exercise env
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2025-08-05 09:37:45 +08:00
parent 66dacb1dfc
commit edb9aaaa43
2 changed files with 10 additions and 7 deletions

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@@ -15,10 +15,10 @@
For errata and more stuff, see \url{https://sarielhp.org/book/}
\section{Grid}
\begin{oneshot}{1.1}
\begin{exercise}\label{ex1.1}
Let $P$ be a max cardinality point set contained in the $d$-dimensional unit hypercube such that the smallest distance of point pairs in $P$ is 1. Prove that
\[\left( \floor{\sqrt{d}}+1 \right)^d \leq |P|\leq \left( \ceil{\sqrt{d}}+1 \right)^d. \]
\end{oneshot}
\end{exercise}
hmm... the first exercise in this book is wrong. See \url{https://sarielhp.org/book/errata.pdf}.
The stated lowerbound is actually an upperbound.
\begin{proof}
@@ -36,9 +36,9 @@ n &\geq 1/\vol(1b^d)\\
The last line is greater than $(\sqrt{d}/5)^d$ for large enough $d$.
\end{proof}
\begin{oneshot}{1.2}
\begin{exercise}
Compute clustering radius
\end{oneshot}
\end{exercise}
\end{document}

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@@ -26,12 +26,14 @@
\setCJKsansfont{Source Han Serif SC}
\setCJKmonofont{Source Han Serif SC}
\RequirePackage[charter]{mathdesign} % math font only for serif mode
\RequirePackage{amsmath}
\RequirePackage{eucal}
\RequirePackage{microtype}
\fi
% \setCJKmainfont{SourceHanSerifSC-Regular.otf}[BoldFont={SourceHanSerifSC-Bold.otf}, ItalicFont=SourceHanSerifSC-Regular.otf]
\RequirePackage[margin=1in]{geometry}
\RequirePackage{amsmath}
\RequirePackage[dvipsnames]{xcolor}
\RequirePackage[colorlinks=true,urlcolor=Blue,citecolor=Green,linkcolor=BrickRed,unicode]{hyperref}
@@ -43,8 +45,6 @@
\RequirePackage{graphicx} % essentials
% \RequirePackage{microtype}
\RequirePackage{eucal}
\RequirePackage[nocompress]{cite} % other convenient stuff
\RequirePackage{enumerate}
%\usepackage{pgf,tikz}
@@ -57,18 +57,21 @@
\newaliascnt{corollary}{theorem}
\newaliascnt{conjecture}{theorem}
\newaliascnt{proposition}{theorem}
\newaliascnt{exercise}{theorem}
\newtheorem{lemma}{Lemma}[section]
\newtheorem{corollary}{Corollary}[section]
\newtheorem{conjecture}{Conjecture}[section]
\newtheorem{proposition}{Proposition}[section]
\newtheorem{problem}{Problem}
\newtheorem{exercise}{Ex}[section]
\newcommand{\lemmaautorefname}{Lemma}
\newcommand{\corollaryautorefname}{Corollary}
\newcommand{\conjectureautorefname}{Conjecture}
\newcommand{\propositionautorefname}{Proposition}
\newcommand{\problemautorefname}{Problem}
\newcommand{\exerciseautorefname}{Exercise}
\newenvironment{definition}[1][Definition]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}