ttf create mode 100644 Fonts/Libre/LibreBaskerville-Medium.ttf create mode 100644 Fonts/Libre/LibreBaskerville-MediumItalic.ttf create mode 100644 Fonts/Libre/LibreBaskerville-Regular.ttf create mode 100644 Fonts/NotoSans/NotoSans-Bold.ttf create mode 100644 Fonts/NotoSans/NotoSans-BoldItalic.ttf create mode 100644 Fonts/NotoSans/NotoSans-Italic.ttf create mode 100644 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zW~OI)y8HiT_FdO;)GVAdIZYdO%v#i`EF6nA_-$4_Poz$%+u*BN^CXse!n_UYdKGgLQPO@AkeJ1O2e?;TaP{zv0JV!&$!b}miCIoyU_+UrW1kZ#!Zj9srw&)EHpl9*)ux9+1C zO4pQhmAK@2#xrHhLT@QjfQhq?#G!43GXg6h@N_b)d;03z_h9`0jLttU<*@S?esQjo literal 0 HcmV?d00001 diff --git a/cartography/cartography_lv_1_1.tex b/cartography/cartography_lv_1_1.tex new file mode 100644 index 0000000..e7dc915 --- /dev/null +++ b/cartography/cartography_lv_1_1.tex @@ -0,0 +1,476 @@ +% !TEX TS-program = xelatex +\documentclass{../leelavati} + +\begin{document} +\selectlanguage{odia} + +\title{\LARGE ମର୍କେଟର୍ ମାନଚିତ୍ରର କାହାଣୀ - ଭାଗ ୧ \vskip 0.04in \large The Story of the Mercator Map - Part 1} +\author{\AuthorDual{ସୌମ୍ୟଶାନ୍ତ ନାୟକ}{Soumyashant Nayak}} +\date{} +\maketitle + +\setstretch{1.2} +\begin{abstract} +For centuries, navigating the open ocean was a high-stakes challenge of geometry and survival. This article is the first of a two-part series which follows the transition from the usage of environmental cues to the mathematical precision of modern cartography. We look at the geometric challenges of flattening a round Earth onto a flat grid and why simple maps can lead sailors astray. Ultimately, it is a story of how the vastness of the sea forced us to invent the clever coordinate systems that organized our world. +\end{abstract} + +\setstretch{1.35} + +\section{ନୌଚାଳନାରେ ସଠିକ୍ ଅବସ୍ଥିତି ନିର୍ଣ୍ଣୟର ଜଟିଳତା} + +ଆଜିକାଲି ପକେଟ୍‌ରେ ଧରି ବୁଲୁଥିବା ଗୋଟିଏ ଛୋଟ ସ୍ମାର୍ଟଫୋନ୍ ଭିତରେ ହିଁ ଜିପିଏସ୍ (GPS) ଏବଂ ଗୁଗୁଲ୍ ମ୍ୟାପ୍ସ (Google Maps) ପରି ଡିଜିଟାଲ୍ ମାନଚିତ୍ର ରହୁଛି। ତେଣୁ ନୌଚାଳନା ଯେ ଦିନେ 'ସଠିକ୍ ଅବସ୍ଥିତି' ଜାଣିବା ଉପରେ ଆଧାରିତ ନଥିଲା, ସେକଥା ଭାବି ହୁଏ ନାହିଁ। ଅଥଳ ସମୁଦ୍ର ମଝିରେ ଥରେ କୂଳ ଆଖି ଆଗରୁ ହଜିଗଲା ପରେ, ନିଜର ସଠିକ୍ ଅବସ୍ଥିତି ଜାଣିବା ଇତିହାସର ଅଧିକାଂଶ ନାବିକଙ୍କ ପାଇଁ ପ୍ରାୟ ଅସମ୍ଭବ ଥିଲା। + +ଯଦିଓ ଦ୍ୱିତୀୟ ଶତାବ୍ଦୀରେ ଗ୍ରୀକ୍ ପଣ୍ଡିତ ଟଲେମି (Ptolemy) ତାଙ୍କ ପୁସ୍ତକ 'ଜିଓଗ୍ରାଫିଆ' (Geographia) ରେ ପୃଥିବୀକୁ ଅକ୍ଷାଂଶ (latitude) ଓ ଦ୍ରାଘିମାର (longitude) ଏକ ଗ୍ରିଡ୍ ଭାବେ ବର୍ଣ୍ଣନା କରିସାରିଥିଲେ, ତଥାପି ସେହି ଦୁଇଟି ସ୍ଥାନାଙ୍କ (coordinate) ମାଧ୍ୟମରେ ବାସ୍ତବ ଜଗତରେ ପଥ ଖୋଜିବା ପାଇଁ ମଣିଷକୁ ଆହୁରି ଅନେକ ଶତାବ୍ଦୀ ସଂଘର୍ଷ କରିବାକୁ ପଡ଼ିଥିଲା। + +ଏହା ବୁଦ୍ଧିମତାର ବିଫଳତା ନଥିଲା; ବରଂ ଏହା ପୃଥିବୀର ପ୍ରାକୃତିକ ସଂରଚନାର ଏକ ପରିଣାମ ଥିଲା। ପୃଥିବୀ ନିଜ ଅକ୍ଷ ଚାରିପଟେ ଆବର୍ତ୍ତନ କରୁଥିବାରୁ ଏହା ସ୍ୱାଭାବିକ ଭାବେ ଦୁଇଟି ମେରୁ (pole) ସୃଷ୍ଟି କରେ ଏବଂ ଏହି ଦୁଇ ମେରୁଠାରୁ ସମାନ ଦୂରତାରେ ରହିଥାଏ ବିଷୁବବୃତ୍ତ (equator)। ଏହି ଭୌଗୋଳିକ ତଥ୍ୟ ହିଁ ଅକ୍ଷାଂଶକୁ ବ୍ୟାଖ୍ୟା କରିବା ଏବଂ ମାପିବା ପାଇଁ ଏକ ସ୍ୱାଭାବିକ ଆଧାର ପ୍ରଦାନ କରେ। ସେଥିପାଇଁ ସୂର୍ଯ୍ୟ କିମ୍ବା ତାରାମାନଙ୍କ ସାହାଯ୍ୟରେ ଅକ୍ଷାଂଶ ଆକଳନ ସହଜରେ କରାଯାଇପାରୁଥିଲା (ସମସ୍ୟା \ref{artprob:altitude} ଦେଖ)। + +\begin{figure}[H] + \centering +\begin{tikzpicture} +\node[anchor=center, inner sep=0] (image) at (0,0) { +\includegraphics[width=.77\linewidth, angle=0]{grid_Orthographic.pdf} + }; +\def\r{2.64} +\coordinate (O) at (0,0); +\fill (O) circle (1.2pt) node[below] {$\textbf{O}$}; +\coordinate (N) at (0,\r); +\fill (N) circle (1.2pt) node[above left] {$N$}; +\draw[thick,dashed,->] (N) -- ++(0,1.0) +node[above] {ଧ୍ରୁବତାରା}; +\coordinate (S) at (0,-\r); +\fill (S) circle (1.2pt) node[below] {$S$}; + +\coordinate (P) at ($(O)+(25:\r)$); +\draw[dashed] (O) -- (P); +\coordinate (H) at ($(P)+(115:2cm)$); +\coordinate (PN) at ($(P) + (0,2.4)$); +\fill (P) circle (1.2pt) node[right] {$\textbf{P}$}; +\draw[thick,dashed,->] (P) -- (PN) node[above] {ଧ୍ରୁବତାରା}; +\draw[thick, ->] (P) -- (H) node[shift={(130:0.3)}] {ଉତ୍ତରଦିଗ}; +\draw[thick] (P) -- ++(-60:1cm); + +\foreach \a/\lbl in { + -60/{60^\circ S}, + -40/{40^\circ S}, + -20/{20^\circ S}, + 0/{0^\circ}, + 20/{20^\circ N}, + 40/{40^\circ N}, + 60/{60^\circ N} +}{ + \node[left] at ($(O)+(180-\a:\r)$) {$\lbl$}; +} + +\coordinate (E) at (\r,0); +\tkzMarkAngle[size=0.8, mark=none, arc=l](E,O,P) +\tkzLabelAngle[pos=1.2](E,O,P){$\phi$} + +\tkzMarkAngle[size=0.8, mark=none, arc=l](PN,P,H) +\tkzLabelAngle[pos=1.2](PN,P,H){$\psi$} + +\end{tikzpicture} + \caption{ଅବସ୍ଥିତି $P$ ଠାରେ ଉତ୍ତରଦିଗ ଓ ଧ୍ରୁବତାରାର ଦିଗ} + \label{fig:alt_lat} +\end{figure} + +\begin{artprobox} +ପ୍ରତିଛବି \ref{fig:alt_lat} ରେ, ଅକ୍ଷାଂଶ $\phi$ ର ସହାୟତାରେ $\psi$ କୋଣର ମାପ ନିର୍ଣ୍ଣୟ କର। +\end{artprobox} + +\begin{artprobox}[altitude] +ଧର, $P$ ପୃଥିବୀ ପୃଷ୍ଠରେ ତୁମ ଅବସ୍ଥିତିକୁ ସୂଚାଉଛି। ରାତିର ଆକାଶକୁ ନିରୀକ୍ଷଣ କରି ଏବଂ ସେକ୍ସଟାଣ୍ଟ (sextant) ପରି ଏକ କୋଣମାପକ ଯନ୍ତ୍ର ସାହାଯ୍ୟରେ କୋଣ $\psi$ ନିର୍ଣ୍ଣୟ କରିବା ପାଇଁ ଏକ କୌଶଳ ପ୍ରସ୍ତୁତ କର। ଉପରୋକ୍ତ ସମସ୍ୟାର ସମାଧାନକୁ ଭିତ୍ତି କରି ଓ $\psi$ ବ୍ୟବହାର କରି, ନିଜର ଅକ୍ଷାଂଶ ନିର୍ଣ୍ଣୟ କର। +\end{artprobox} +\vspace{-.1cm} + +\begin{figure}[H] + \centering +\begin{tikzpicture}[scale=.7] + +\coordinate (p) at (0,.7); +\node at (p) {\faStar}; + +\draw[black, dashed, thick] (p) -- (0,-2); +\node[left] at (0,-.3) {$\psi$}; +\node[above] at (0,.9) {ଧ୍ରୁବତାରା}; + +\node at (3.75,2.5) {ତାରାର}; +\node at (3.75,2) {ଅହୋରାତ୍ର ବୃତ୍ତ}; + +\tkzDrawArc[R, color=magHighlight, dashed, thick, ->](p, 1.5cm)(0, 330) +\coordinate (s1) at ($(p) + (-15:1.5cm)$); +\node[scale=.5] at (s1) {\faStar}; + +\tkzDrawArc[R, color=magHighlight, dashed, thick, ->](p, 3cm)(20, 240) +\tkzDrawArc[R, color=magHighlight, dashed, thick, ->](p, 3cm)(300, 370) +\coordinate (s1) at ($(p) + (15:3cm)$); +\node[scale=.5] at (s1) {\faStar}; + +\draw[magHighlight, line width=1pt] + (-4,-2.5) .. controls (0,-1.9) .. (4,-2.5); + + \node[scale=3.5, text=black!80] at (0,-2.2) {\faUser}; + +\end{tikzpicture} + \caption{ଧ୍ରୁବତାରାର କୌଣିକ ଉଚ୍ଚତା $\psi$} + \label{fig:pole_star_horizon} +\end{figure} +\vspace{-.2cm} + + +ବିଷୁବବୃତ୍ତ ଯେପରି ଅକ୍ଷାଂଶ ପାଇଁ ଏକ ପ୍ରାକୃତିକ ଆଧାର, ଦ୍ରାଘିମା ପାଇଁ ସେପରି କୌଣସି ସ୍ଵାଭାବିକ ଆରମ୍ଭ ବିନ୍ଦୁ (origin) ନାହିଁ। ଆଜି ଆମେ ବ୍ୟବହାର କରୁଥିବା 'ଗ୍ରୀନଉଇଚ୍ ମେରିଡିଆନ୍' (Greenwich Meridian) କେବଳ ଏକ ସର୍ବସମ୍ମତ ଇଚ୍ଛାଧୀନ ନିଷ୍ପତ୍ତି ମାତ୍ର। ଦ୍ରାଘିମା ନିର୍ଣ୍ଣୟ କରିବା ପାଇଁ ନିଜର ସ୍ଥାନୀୟ ସମୟକୁ (local time) ଏକ ନିର୍ଦ୍ଦିଷ୍ଟ ଆଧାର ଦ୍ରାଘିମାର (reference longitude) ସମୟ ସହିତ ତୁଳନା କରିବାକୁ ପଡ଼ିଥାଏ। ସାମୁଦ୍ରିକ କାଳମାପକର (marine chronometer) ଉଦ୍ଭାବନ ପୂର୍ବରୁ, ଦୋଳାୟମାନ ଜାହାଜରେ ସଠିକ୍ ସମୟ ରଖିବା ସମ୍ଭବ ନଥିଲା, ଯାହା ଫଳରେ ଦ୍ରାଘିମା ନିର୍ଣ୍ଣୟ କରିବା ଅସମ୍ଭବ ହୋଇପଡ଼ୁଥିଲା। + + +\begin{transtable} +ଅକ୍ଷାଂଶ & latitude & ମେରୁ & pole \\ +ଦ୍ରାଘିମା & longitude & ମାନଚିତ୍ର & map \\ +ବିଷୁବବୃତ୍ତ & equator & ଅକ୍ଷ & axis \\ +କାଳମାପକ & chronometer & ଆବର୍ତ୍ତନ & rotation\\ +ନୌଚାଳନା & navigation & ସ୍ଥାନାଙ୍କ & coordinate +\end{transtable} + +\section{ମାନଚିତ୍ର ବିହୀନ ପାରମ୍ପରିକ ନୌଚାଳନା} + +ଜଣେ ନାବିକ ନିଜର ଉତ୍ତର-ଦକ୍ଷିଣ ଅବସ୍ଥିତି ଜାଣିପାରୁଥିଲେ ମଧ୍ୟ, ପୂର୍ବ-ପଶ୍ଚିମ ଅବସ୍ଥିତିରେ ସବୁବେଳେ ଅନିଶ୍ଚିତତା ରହୁଥିଲା। +\begin{questionbox} +ଏହି ସମସ୍ୟା ସତ୍ତ୍ୱେ ଜାହାଜଗୁଡ଼ିକ ନିୟମିତ ଭାବେ ସମୁଦ୍ର ପାର ହେଉଥିଲେ; ଏହା କିପରି ସମ୍ଭବ ହେଉଥିଲା? +\end{questionbox} + +ମହାନଦୀର ମୁହାଣରୁ ଦକ୍ଷିଣ-ପୂର୍ବ ଏସିଆ ଅଭିମୁଖେ ଯାତ୍ରା କରୁଥିବା କଳିଙ୍ଗର ନାବିକମାନଙ୍କ କଥା ଚିନ୍ତା କରନ୍ତୁ। ସେମାନଙ୍କର ନୌଚାଳନା କୌଣସି ମାନଚିତ୍ର କିମ୍ବା ଅକ୍ଷାଂଶ-ଦ୍ରାଘିମାର ସ୍ଥାନାଙ୍କ ଗ୍ରିଡ୍ ଉପରେ ନିଜର ଅବସ୍ଥିତି ଚିହ୍ନଟ କରିବା ଉପରେ ନିର୍ଭର କରୁନଥିଲା। ବରଂ, ଏହା ପରିବେଶର ଏକ ଗଭୀର ବୁଝାମଣା ଉପରେ ଆଧାରିତ ଥିଲା। + +ସେମାନେ ମୌସୁମୀ ବାୟୁର ଗତିପଥକୁ ଅନୁସରଣ କରୁଥିଲେ, ଯାହା ଏକ ନିର୍ଦ୍ଦିଷ୍ଟ ସମୟ-ଚକ୍ର ଅନୁସାରେ ନିଜର ଦିଗ ପରିବର୍ତ୍ତନ କରିଥାଏ। ସମ୍ଭବ ହେଲେ ସେମାନେ ଉପକୂଳ ଅନୁସରଣ କରୁଥିଲେ, ଗୋଟିଏ ବନ୍ଦରରୁ ଅନ୍ୟ ବନ୍ଦରକୁ ଯାଉଥିଲେ ଏବଂ ଦ୍ୱୀପପୁଞ୍ଜଗୁଡ଼ିକୁ ପାହାଚ ଭାବରେ ବ୍ୟବହାର କରୁଥିଲେ। ସେମାନଙ୍କୁ ସମୁଦ୍ରରୁ ବିଭିନ୍ନ ସଙ୍କେତ ପଢ଼ିବାକୁ ପଡ଼ୁଥିଲା: ଯଥା ଲହରୀର ଦିଗ ବା ଗତି, ପକ୍ଷୀ ଓ ଜଳଜ ଉଦ୍ଭିଦମାନଙ୍କର ଉପସ୍ଥିତି, ସମୁଦ୍ର ପାଣିର ରଙ୍ଗରେ ପରିବର୍ତ୍ତନ ଏବଂ ପବନରେ ଭାସି ଆସୁଥିବା ସ୍ଥଳଭାଗର ବାସ୍ନା। + +କିନ୍ତୁ, ଯେତେବେଳେ ସମୁଦ୍ର ଯାତ୍ରାର ପରିସର ବୃଦ୍ଧି ପାଇଲା, ସେତେବେଳେ ପରିବେଶର ଏହି ସୂକ୍ଷ୍ମ ଅନୁଭବ ଏବଂ ପରୋକ୍ଷ ସଙ୍କେତ ସୀମିତ ହୋଇପଡ଼ିଲା। ଆନ୍ତଃ-ମହାସାଗରୀୟ ଯାତ୍ରାର ଅର୍ଥ ଥିଲା ସ୍ଥଳଭାଗ ନ ଦେଖି ସପ୍ତାହ ସପ୍ତାହ ଧରି ସମୁଦ୍ର ମଧ୍ୟରେ ରହିବା। ଏଠାରେ ପରିଚିତ ଚିହ୍ନ ଅପେକ୍ଷା ପଥ ନିର୍ଣ୍ଣୟ କରିବାର ଗାଣିତିକ ପଦ୍ଧତି ଅତ୍ୟାବଶ୍ୟକ ହୋଇପଡ଼ିଲା। କିନ୍ତୁ ଗଣିତର ପ୍ରୟୋଗ ପୂର୍ବରୁ ଆମକୁ ଏହା ବୁଝିବାକୁ ହେବ ଯେ ମାନଚିତ୍ର ପ୍ରକୃତରେ କିପରି ବିବର୍ତ୍ତିତ ହୋଇଥିଲା। + + +\section{ନୌଚାଳନା ପାଇଁ ବିଶ୍ୱ ମାନଚିତ୍ରର ସୃଷ୍ଟି} + +ମାନଚିତ୍ରର ଇତିହାସ ବହୁ ପୁରୁଣା ହେଲେ ମଧ୍ୟ, ଦୀର୍ଘ ସମୟ ପର୍ଯ୍ୟନ୍ତ ଏହାର ନୌଚାଳନା ସହିତ କୌଣସି ସିଧାସଳଖ ସମ୍ପର୍କ ନଥିଲା। ପ୍ରାଥମିକ ସମୟର ମାନଚିତ୍ରଗୁଡ଼ିକ, ଯେପରିକି ବାବିଲୋନୀୟ ମୃଣ୍ମୟ ଫଳକ (Babylonian clay tablets) କିମ୍ବା ମଧ୍ୟଯୁଗୀୟ 'ମାପ୍ପା ମୁଣ୍ଡି' (Mappa Mundi), ବାସ୍ତବିକ ପଥ ପ୍ରଦର୍ଶନ ପାଇଁ ଉଦ୍ଦିଷ୍ଟ ନ ହୋଇ ମୁଖ୍ୟତଃ ପ୍ରତୀକାତ୍ମକ ଓ ସୂଚନାତ୍ମକ ଥିଲେ। ମୌଳିକ ଭାବେ, ସେଗୁଡ଼ିକ କେବଳ ସ୍ଥାନୀୟ ସମ୍ପର୍କକୁ ଦର୍ଶାଉଥିଲେ - ଯେପରିକି ପାହାଡ଼ରୁ ବାହାରୁଥିବା ନଦୀ, ରାସ୍ତା ଦ୍ୱାରା ସଂଯୁକ୍ତ ସହର କିମ୍ବା ଧାର୍ମିକ ସ୍ଥଳ। ଏଥିରେ ଦିଗ ବା ଦୂରତାର ସଠିକତା ଅପେକ୍ଷା ସାଙ୍କେତିକ ସୂଚନାକୁ ଅଧିକ ଗୁରୁତ୍ୱ ଦିଆଯାଉଥିଲା। + +କାଳକ୍ରମେ ମାନଚିତ୍ରଗୁଡ଼ିକ ଅଧିକ ବିସ୍ତୃତ ହେଲେ। ସେତେବେଳେ ମଧ୍ୟ ସେଗୁଡ଼ିକ ମୁଖ୍ୟତଃ ସ୍ଥାନୀୟ ଅଞ୍ଚଳ ମଧ୍ୟରେ ସୀମିତ ଥିଲା: ଯେପରିକି ବନ୍ଦରର ନକ୍ସା, ନଦୀ ଅବବାହିକା (river basin) କିମ୍ବା ସ୍ଥଳପଥ। ସେତେବେଳେ ବିଶ୍ୱସ୍ତରୀୟ ଜ୍ୟାମିତିର ବିଶେଷ ଆବଶ୍ୟକତା ନଥିଲା। ବାରମ୍ବାର ନୌଚାଳନା କରି ନାବିକମାନେ ଏକ ଉପକୂଳର ସଠିକ୍ ମାନଚିତ୍ର ପ୍ରସ୍ତୁତ କରିପାରୁଥିଲେ। ମାତ୍ର ମହାସାଗର ପରି ବିଶାଳ ପରିସର ପାଇଁ ଏତିକି ଜ୍ଞାନ ଯଥେଷ୍ଟ ନଥିଲା। + +୧୪୯୨ ମସିହାରେ, ସ୍ପେନ୍‌ର (Spain) ରାଜକୀୟ ଅନୁଦାନରେ ଖ୍ରୀଷ୍ଟୋଫର୍ କଲମ୍ବସ୍ (Christopher Columbus) ଏକ ଦୁଃସାହସିକ ଆବିଷ୍କାର ଅଭିଯାନ ଆରମ୍ଭ କରିଥିଲେ। ପୃଥିବୀର ପରିଧିକୁ ନେଇ ପ୍ରଚଳିତ ବିଭିନ୍ନ ମତବାଦ ମଧ୍ୟରେ କଲମ୍ବସ୍‌ଙ୍କ ଗଣନା ତ୍ରୁଟିପୂର୍ଣ୍ଣ ଥିଲା; ସେ କେବଳ ପୃଥିବୀର ଆକାରକୁ ଛୋଟ ମାପିନଥିଲେ, ବରଂ ଏସିଆର ପରିସରକୁ ମଧ୍ୟ ଅତ୍ୟଧିକ ବଡ଼ ବୋଲି ଅନୁମାନ କରିଥିଲେ। ନିଜର ଏହି ଭୁଲ୍ ଗଣନା ଯୋଗୁଁ, କଲମ୍ବସ୍ ୟୁରୋପରୁ ପଶ୍ଚିମ ଦିଗ ଦେଇ ଏସିଆ ପହଞ୍ଚିବାର ପ୍ରକୃତ ଦୂରତାକୁ ଯଥେଷ୍ଟ କମ୍ କରି ଆକଳନ କରିଥିଲେ। ସେ ବିଶ୍ୱାସ କରୁଥିଲେ ଯେ ଆଟଲାଣ୍ଟିକ୍ ମହାସାଗରରେ ପଶ୍ଚିମାଭିମୁଖୀ ଯାତ୍ରାର ଅଳ୍ପ କିଛି ସପ୍ତାହ ମଧ୍ୟରେ ସେ ସିଧାସଳଖ ଏସିଆର ଉପକୂଳରେ ପହଞ୍ଚିଯିବେ। କୌଣସି ସଠିକ୍ ମାନଚିତ୍ର ବିନା, ସେ କେବଳ କମ୍ପାସ୍ ଏବଂ ଜାହାଜର ଗତି ଓ ଦିଗର ଏକ ଆନୁମାନିକ ହିସାବ (dead reckoning) ରଖି ସୌଭାଗ୍ୟବଶତଃ ଏକ ଭୂଖଣ୍ଡରେ ପହଞ୍ଚିଥିଲେ, ଯାହାକୁ ଆଜି ଆମେ ଆମେରିକା ଭାବେ ଜାଣୁ। କିନ୍ତୁ ମୃତ୍ୟୁ ପର୍ଯ୍ୟନ୍ତ ସେ ଏହି ଭୂଖଣ୍ଡକୁ ଏସିଆ ବୋଲି ଭାବି ଭ୍ରମରେ ରହିଲେ। + +ପଞ୍ଚଦଶ ଶତାବ୍ଦୀର ଶେଷ ଭାଗର ଏହି ଅନ୍ୱେଷଣ, ଷୋଡ଼ଶ ଶତାବ୍ଦୀ ବେଳକୁ ଏକ ବିଶାଳ ବାଣିଜ୍ୟିକ ସମ୍ଭାବନାରେ ପରିଣତ ହେଲା। ଆଟଲାଣ୍ଟିକ୍ ମହାସାଗରର ଅଜ୍ଞାତ ଜଳରାଶି ମଧ୍ୟକୁ ପ୍ରବେଶ କରୁଥିବା ୟୁରୋପୀୟ ନାବିକମାନଙ୍କ ନିମନ୍ତେ ପୂର୍ବରୁ ବ୍ୟବହୃତ ଉପକୂଳବର୍ତ୍ତୀ ମାନଚିତ୍ରଗୁଡ଼ିକ ଖୋଲା ସମୁଦ୍ରରେ ନିରର୍ଥକ ପ୍ରମାଣିତ ହେଲା। ସେଠାରେ ହଜାର ହଜାର ମାଇଲ୍ ପର୍ଯ୍ୟନ୍ତ କୌଣସି ସ୍ଥଳଭାଗର ସଙ୍କେତ ନଥିଲା କିମ୍ବା ପଥ ପ୍ରଦର୍ଶନ ପାଇଁ ପରିଚିତ ପକ୍ଷୀଙ୍କ ଦେଖା ମଧ୍ୟ ମିଳୁନଥିଲା। + +ଫଳସ୍ୱରୂପ, 'ଟ୍ରାନ୍ସ-ଆଟଲାଣ୍ଟିକ୍' ଯାତ୍ରାକୁ ନିରାପଦ, ନିର୍ଭରଯୋଗ୍ୟ ଓ ପୁନରାବୃତ୍ତି ଯୋଗ୍ୟ କରିବା ପାଇଁ ମାନଚିତ୍ରର ପରିକଳ୍ପନାକୁ ସ୍ଥାନୀୟ ବର୍ଣ୍ଣନା ପରିସରରୁ ବାହାର କରି ଏକ ଜ୍ୟାମିତି ଆଧାରିତ ବିଶ୍ୱ-ମାନଚିତ୍ରରେ (global map) ରୂପାନ୍ତରିତ କରିବା ଅପରିହାର୍ଯ୍ୟ ହୋଇପଡ଼ିଲା। ନାବିକମାନଙ୍କୁ ଏବେ ଏମିତି ଏକ ମାନଚିତ୍ର ଦରକାର ଥିଲା, ଯେଉଁଠାରେ ପ୍ରତ୍ୟେକ ବିନ୍ଦୁର ଏକ ସୁନିଶ୍ଚିତ ସ୍ଥାନାଙ୍କ ରହିବା ସହ ପ୍ରତ୍ୟେକ ରେଖା ସମୁଦ୍ରର ବାସ୍ତବିକ ଦିଗ ସହିତ ମେଳ ଖାଇବ। + +ତେବେ, ଏହି ଗାଣିତିକ ଆବଶ୍ୟକତା ପୂରଣ କରିବାକୁ ହେଲେ ଆମକୁ ସର୍ବପ୍ରଥମେ ପୃଥିବୀର ଗୋଲାକାର ଜ୍ୟାମିତି ଏବଂ ସମତଳ କାଗଜ ମଧ୍ୟରେ ଥିବା ଏକ ମୌଳିକ ଦ୍ୱନ୍ଦ୍ୱକୁ ବୁଝିବାକୁ ହେବ। + +\section{ସମାନ ବ୍ୟବଧାନର ଗ୍ରିଡ୍‌ରେ ଜ୍ୟାମିତିକ ବିକୃତି} + + +ଧର, ଆମେ ଏକ ସମତଳ କାଗଜରେ ସମଗ୍ର ପୃଥିବୀର ମାନଚିତ୍ର ଆଙ୍କିବା ପାଇଁ ଅକ୍ଷାଂଶ ଓ ଦ୍ରାଘିମାକୁ ସମାନ ବ୍ୟବଧାନରେ କିଛି ଭୂସମାନ୍ତର (horizontal) ଓ ଭୂଲମ୍ବ (vertical) ରେଖା ଦ୍ୱାରା ଚିହ୍ନିତ କଲୁ (ପ୍ରତିଛବି \ref{fig:uniform_grid_map} ଦେଖ)। +\begin{figure}[H] + \centering \includegraphics[width=1.0\linewidth]{world_map_PlateCarree.pdf} + \caption{ସମାନ ବ୍ୟବଧାନର ଗ୍ରିଡ୍‌ } + \label{fig:uniform_grid_map} +\end{figure} + +ପ୍ରଥମ ଦେଖାରେ ଏହା ଯୁକ୍ତିଯୁକ୍ତ ମନେହୁଏ, କାରଣ ଅକ୍ଷାଂଶ ଓ ଦ୍ରାଘିମା ହେଉଛି କେବଳ କୋଣ (angle) ଏବଂ କୋଣୀୟ ମାପ ସବୁ ସ୍ଥାନରେ ସମାନ ମନେହୁଏ। କିନ୍ତୁ ଏହି ସରଳ ଗ୍ରିଡ୍ ଚିତ୍ରଣ, ବାସ୍ତବିକ ଦୂରତା ଓ ଆକୃତିକୁ ନେଇ କିଛି ଭ୍ରାନ୍ତ ଧାରଣା ସୃଷ୍ଟି କରେ। + +ବର୍ତ୍ତମାନ ପୃଥିବୀକୁ $R$ ବ୍ୟାସାର୍ଦ୍ଧ ବିଶିଷ୍ଟ ଏକ ଗୋଲକ ଭାବରେ ବିଚାର କର। ବିଷୁବବୃତ୍ତରୁ ଉତ୍ତରକୁ $\phi$ କୋଣରେ ଥିବା ଏକ ଅକ୍ଷାଂଶ-ବୃତ୍ତର ବ୍ୟାସାର୍ଦ୍ଧ ହେଉଛି, $R \cos \phi$। ତେଣୁ ସେହି ଅକ୍ଷାଂଶ-ବୃତ୍ତର ଲମ୍ବ ହେଉଛି, $2 \pi R \cos \phi $ (ପ୍ରତିଛବି \ref{fig:rad_change} ଦେଖ)। + +\begin{figure} +\centering +\begin{tikzpicture}[scale=1] + +% Parameters +\def\R{2.5} % Earth radius +\def\phi{40} % Latitude angle (for drawing only) + +% Center +\coordinate (O) at (0,0); +\coordinate (N) at (0,\R); +\coordinate (S) at (0,-\R); + +\fill (N) circle (1.2pt); +\fill (S) circle (1.2pt); + +% Earth +\draw[thick] (O) circle (\R); +\draw[dashed] (N)--(S); + +% Equator +\draw (-\R,0) -- (\R,0); +\node[below left] at (0,0) {ବିଷୁବବୃତ୍ତ}; + +% Latitude line +\draw + (0,{\R*sin(\phi)}) -- + ({\R*cos(\phi)},{\R*sin(\phi)}); + +% Radius to latitude +\draw (O) -- ({\R*cos(\phi)},{\R*sin(\phi)}); + +% Horizontal radius (R cos phi) +\draw + (0,{ \R*sin(\phi) }) -- ({\R*cos(\phi)},{\R*sin(\phi)}); +\node[above] at ({0.4*\R*cos(\phi)},{\R*sin(\phi)}) + {$R\cos φ$}; + +% Radius R +\draw[dashed] (O) -- ({\R*cos(\phi)},{\R*sin(\phi)}); +\node at (1.2,1.2) {$R$}; + +% Angle phi +\draw (0,0) ++(0:0.6) arc (0:\phi:0.6); +\node[right] at (0.5,0.25) {$φ$}; + +% Poles +\node[above] at (0,\R) {ଉତ୍ତର ମେରୁ}; +\node[below] at (0,-\R) {ଦକ୍ଷିଣ ମେରୁ}; + +\end{tikzpicture} +\caption{ଅକ୍ଷାଂଶ-ବୃତ୍ତର ବ୍ୟାସାର୍ଦ୍ଧ ପରିବର୍ତ୍ତନ} +\label{fig:rad_change} +\end{figure} + +\begin{table}[h] +\centering +\renewcommand{\arraystretch}{2} +\begin{tabular}{|c|c|c|} +\hline +\textbf{ଅକ୍ଷାଂଶ ($\phi$) } & $\bm{\cos} (\phi)$ & \textbf{ଅକ୍ଷାଂଶ-ବୃତ୍ତର ଲମ୍ବ}\\ +\hline +$0^\circ$ & $1$ & $6.28 \times R$ \\ +\hline +$30^\circ$ & $\frac{\sqrt{3}}{2}$ & $5.44 \times R$ \\ +\hline +$45^\circ$ & $\frac{1}{\sqrt{2}}$ & $4.44 \times R$ \\ +\hline +$60^\circ$ & $\frac{1}{2}$ & $3.14 \times R$ \\ +\hline +$90^\circ$ & 0 & $0$ \\ +\hline +\end{tabular} +\caption{କିଛି ସାଧାରଣ କୋଣ ପାଇଁ ଅକ୍ଷାଂଶ-ବୃତ୍ତର ଲମ୍ବ} +\label{tab:cos_val} +\end{table} + + +ଟେବୁଲ୍‌ \ref{tab:cos_val} ରୁ ସ୍ପଷ୍ଟ ହେଉଛି ଯେ, ପୃଥିବୀର ମେରୁ ଆଡ଼କୁ ଗଲେ ଅକ୍ଷାଂଶ-ବୃତ୍ତଗୁଡ଼ିକର ପରିଧି କ୍ରମଶଃ ହ୍ରାସ ପାଇଥାଏ। ଫଳସ୍ୱରୂପ, ସମାନ ଅକ୍ଷାଂଶରେ ଅବସ୍ଥିତ ଏକ ନିର୍ଦ୍ଦିଷ୍ଟ ଦ୍ରାଘିମା-ପାର୍ଥକ୍ୟ (longitude difference) ବିଶିଷ୍ଟ ଦୁଇଟି ସ୍ଥାନର ବାସ୍ତବ ପୂର୍ବ-ପଶ୍ଚିମ ଦୂରତା ମଧ୍ୟ ସେହି ଅନୁପାତରେ ସଙ୍କୁଚିତ ହୋଇଯାଏ। ଉଦାହରଣ ସ୍ୱରୂପ, ବିଷୁବବୃତ୍ତ ଉପରେ ଏକ ନିର୍ଦ୍ଦିଷ୍ଟ ଦ୍ରାଘିମା-ପାର୍ଥକ୍ୟ ଥିବା ଦୁଇଟି ବିନ୍ଦୁ ମଧ୍ୟରେ ଯେତିକି ବାସ୍ତବ ଦୂରତା ଥାଏ, $45^{\circ}$ ଅକ୍ଷାଂଶରେ ତାହାର ମାତ୍ର $71 \%$ ହୁଏ (ଯେହେତୁ $\cos 45^{\circ} \approx 0.71$)। କିନ୍ତୁ ଆମ ସମତଳ ଗ୍ରିଡ୍‌ରେ ଏହି ଦୂରତାକୁ ସବୁ ସ୍ଥାନରେ ସମାନ ଦେଖାଯାଉଥିବାରୁ, ବାସ୍ତବିକତା ଏବଂ ମାନଚିତ୍ର ମଧ୍ୟରେ ଏକ ବଡ଼ ଧରଣର ଅସଙ୍ଗତି ସୃଷ୍ଟି ହୁଏ। + +ଏହାକୁ ବୁଝିବା ପାଇଁ କଳ୍ପନା କର ଯେ ତୁମେ ଅକ୍ଷାଂଶ $\phi$ ରେ ପୃଥିବୀର ଏକ ଅତ୍ୟଣୁ (infinitesimal) ଅଞ୍ଚଳକୁ ବଡ଼ କରି ଦେଖୁଛ, ଯାହାର ବିସ୍ତାର ହେଉଛି Δϕ ଅକ୍ଷାଂଶ-ପାର୍ଥକ୍ୟ ଏବଂ Δλ ଦ୍ରାଘିମା-ପାର୍ଥକ୍ୟ (ଏଠାରେ ରେଡିଆନ୍ ଏକକ ବ୍ୟବହୃତ)। ତେବେ ଗୋଲକ ଉପରେ ଏହାର ଉତ୍ତର-ଦକ୍ଷିଣ ପାର୍ଶ୍ୱର ପ୍ରକୃତ ଦୂରତା $R \Delta \phi$ ହୋଇଥିବା ବେଳେ ପୂର୍ବ-ପଶ୍ଚିମ ପାର୍ଶ୍ୱର ପ୍ରକୃତ ଦୂରତା ହେଉଛି $R \cos \phi \Delta \lambda$ (ପ୍ରତିଛବି \ref{fig:dist_change} ଦେଖ)। + +\begin{figure}[H] + \centering +\begin{tikzpicture}[scale=1] + +\begin{scope} +\node at (-2,2.3) {\textbf{Earth}}; +\coordinate (O) at (0,0); +\draw[thick] (O) ++(20:2.2) + arc (20:160:2.2); +% Latitude line +\draw[dashed] (-1.8,1.0) -- (1.8,1.0); +\node[left] at (-2,1.0) {$\phi$}; + +% Local patch +\draw[fill=magHighlight!40] (-0.6,0.8) rectangle (0.6,1.3); + +% North–South arrow +\draw[<->] (-.8,0.65) -- (-.8,1.5); +\node[left] at (-.8,.8) {$R\; \Delta \phi$}; + +\draw[<->] (.8,0.65) -- (.8,1.5); +\node[right] at (.8,.8) {N-S}; + +\draw[<->] (-0.6,0.5) -- (0.6,0.5); +\node[below] at (0,0.5) {$R\cos\phi \; \Delta \lambda$}; + +\draw[<->] (-0.6,1.5) -- (0.6,1.5); +\node[above] at (0,1.5) {E-W}; + +\end{scope} + +\begin{scope}[yshift=-3cm] + +\node at (-2,2.5) {\textbf{Map}}; + +\draw[thick] (-2.2,.75) -- (-2.2,2.2)--(2.2,2.2) -- (2.2,.75); + +% Latitude line +\draw[dashed] (-2.2,1.0) -- (2.2,1.0); +\node[left] at (-2.2,1.0) {$\phi$}; + +% Distorted patch +\draw[fill=magHighlight!50] (-.75,.8) rectangle (.75,1.3); + +% North–South arrow +\draw[<->] (-.95,0.65) -- (-.95,1.5); +\node[left] at (-.95,.8) {$\Delta \phi$}; + +\draw[<->] (.95,0.65) -- (.95,1.5); +\node[right] at (.95,.8) {N-S}; + +\draw[<->] (-0.75,0.5) -- (0.75,0.5); +\node[below] at (0,0.5) {$\Delta \lambda$}; + +\draw[<->] (-0.75,1.5) -- (0.75,1.5); +\node[above] at (0,1.5) {E-W}; + +\end{scope} + +\end{tikzpicture} +\caption{ମାନଚିତ୍ରରେ ପୂର୍ବ-ପଶ୍ଚିମ ଦୂରତାର ପ୍ରସାରଣ} +\label{fig:dist_change} +\end{figure} + +ଆମ ମାନଚିତ୍ରରେ ଆୟତକ୍ଷେତ୍ରର ପାର୍ଶ୍ୱଗୁଡ଼ିକ $\Delta \phi$ ଏବଂ $\Delta \lambda$ ସହିତ ସମାନୁପାତିକ ଅଟେ। ଫଳସ୍ୱରୂପ, ଭୂପୃଷ୍ଠର ପ୍ରକୃତ ଦୂରତା ଅନୁପାତ ତୁଳନାରେ ଏହି ଆୟତକ୍ଷେତ୍ରଟି ମାନଚିତ୍ରରେ ଭୂସମାନ୍ତର ଭାବେ $\frac{1}{\cos \phi} = \sec \phi$ ଗୁଣ ପ୍ରସାରିତ ହୋଇ ଦେଖାଯାଏ। + + + +ଏହି ଅସମାନ ପ୍ରସାରଣ ଯୋଗୁଁ ମାନଚିତ୍ରର ଉପଯୋଗିତା କ୍ଷେତ୍ରରେ କିଛି ପ୍ରତିବନ୍ଧକ ସୃଷ୍ଟି ହୁଏ। ଯଦି ପୃଥିବୀ ପୃଷ୍ଠରେ ଏକ ନିର୍ଦ୍ଦିଷ୍ଟ ପଥ ଉତ୍ତର ଦିଗ ସହିତ $\theta$ କୋଣ ସୃଷ୍ଟି କରେ, ତେବେ ଆମ ମାନଚିତ୍ରରେ ସେହି ପଥଟି ଏକ ଭିନ୍ନ କୋଣ $\theta '$ ସୃଷ୍ଟି କରିବ। ଏହି ଦୁଇ କୋଣ ମଧ୍ୟରେ ସମ୍ପର୍କ ହେଉଛି, +\begin{equation} +\label{eqn:non_conform} +\tan \theta '= \sec \phi \tan \theta \quad \text{।} +\end{equation} + +\begin{figure}[H] + \centering +\begin{tikzpicture} +\begin{scope} +\coordinate (P) at (0,0); +\fill (P) circle (2pt) node[left] {$P$}; +% North direction +\draw[thick,->] (P) -- (0,1); +\node[above] at (0,1) {$N$}; + +% Arbitrary direction +\draw[thick,->] (P) -- (1.3,1); +\node[above] at (1.2,1) {$D$}; + +\draw[thick,dashed] (0,1) -- (1.2,1); + +% Angle marking +\draw (0,0) ++(90:0.5) arc (90:35:0.5); +\node[above] at (0.35,0.4) {$\theta$}; + +\draw[<->] (-.5,0) -- (-.5,1); +\node[left] at (-.5,.5) {$N-S$}; + +\draw[<->] (0,-.5) -- (1.3,-0.5); +\node[below] at (.65,-0.5) {$R\cos\phi \; \Delta \lambda$}; +\end{scope} + +\begin{scope}[xshift = 2.5cm] +\coordinate (P) at (0,0); +\fill (P) circle (2pt) node[left] {$P$}; +% North direction +\draw[thick,->] (P) -- (0,1); +\node[above] at (0,1) {$N$}; + +% Arbitrary direction +\draw[thick,->] (P) -- (1.5,1); +\node[above] at (1.4,1) {$D'$}; + +\draw[thick,dashed] (0,1) -- (1.5,1); + +% Angle marking +\draw (0,0) ++(90:0.5) arc (90:35:0.5); +\node[above] at (0.35,0.4) {$\theta'$}; + +\draw[<->] (0,-.5) -- (1.5,-0.5); +\node[below] at (.65,-0.5) {$R \; \Delta \lambda$}; +\end{scope} +\end{tikzpicture} + \caption{ମାନଚିତ୍ରରେ ଅନୁକୋଣତାର କ୍ଷୟ} + \label{fig:non_conform} +\end{figure} + +ଏଠାରେ ଉଲ୍ଲେଖଯୋଗ୍ୟ ଯେ, ଯଦିଓ ଏହି ମାନଚିତ୍ରରେ ଯେକୌଣସି ଦୁଇଟି ରେଖା ମଧ୍ୟରେ ଥିବା କୋଣର ବିକୃତି ଘଟିଥାଏ, ଏହି ସୂତ୍ରଟି କେବଳ ଉତ୍ତର ଦିଗ ସହିତ ସମ୍ପର୍କିତ କୋଣର ପରିବର୍ତ୍ତନକୁ ପ୍ରକାଶ କରେ। + + +\begin{artprobox} +ପ୍ରତିଛବି \ref{fig:non_conform} ସାହାଯ୍ୟରେ ସମୀକରଣ \ref{eqn:non_conform} କୁ ପ୍ରମାଣ କର। +\end{artprobox} + +ବିଷୁବବୃତ୍ତ ($\phi = 0^{\circ}$, $\cos 0^{\circ} = 1$) ବ୍ୟତୀତ ଅନ୍ୟ ସବୁ ସ୍ଥାନରେ କୋଣଗୁଡ଼ିକରେ ଏହି ପରିବର୍ତ୍ତନ ଘଟିଥାଏ। ଆମ ମାନଚିତ୍ରର ଗ୍ରିଡ୍ ଦେଖିବାକୁ ପରିଷ୍କାର ମନେହୁଏ ସତ, କିନ୍ତୁ ଏହାର ଅନୁକୋଣତା (conformality) ନ ଥାଏ - ଅର୍ଥାତ୍ ମାନଚିତ୍ରରେ ଦର୍ଶାଯାଇଥିବା ଦୁଇଟି ରେଖା ମଧ୍ୟରେ ଥିବା କୋଣ ପ୍ରାୟତଃ ବାସ୍ତବିକ କୋଣ ସହ ସମାନ ରହେ ନାହିଁ। + +\begin{transtable} +ଗୋଲକ & sphere & ଅତ୍ୟଣୁ & infinitesimal\\ +ବିକୃତି & distortion & ପରିଧି & circumference \\ +ବ୍ୟାସାର୍ଦ୍ଧ & radius & ବର୍ଗକ୍ଷେତ୍ର & square \\ +ବୃତ୍ତ & circle & ଆୟତକ୍ଷେତ୍ର & rectangle \\ +ଉପବୃତ୍ତ & ellipse & ଅନୁକୋଣତା & conformality +\end{transtable} + +କୋଣଗୁଡ଼ିକୁ ଅକ୍ଷୁଣ୍ଣ ରଖିବା ଏବଂ ଅତ୍ୟଣୁ ସ୍ତରର ଆକୃତିଗୁଡ଼ିକୁ ବଜାୟ ରଖିବା\textemdash ଏ ଉଭୟ ଓତପ୍ରୋତ ଭାବେ ଜଡ଼ିତ। ଯଦି ମାନଚିତ୍ରରେ ପରସ୍ପରକୁ ଛେଦ କରୁଥିବା ରେଖାଗୁଡ଼ିକ ମଧ୍ୟରେ ଥିବା କୋଣ ଅପରିବର୍ତ୍ତିତ ରହେ, ତେବେ ପ୍ରତ୍ୟେକ ଅତ୍ୟଣୁ ସ୍ତରର ଆକୃତି ଏକ ସମାନୁପାତିକ ପରିମାପରେ ବଜାୟ ରହିଥାଏ। ଏହାର ବିପରୀତ ପକ୍ଷରେ, ଯଦି ଅନୁକୋଣତା (conformality) ବଜାୟ ନରହେ, ତେବେ ଅତ୍ୟଣୁ ସ୍ତରରେ ବାସ୍ତବିକ ଆକୃତିଗୁଡ଼ିକ ବିକୃତ ହୋଇଯାଏ। + +ଏହାକୁ ଅଧିକ ସ୍ପଷ୍ଟ ଭାବେ କହିଲେ: ଏକ ଉପାଦେୟ ମାନଚିତ୍ରରେ ଛୋଟ ବର୍ଗକ୍ଷେତ୍ରଗୁଡ଼ିକ (square) ଆକାରରେ ବଡ଼ ବା ଛୋଟ ହୋଇପାରନ୍ତି, କିନ୍ତୁ ସେଗୁଡ଼ିକ ପ୍ରସାରିତ ହୋଇ ଆୟତକ୍ଷେତ୍ର (rectangle) ରେ ପରିଣତ ନ ହୋଇ ବର୍ଗକ୍ଷେତ୍ର ହୋଇ ହିଁ ରହନ୍ତି। ସେହିପରି, ଛୋଟ ବୃତ୍ତଗୁଡ଼ିକ (circle) ବିକୃତ ହୋଇ ଉପବୃତ୍ତର (ellipse) ରୂପ ନେବା ପରିବର୍ତ୍ତେ ନିଜର ବୃତ୍ତାକାର ବଜାୟ ରଖନ୍ତି। + +ଆମର ଏହି ସରଳ ଗ୍ରିଡ୍‌ରେ ଅନୁକୋଣତା ନଷ୍ଟ ହେଉଥିବାରୁ, ଏହା କେବଳ ଦୂରତାକୁ ନୁହେଁ, ବରଂ ସ୍ଥାନୀୟ ସ୍ତରରେ ମାନଚିତ୍ରର ପ୍ରତିଟି ଆକୃତିକୁ ମଧ୍ୟ ବିଗାଡ଼ି ଦିଏ। + +\section{ମର୍କେଟର୍‌ଙ୍କ ଦୃଷ୍ଟିକୋଣ} + +ଦ୍ୱାଦଶ-ତ୍ରୟୋଦଶ ଶତାବ୍ଦୀ ବେଳକୁ ସାମୁଦ୍ରିକ ଯାତ୍ରାରେ ଚୁମ୍ବକୀୟ କମ୍ପାସର (magnetic compass) ବ୍ୟବହାର ନାବିକମାନଙ୍କୁ ଏକ ନୂତନ ସାମର୍ଥ୍ୟ ପ୍ରଦାନ କଲା। ଆକାଶ ମେଘାଚ୍ଛନ୍ନ ହେଉ କିମ୍ବା ଜାହାଜ କୂଳରୁ ବହୁ ଦୂରକୁ ଚାଲିଯାଉ—ଉତ୍ତର ଦିଗର ଏହି ଅଚ୍ୟୁତ ସୂଚନା ନାବିକମାନଙ୍କୁ ନିଜ ଯାତ୍ରାପଥ ସମ୍ପର୍କରେ ଏକ ସ୍ପଷ୍ଟ ଧାରଣା ଦେଇପାରିଲା। + +ସେ ସମୟରେ ନାବିକମାନେ ମୁଖ୍ୟତଃ 'ଡେଡ୍ ରେକନିଂ' (dead reckoning) ପଦ୍ଧତି ଉପରେ ନିର୍ଭର କରୁଥିଲେ। ପ୍ରତି ମୁହୂର୍ତ୍ତରେ ନିଜର ସଠିକ୍ ଭୌଗୋଳିକ ଅବସ୍ଥିତି ଗଣନା କରିବା ପରିବର୍ତ୍ତେ, ସେମାନେ କେବଳ କମ୍ପାସର ଦିଗକୁ ଅକ୍ଷୁଣ୍ଣ ରଖିବା ଉପରେ ଗୁରୁତ୍ୱ ଦେଉଥିଲେ। ଯାତ୍ରା ଆରମ୍ଭ କରିବା ପୂର୍ବରୁ ସାମୁଦ୍ରିକ ମାନଚିତ୍ର ବା ନିର୍ଦ୍ଦେଶାବଳୀ ସହାୟତାରେ ଦୁଇଟି ବନ୍ଦର ମଧ୍ୟରେ ଏକ ସ୍ଥିର କୋଣ (constant bearing) ନିର୍ଦ୍ଧାରଣ କରାଯାଉଥିଲା ଏବଂ ସେହି ଅନୁସାରେ ଜାହାଜ ଚଲାଯାଉଥିଲା। + +ତେବେ ଏଠାରେ ଏକ ଗାଣିତିକ ଜଟିଳତା ଥିଲା। ଯଦି ଏକ ଜାହାଜ କମ୍ପାସର କଣ୍ଟା ସହିତ ଏକ ସ୍ଥିର କୋଣ ବଜାୟ ରଖି ଅଗ୍ରସର ହୁଏ, ତେବେ ତାହା ପୃଥିବୀ ପୃଷ୍ଠରେ ଏକ କୁଣ୍ଡଳୀ (spiral) ସଦୃଶ ପଥ ଅନୁସରଣ କରେ (ପ୍ରତିଛବି \ref{fig:straight_vs_rhumb} ଦେଖ) । ଏହି ବକ୍ର ପଥକୁ 'ରମ୍ବ ଲାଇନ' (Rhumb line) ବା 'ଲକ୍ସୋଡ୍ରୋମ୍' (Loxodrome) କୁହାଯାଏ, ଯାହା ପ୍ରତ୍ୟେକ ଦ୍ରାଘିମା ରେଖାକୁ ଏକ ସମାନ କୋଣରେ ଛେଦ କରିଥାଏ। ସେ ସମୟର ପାରମ୍ପରିକ ସମତଳ ମାନଚିତ୍ରଗୁଡ଼ିକରେ ଏହି ବକ୍ର ଗତିପଥକୁ ସଠିକ୍ ଭାବେ ଚିତ୍ରଣ କରିବା କଷ୍ଟକର ଥିଲା। + +ଷୋଡ଼ଶ ଶତାବ୍ଦୀର ବିଶିଷ୍ଟ ମାନଚିତ୍ରକାର ଜେରାର୍ଡସ୍ ମର୍କେଟର୍ (Gerardus Mercator) ଏହି ସମସ୍ୟାକୁ 'ଯାତ୍ରା-ପୂର୍ବ ଯୋଜନା' ଦୃଷ୍ଟିକୋଣରୁ ବିଚାର କଲେ। ୧୫୬୯ ମସିହାରେ ସେ ଏକ ଅଭିନବ ‘ମାନଚିତ୍ର ଅଭିକ୍ଷେପ’ (map projection) ଉଦ୍ଭାବନ କଲେ, ଯାହାର ମୁଖ୍ୟ ଲକ୍ଷ୍ୟ ଥିଲା ମାନଚିତ୍ର ଓ କମ୍ପାସ ମଧ୍ୟରେ ଥିବା ଏହି ଗାଣିତିକ ଅସଙ୍ଗତିକୁ ଦୂର କରିବା। + +ମର୍କେଟର୍ ଚାହୁଁଥିଲେ ଯେ କମ୍ପାସର ସ୍ଥିର ଦିଗଗୁଡ଼ିକ ମାନଚିତ୍ରରେ ବକ୍ର ରେଖା ପରିବର୍ତ୍ତେ ସରଳ ରେଖା ଭାବରେ ଦେଖାଯାଉ। ଏହାଦ୍ୱାରା ଜଣେ ନାବିକ କେବଳ ଏକ ମାପକାଠି (ruler) ସାହାଯ୍ୟରେ ଦୁଇଟି ବିନ୍ଦୁ ମଧ୍ୟରେ ସରଳ ରେଖା ଟାଣି, ଏକ କୋଣମାପକ (protractor) ସାହାଯ୍ୟରେ ଉତ୍ତର ଦିଗ ସହିତ ଏହାର କୋଣ ମାପି, ନିଜର ପଥ ନିରୂପଣ କରିପାରିବେ ଏବଂ ଯାତ୍ରା ସମୟରେ କୌଣସି ଜଟିଳ ଗଣନା ନକରି ସେହି ସ୍ଥିର ଦିଗରେ ଗତି କରି ଗନ୍ତବ୍ୟ ସ୍ଥଳରେ ପହଞ୍ଚି ପାରିବେ। + +\begin{figure}[H] + \centering + \begin{tikzpicture} + % 1. Place the image as a node + \node[inner sep=0pt, anchor=south west] (map) at (0,0) + {\includegraphics[width=1\linewidth]{rhumb_lines_PlateCarree.pdf}}; + + \node[below, font=\odiafont] at (3.8, 2.9) {ରମ୍ବ ଲାଇନ}; + + \node[font=\odiafont] at (5.5, 3.25) {\textmb{ଆଫ୍ରିକା}}; + + \node[font=\odiafont] at (2.22, 1.9) {\textmb{ଦକ୍ଷିଣ}}; + \node[font=\odiafont] at (2.22, 1.5) {\textmb{ଆମେରିକା}}; + + \end{tikzpicture} + \caption{ଆମ ମାନଚିତ୍ରରେ ରମ୍ବ ଲାଇନ ବନାମ ସରଳ ରେଖା} + \label{fig:straight_vs_rhumb} +\end{figure} + +\begin{questionbox} +କିନ୍ତୁ ମର୍କେଟର୍ ଏହି ଅସମ୍ଭବକୁ ସମ୍ଭବ କଲେ କିପରି? କେଉଁ ଗାଣିତିକ ଯାଦୁ ବଳରେ ସେ ମାନଚିତ୍ରକୁ ଏପରି ଭାବେ ବଦଳାଇଲେ, ଯାହା ଫଳରେ ବକ୍ର ପଥଗୁଡ଼ିକ ସରଳ ରେଖାରେ ପରିଣତ ହୋଇଗଲେ? +\end{questionbox} + +ଏହି ଜ୍ୟାମିତିକ ରହସ୍ୟ ଏବଂ ମର୍କେଟର୍ ମାନଚିତ୍ରର ଗାଣିତିକ ସୂତ୍ର ଜାଣିବା ପାଇଁ ପଢ଼ନ୍ତୁ ଏହି ପ୍ରବନ୍ଧର ପରବର୍ତ୍ତୀ ଭାଗ (ଆସନ୍ତା ମାର୍ଚ୍ଚ ୨୦୨୬ ସଂଖ୍ୟାରେ ପ୍ରକାଶ ପାଇବ)। + + +\begin{transtable} +ଅଭିକ୍ଷେପ & projection & ମାପକାଠି & ruler \\ +ସରଳ ରେଖା & straight line & କୋଣମାପକ & protractor \\ +ବକ୍ର ରେଖା & curve & କୁଣ୍ଡଳୀ & spiral +\end{transtable} + + +{\small +\vskip 0.05in +\affiliation{Assistant Professor, Statistics \& Mathematics Unit, Indian Statistical Institute, Bangalore} +\email{soumyashant@leelavati.in} +} + +\vskip 0.2in + +\begin{leelabox}[leelaAccent, title=Kaprekar's Curious Procedure] +\noindent +Begin with any four-digit number whose digits are not all equal. + +\medskip +Rearrange its digits to form the largest possible number and the smallest possible number, and subtract the smaller from the larger. + +\medskip +Apply the same procedure repeatedly to the result you obtain. + +\medskip +No matter which number you start with, something unexpected happens in the end. +Try to discover what it is. + +\medskip +This is called \textsb{Kaprekar's routine}, named after Dattatreya Ramchandra Kaprekar (ଦତ୍ତାତ୍ରେୟ ରାମଚନ୍ଦ୍ର କାପ୍ରେକର). Despite having no formal postgraduate training and working as a schoolteacher, he published extensively and became well known in recreational mathematics circles. +\end{leelabox} + + +\end{document} diff --git a/cartography/grid_Orthographic.pdf b/cartography/grid_Orthographic.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0507661262e460e08a7c729625d9a9af189d5766 GIT binary patch literal 8690 zcmZ`gSByScYr{3Z5+^E5MdxeA0jJDigrU?CL;b(pyKX^g^2u~05#RIbwb-= zArgPM%6?c?1FQ`e4H5k#plgH0qA_j|u}hZ}YH-g6<>=-B5&x6LxZ4?^u@DQOt&$2b z3fd0~fvULzBOw1o#XnIEa_1l8!2kUKmvdiEk3j>|{V_gNAMNGtjj;os=W>3azZM$h zXoGb313JQhFB}0Ak`Vq2?f|C%JQ`5%1(Ez?Km|89cff;RCjav|F6qC{PZRCtfV~HS z|JhT;(FJ&72vo%dI0hxOojVGBIk*=VgSK%c^~>JQR!b1msE$~z!_|hhj!7souB#6{ zxB`-Yg~u5|@b!&=wtb@oa}oorocm7OnOu!<;r?rx4}~Eor@KE-pU?i>F_HUucvNeB z|Hs{5XWMe^3!5V+yA+jsXCgn($NAesdhg#qAw3zl?pPo;(K*?NjwBxcItK|&$o<^k z+&s3HyCCTJPGNbrIBv3aTDmUQlghLkc0bBkJ+_jn@^e6JrtjAN2HTOjRqInCOU0=b 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zDa?f+bpj`f>I6cDUxGlzScM3`I)K)276suIc8HP`3U90+t-}m0yy<{}Ff*gW1xJ*x z0Rn_NFomPSLNJ`!QPIlZvhYaOg4MwsgkGfhtzSGz8+w!TUX3s--Kd^nr}k!E4-+T*fD)UJtJEBdBds(@Bn=Q z3aANZ6G;0)BZq4cD*jE-1bpy>wR-_5vVr~_zQ3O*vKd=UUrfB{Oec}Fw8cCV%w_oyK+a|mz#BjO2NEU@;N^pSmBC66{}A@D45#97W20mk0O=SR zb*wIh3IZ}pmjV*`Xc~XK@MeRd@6Y0r>+Qh8#E?_(}+~ h#R|3$NEbjubWY>(nOwdQf;g2%p%FAS&1}sH{|B0N!|wn9 literal 0 HcmV?d00001 diff --git a/latex_instructions.txt b/latex_instructions.txt new file mode 100644 index 0000000..8283a33 --- /dev/null +++ b/latex_instructions.txt @@ -0,0 +1,10 @@ + +1. As long as you respect the folder structure, everything should work fine. Otherwise, remember that, in Latex, the path is always relative to the .tex file, not .cls file. So, you should set the correct relative paths to font from CLS (../../Fonts/...). + +2. If you want to compile from multiple places, Give absolute paths to fonts. Something like, /Users/.../Fonts/.. + +3. When importing cls file in tex file, remember to either keep them in the same folder, and do \documentclass{leelavati}. Otherwise, give the right relative path to the CLS, like \documentclass{../leelavati} in the current structure. + +4. We have done some Latex magic so that you do not have to keep writing \begin{english} \end{english}, or \begin{odia} \end{odia} to switch between English and Odia. However, as a result, using other fonts becomes an issue. Like, constructing the chessboard in the rooks-fighting.tex file. So, you would need to use \XeTeXinterchartokenstate=0 for those special cases. A small price to pay in our opinion :) + +5. \setstretch{} sets the line spacing, with the recommended values of 1.1 to 1.2 for english and 1.25 to 1.35 for Odia. \ No newline at end of file diff --git a/leelavati.cls b/leelavati.cls new file mode 100644 index 0000000..eaff867 --- /dev/null +++ b/leelavati.cls @@ -0,0 +1,61 @@ +% leelavati.cls — Author class (XeLaTeX, KOMA-Script) +% (MODULARIZED VERSION) +\NeedsTeXFormat{LaTeX2e} +\ProvidesClass{leelavati}[2025/12/08 v1.1 leelavati Author Class (Modular)] + +% ------------------------------- +% Engine guard + base class options +% ------------------------------- +\RequirePackage{iftex} +\ifXeTeX\else + \ClassError{leelavati}{This class requires XeLaTeX}{Use xelatex to compile.} +\fi + +% ------------------------------- +% Core packages (ONLY those needed for the engine/structure) +% ------------------------------- + +% Pass any user options through to scrbook +\DeclareOption*{\PassOptionsToClass{\CurrentOption}{scrbook}} +% Defaults (user options still win) - Uses KOMA-Script paper size format +\PassOptionsToClass{10pt,twocolumn,oneside,openany,titlepage=false}{scrbook} +\ProcessOptions\relax + +% Load KOMA base class and activate KOMA-native layout +\LoadClass{scrbook} + +\usepackage[paperwidth=18cm, paperheight=24cm, left=1.25cm, right=1.25cm, top=1.7cm, bottom=1.9cm, footskip=30pt]{geometry} + +% ------------------------------- +% Load External Definitions (The best practice!) +% ------------------------------- +\RequirePackage{../leelavati_defs} +% ------------------------------- +% Hyperref last (essential) +% ------------------------------- +\RequirePackage[hidelinks]{hyperref} + +\makeatletter +\renewcommand{\maketitle}{% + \stepcounter{chapter} % Keep your article numbering consistent + + \twocolumn[ + \vspace*{0.0em} + % 1. Typeset the Title using the internal \@title + {\centering + \par + \setkomafont{title}{\anekfont\color{magHighlight}\Large\sbseries\selectfont} + \usekomafont{title}\@title\par + \vspace{0.2cm} + } + + % 2. Typeset the Author using the internal \@author + {\centering + \normalsize \@author\par + \vspace{0.2in} + } + ]% + \phantomsection +} +\makeatother +\endinput \ No newline at end of file diff --git a/leelavati_defs.sty b/leelavati_defs.sty new file mode 100644 index 0000000..24a1acc --- /dev/null +++ b/leelavati_defs.sty @@ -0,0 +1,591 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{leelavati_defs}[2025/12/08 v1.0 Leelavati Shared Definitions] + +% ------------------------------- +% 1. Requirements for Definitions +% ------------------------------- +% Packages needed by commands defined *within* this file. +\RequirePackage{booktabs} +\RequirePackage{amsthm, amssymb} +\RequirePackage{array} +\RequirePackage{ucharclasses} +\RequirePackage{tikz} +\RequirePackage{tkz-euclide} +\RequirePackage{microtype} +\usetikzlibrary{calc,patterns,intersections,through, decorations, decorations.fractals, arrows.meta} +\RequirePackage[dvipsnames,svgnames,table]{xcolor} +\RequirePackage[nodisplayskipstretch]{setspace} %nodisplayskipstretch keeps space above and below math equations constant, without stretch +\RequirePackage{tcolorbox} +\tcbuselibrary{breakable,skins} +\RequirePackage{fontawesome5} +\RequirePackage{needspace} +\RequirePackage{polyglossia} % For language setup commands +\RequirePackage{fontspec} % For font commands +\RequirePackage{mathtools} +\RequirePackage{unicode-math} +\RequirePackage{graphicx} +\RequirePackage{subcaption} +\RequirePackage{float} +\RequirePackage{microtype} +\setlength{\emergencystretch}{2em} +\RequirePackage{wrapfig} +\RequirePackage{caption} +\RequirePackage{scrlayer-scrpage} +\RequirePackage{chessboard} +\RequirePackage{xskak} +\RequirePackage[normalem]{ulem} +\RequirePackage{bm} +\RequirePackage{tfrupee} + + +% ------------------------------- +% 2. Colors and Constants +% ------------------------------- +%\definecolor{magHighlight}{HTML}{00AEEF} % Duotone CYAN +%\definecolor{magHighlight}{HTML}{FF00FF} % Duotone MAGENTA +\definecolor{magHighlight}{HTML}{005F99} % Duotone format ready + + +\definecolor{indigo}{RGB}{0,0,120} +\newcommand{\sbseries}{\fontseries{sb}\selectfont} +\newcommand{\mbseries}{\fontseries{mb}\selectfont} + +\DeclareTextFontCommand{\textsb}{\sbseries} +\DeclareTextFontCommand{\textmb}{\mbseries} + +% ------------------------------- +% 3. Languages and Fonts +% ------------------------------- +\setmainlanguage{english} +\setotherlanguage[numerals=odia,changecounternumbering=true]{odia} + +\newcommand*\LeelaFontPath{../Fonts/NotoSans/} +\newcommand*\LeelaHeaderFontPath{../Fonts/Anek/} +\newcommand*\DejavuFontsPath{../Fonts/dejavu-sans-mono/} +\newcommand*\LibreFontsPath{../Fonts/Libre/} + +%change math env to noto sans as well +\setmathfont[Path=\LeelaFontPath,Extension=.otf]{NotoSansMath-Regular} +\setmonofont[Path=\DejavuFontsPath,Extension=.ttf,UprightFont=*,BoldFont=*-Bold,ItalicFont=*-Oblique,BoldItalicFont=*-BoldOblique]{DejaVuSansMono} + +\setmainfont[Path=\LeelaFontPath, Extension=.ttf,UprightFont=*-Regular, BoldFont=*-Bold,ItalicFont=*-Italic, BoldItalicFont=*-BoldItalic,FontFace={mb}{n}{Font={*-Medium}},FontFace={sb}{n}{*-SemiBold}]{NotoSans} + +\newfontfamily\englishfont[Path=\LeelaFontPath, Extension=.ttf,UprightFont=*-Regular, BoldFont=*-Bold,ItalicFont=*-Italic, BoldItalicFont=*-BoldItalic,FontFace={mb}{n}{Font={*-Medium}}, FontFace={sb}{n}{*-SemiBold}]{NotoSans} + +\newfontfamily\dispatchfont[Path=\LibreFontsPath,Extension=.ttf,UprightFont=*-Regular, BoldFont=*-Bold,ItalicFont=*-Italic, BoldItalicFont=*-BoldItalic,FontFace={mb}{n}{Font={*-Medium}}]{LibreBaskerville} + +%add FakeSlant=0.12 later to imitate italics +\newfontfamily\odiafont[Path=\LeelaFontPath, Extension=.ttf, Script=Odia, Mapping=odianumerals,UprightFont=*-Regular, BoldFont=*-Bold,ItalicFont=*-Regular, BoldItalicFont=*-Bold,FontFace={mb}{n}{Font={*-Medium}}, FontFace={sb}{n}{*-SemiBold}]{NotoSansOriya} + +\newfontfamily\odiafontsf[Path=\LeelaFontPath, Extension=.ttf, Script=Odia, UprightFont=*-Regular, BoldFont=*-Bold,ItalicFont=*-Regular, BoldItalicFont=*-Bold, FontFace={mb}{n}{Font={*-Medium}}, FontFace={sb}{n}{*-SemiBold}]{NotoSansOriya} + +\newfontfamily\odiafonttt[Path=\LeelaFontPath, Extension=.ttf, Script=Odia,UprightFont=*-Regular, BoldFont=*-Bold,ItalicFont=*-Regular, BoldItalicFont=*-Bold, FontFace={mb}{n}{Font={*-Medium}}, FontFace={sb}{n}{*-SemiBold}]{NotoSansOriya} + +\newfontfamily\anekfont[Path=\LeelaHeaderFontPath, Extension=.ttf, Script=Odia, Mapping=odianumerals,UprightFont=*-Regular, BoldFont=*-Bold, FontFace={mb}{n}{Font={*-Medium}}, FontFace={sb}{n}{*-SemiBold}]{AnekOdia} + +% Convenience & Auto Switching +\DeclareRobustCommand{\textodia}[1]{{\odiafont #1}} +\newcommand{\textodialang}[1]{\bgroup\selectlanguage{odia}#1\egroup} +\setDefaultTransitions{\englishfont}{} +\setTransitionsFor{Oriya}{\odiafont}{\englishfont} + +% ------------------------------- +% 4. Sectioning & Heading Fonts (KOMA-native) +% ------------------------------- +\setkomafont{chapter}{\XeTeXinterchartokenstate=0\anekfont\color{magHighlight}\large\sbseries\selectfont} + +% For Sections +\setkomafont{section}{% + \XeTeXinterchartokenstate=0% + \anekfont% + \color{magHighlight}% + \normalsize% + \fontseries{sb}\selectfont% <-- Use the series switch directly +} + +\RedeclareSectionCommand[beforeskip=.1\baselineskip,afterskip=.1\baselineskip]{section} +\RedeclareSectionCommand[beforeskip=.1\baselineskip,afterskip=.1\baselineskip]{subsection} +\RedeclareSectionCommand[beforeskip=.1\baselineskip,afterskip=0.0\baselineskip]{subsubsection} + +\newcommand{\en}[1]{{\englishfont #1}} +\newcommand{\od}[1]{{\odiafont #1}} + + +% ------------------------------- +% 5. Spacing & Typographic Robustness +% ------------------------------- +\setlength{\parskip}{0.4em} +\setlength{\parindent}{0pt} + +\RequirePackage{etoolbox} + +% Column separation must stay here +\setlength{\columnsep}{6mm} + +\makeatletter +\newtoks\leela@everydisplay +\leela@everydisplay=\everydisplay +\everydisplay{% + \the\leela@everydisplay + \setlength{\parskip}{0pt}% + \setlength{\baselineskip}{\normalbaselineskip}% + \abovedisplayskip=3pt plus 2pt minus 2pt + \belowdisplayskip=3pt plus 2pt minus 2pt + \abovedisplayshortskip=1pt plus 1pt minus 1pt + \belowdisplayshortskip=1pt plus 1pt minus 1pt +} +\makeatother + +\AtBeginDocument{% + % Permissive settings for non-hyphenating Odia text + \pretolerance=2000 \tolerance=6000 \emergencystretch=2em \hyphenpenalty=200 \exhyphenpenalty=100 \widowpenalty=10000 \clubpenalty=10000 \righthyphenmin=2 + \hfuzz=0.5pt \vfuzz=5pt \hbadness=10000 \vbadness=10000 + \lineskiplimit=-2pt + \lineskip=0pt%0.6ex + \XeTeXuseglyphmetrics=1\relax + % float hygiene (2-col) + \setcounter{topnumber}{2} + \setcounter{totalnumber}{3} + \renewcommand{\topfraction}{0.9} + \renewcommand{\textfraction}{0.07} + \renewcommand{\floatpagefraction}{0.8} + \setcounter{dbltopnumber}{2} + \renewcommand{\dbltopfraction}{0.9} + \renewcommand{\dblfloatpagefraction}{0.8} +} + +% ------------------------------- +% 6. Localized Numerals in counters (Relies on polyglossia) +% ------------------------------- +\makeatletter +\renewcommand{\thepage}{\localnumeral*{page}} +\renewcommand{\thesection}{\localnumeral*{section}} +\renewcommand{\thesubsection}{\thesection.\localnumeral*{subsection}} +\renewcommand{\thesubsubsection}{\thesubsection.\localnumeral*{subsubsection}} +\renewcommand{\thefigure}{\localnumeral*{figure}} +\renewcommand{\thetable}{\localnumeral*{table}} +\renewcommand{\theequation}{\localnumeral*{equation}} +\renewcommand{\theenumi}{\localnumeral*{enumi}} +\renewcommand{\theenumii}{\localnumeral*{enumii}} +\renewcommand{\theenumiii}{\localnumeral*{enumiii}} +\renewcommand{\theenumiv}{\localnumeral*{enumiv}} +\renewcommand{\thefootnote}{\localnumeral*{footnote}} +\makeatother + +% ------------------------------- +% 7. Tcolorbox and Caption Styles +% ------------------------------- +\tcbset{ + leela/.style={ + enhanced, + breakable, + boxrule=0.8pt, + arc=1mm, + colback=white, + colframe=black!20, + % Title Styling for default (Non-Accent) + colbacktitle=white, % Background of the title bar + coltitle=black, % Color of the title text + fonttitle={\XeTeXinterchartokenstate=0\anekfont\large\sbseries}, % Removed \color{white} + left=3pt, right=3pt, top=5pt, bottom=5pt, + center title, + before skip=8pt, after skip=8pt + }, + leelaAccent/.style={ + colback=magHighlight!10, + colframe=magHighlight, + % Override title colors for the Accent version + colbacktitle=magHighlight, + coltitle=white, + center title, + before skip=8pt, after skip=8pt + } +} + +\newtcolorbox{leelabox}[1][]{leela,#1} +\newtcolorbox{leelaauthor}[1][]{leela,colback=black!3,colframe=black!25,#1} + +\DeclareCaptionFont{leelaMB}{\sbseries} +\DeclareCaptionFont{leelaHL}{\color{magHighlight}} +\DeclareCaptionFont{leelaSmall}{\small} +\captionsetup{font=small,labelfont = {leelaHL,leelaMB}, labelsep=colon, textfont = leelaSmall, position = bottom,labelsep = colon,aboveskip = 6pt,belowskip = 0pt} + +% ------------------------------- +% 8. Footer Definition +% ------------------------------- +\newcommand{\JournalName}{Leelavati $\;\;\bullet\;\;$ ଲୀଳାବତୀ} +\newsavebox{\leelaFooterBox} +\tikzset{ + konark/.style ={draw=black!100, fill=black!60}, + footerwave/.style={draw=black!100, line width=1pt, smooth}, + footerline/.style={draw=black!100, line width=1pt, smooth} +} +\AtBeginDocument{% + \sbox{\leelaFooterBox}{% + \begin{tikzpicture}[x=1pt,y=1pt,baseline=0] + \pgfmathsetlengthmacro{\HalfTW}{0.5*\textwidth} + \def\Yline{0} + \useasboundingbox (-\HalfTW,-5) rectangle (\HalfTW,5); + \begin{scope}[xshift=-12] + \draw[konark, even odd rule] (0,0) circle (10) (0,0) circle (8); + \draw[konark] (0,0) circle (3); + \foreach \x in {0,...,7}{ + \draw[konark] (22.5+45*\x:10) circle (1); + \draw[konark, rotate=45*\x] (0,0)--(3:10)--(10,0)--(-3:10)--cycle; + } + \end{scope} + \begin{scope}[xshift=12] + \draw[konark, even odd rule] (0,0) circle (10) (0,0) circle (8); + \draw[konark] (0,0) circle (3); + \foreach \x in {0,...,7}{ + \draw[konark] (22.5+45*\x:10) circle (1); + \draw[konark, rotate=45*\x] (0,0)--(3:10)--(10,0)--(-3:10)--cycle; + } + \end{scope} + \draw[footerwave,domain=-60:0,variable=\t,samples=60] + plot({\t-25},{ 10*exp(\t/30)*sin(-15*(\t))}); + \draw[footerwave,domain=0:60,variable=\t,samples=60] + plot({\t+25},{ 10*exp(-\t/30)*sin( 15*(\t))}); + \draw[footerline] (-\HalfTW,\Yline) -- (-85,\Yline); + \draw[footerline] (\HalfTW,\Yline) -- (85,\Yline); + \end{tikzpicture}% + }% +} +\newcommand{\footerlogo}{\raisebox{4mm}[0pt][0pt]{\usebox{\leelaFooterBox}}} + +\clearpairofpagestyles +\setkomafont{pagefoot}{\normalfont\sffamily\upshape} +\newcommand{\footerfont}{\fontsize{8}{10}\selectfont} + +\cfoot*{\footerlogo} +\ifoot*{\footerfont\textsf{\textbf{\JournalName}}} +\ofoot*{\footerfont\bfseries \pagemark} + +\makeatletter +\pretocmd{\@maketitle}{\vspace*{1cm}}{}{} +\makeatother + +\pagestyle{scrheadings} +\KOMAoptions{headsepline=false,footsepline=false} + + +% ------------------------------- +% 9. Author and Content Helpers +% ------------------------------- +\DeclareRobustCommand{\AuthorDual}[2]{% + \par % Ensure we are in a new paragraph + \noindent + % Create a box spanning the full line width to center its contents + \makebox[\textwidth][c]{% + \kern -1mm + % 1. LEFT NAME: Put in a zero-width box aligned to the Right (r). + % This pushes the text to the LEFT of the center point. + \makebox[0pt][r]{% + % Use a parbox to allow wrapping if the name is long + \parbox{0.45\linewidth}{\raggedleft\odiafont\color{magHighlight}\bfseries #1}% + \hspace{4mm}% The gap between Left Name and Bullet + }% + % + % 2. THE BULLET: Sits exactly at the center + \makebox[0pt][c]{ + \raisebox{-0.2ex}{\textperiodcentered}% + } + % + % 3. RIGHT NAME: Put in a zero-width box aligned to the Left (l). + % This pushes the text to the RIGHT of the center point. + \makebox[0pt][l]{% + \hspace{4mm}% The gap between Bullet and Right Name + % Use a parbox to allow wrapping if the name is long + \parbox{0.45\linewidth}{\raggedright\englishfont\color{magHighlight}\bfseries #2}% + }% + }% +} + + +% Author Note Environment +\makeatletter +\newcommand{\AuthorNote}[1]{% + \par\medskip % Ensure it starts on a new line with some spacing + \Needspace{6\baselineskip} % Prevents the box from being cut off at the bottom + \begin{tcolorbox}[ + enhanced, + boxrule=0.5pt, + arc=2mm, + colback=white, + colframe=black, + left=6pt, + right=6pt, + top=4pt, + bottom=4pt, + breakable=true, % Allows it to break across columns if very long + width=\linewidth % Forces the box to match the current column width + ] + \noindent\footnotesize + #1 + \end{tcolorbox} + \par\medskip +} +\makeatother + + +% Hook for Odia +\gappto\captionsodia{% + \def\abstractname{Abstract}% +} +% Hook for English +\gappto\captionsenglish{% + \def\abstractname{ସାରାଂଶ}% +} + +\newenvironment{abstract}{% +\par\small\vspace{0pt} +{\noindent\color{magHighlight}\rule[\ht\strutbox]{\linewidth}{1.0pt}\par\vspace{-.4cm}} +\noindent\textbf{\color{magHighlight}\abstractname. }\ignorespaces +}{\par\vspace{-0.35cm} +{\noindent\color{magHighlight}\rule{\linewidth}{1.0pt}\par}} + +\newcommand{\sectionheader}[2]{% + \par\addvspace{1em} % Adds space above the section + {\color{magHighlight}\hrule height 1.0pt} + \vspace{2pt} + \noindent + \textbf{\color{magHighlight}% + #1 \hfill #2% + } + \par\vspace{2pt} + {\color{magHighlight}\hrule height 1.0pt} + \addvspace{0.5em} % Space below the section +} + +\newcommand{\algebra}{\sectionheader{Algebra}{ବୀଜଗଣିତ}} + +\newcommand{\numbertheory}{\sectionheader{Number Theory}{ସଂଖ୍ୟା ତତ୍ତ୍ୱ}} + +\newcommand{\geometryh}{\sectionheader{Geometry}{ଜ୍ୟାମିତି}} + +\newcommand{\trigonometry}{\sectionheader{Trigonometry}{ତ୍ରିକୋଣମିତି}} + +\newcommand{\calculus}{\sectionheader{Calculus}{କଳନ ଗଣିତ}} + +\newcommand{\combinatorics}{\sectionheader{Combinatorics}{ସଂଯୋଗ ଗଣିତ}} + +\newcommand{\probability}{\sectionheader{Probability}{ସମ୍ଭାବ୍ୟତା ଗଣିତ}} + + + +\newcommand{\funfactname}{\iflanguage{odia}{ତୁମେ ଜାଣିଛ କି?}{Did you know ?}} +\NewDocumentEnvironment{funfact}{O{\funfactname}}{% + \begin{leelabox}[leelaAccent, title={\faLightbulb\;\;#1}] +}{% + \end{leelabox} +} + +% Author Info Macros +\newcommand{\affiliation}[2][1.8em]{% + \par + \hangindent=#1 + \hangafter=1 + \scalebox{1.1}{\color{magHighlight}\faUniversity}\, #2\par +} + +\newcommand{\email}[1]{% + \scalebox{1.1}{\color{magHighlight}\faEnvelope}\, + \href{mailto:#1}{#1} +} +\newcommand{\phone}[1]{% + \scalebox{1.1}{\color{magHighlight}\faPhone}\, #1\par +} + +\newtcolorbox{quotebox}[2][]{ % Added an optional argument for the attribution + enhanced jigsaw, + breakable, + colback=magHighlight!10, + colframe=white, + boxrule=1pt, + left=7mm, right=2mm, top=1mm, bottom=1.5mm, + before=\vspace{1.25mm}, + after=\vspace{0mm}, + % This adds the attribution at the bottom if the argument is provided + after upper={ + \ifstrempty{#1}{}{ % If argument #1 is not empty + \nopagebreak\vspace{#2} + \begin{flushright} + \textemdash\ \textbf{#1} + \end{flushright} + } + }, + overlay={ + \node[anchor=north west, + font=\fontsize{12pt}{12pt}\selectfont, + text=magHighlight!80] + at ([xshift=.5mm, yshift=1.75mm]frame.north west) {\faQuoteLeft}; + } +} + +\newenvironment{transtable} +{\begin{tcolorbox}[ + colback=magHighlight!10, + colframe=magHighlight, + boxrule=1pt, + arc=1mm, + fontupper=\footnotesize, + boxsep=0pt, + left=1mm, + right=1.5mm, + top=.5mm, + bottom=.5mm, + before upper=\par\noindent, +] +\setlength{\extrarowheight}{0pt} +\begin{tabular*}{\linewidth}{% + @{} l @{\extracolsep{\fill}} r + !{\extracolsep{0pt}\hspace{0.0em}\vrule\hspace{0.0em}} % Forces space 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\ifstrempty{#1}{}{ (#1)}% Add subtitle in () only if #1 is provided + }% + }, + label={artprob:#2} +} + +\NewDocumentEnvironment{artprobox}{o} +{% + \IfNoValueTF{#1} + {\begin{artproboxtemplate}{}{}} + {\begin{artproboxtemplate}{}{#1}} +} +{% + \end{artproboxtemplate} +} + +\newtcolorbox[auto counter, number within = chapter, number freestyle={\noexpand\arabic{\tcbcounter}}]{comprobox}{ + enhanced, + breakable, + colback=magHighlight!10, + colframe=white, + boxrule=1pt, + left=1mm, right=1mm, top=.5mm, bottom=.5mm, + before=\vspace{1.25mm}, + after=\vspace{0mm}, + %title={\color{black}\arabic{\tcbcounter}.}, + title={\color{black}\thetcbcounter.}, + fonttitle=\fontsize{12pt}{12pt}\selectfont\bfseries, + attach title to upper, + after title={\hspace{2mm}}, +} +\newenvironment{compsol}[1][S]{% + \pushQED{\qed}% + \noindent $\blacktriangleright \blacktriangleright$\quad% +\raggedright% +}{% + \popQED% + \medskip% +} + +% Define question box style +\newtcolorbox{questionbox}{ + enhanced, + 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