1

I want to wrap the image with the texts at the right. The way it now appears is below the text. Any help is much appreciated.

\documentclass[12 pt]{article}
\usepackage[margin=.5in]{geometry}               
\geometry{letterpaper}                   
\usepackage{graphicx}
\usepackage{amsmath, amssymb, amsfonts}
\usepackage{epstopdf}
\usepackage{geometry}
\usepackage{enumerate}
\usepackage{bbm}
\usepackage{relsize}
\usepackage{textcomp}
\usepackage{tcolorbox}
\usepackage{wrapfig}
\usepackage{lipsum} 

\geometry{%
  letterpaper,
  lmargin=1 cm,
  rmargin=1 cm,
  tmargin=1 cm,
  bmargin=1 cm,
  footskip=20 pt,
  headheight=12pt}



\begin{document}


\begin{center}
    \textbf{Continued Fraction}
\end{center}


This is a very efficient method of finding the best rational approximations of a real number. Continued fractions are written as fractions within fractions which are added up in a special way, and which may go on indefinitely. Every number can be written as a continued fraction and the finite continued fractions are sometimes used to give approximations to numbers like $\sqrt{2}$ and $\pi$.

\medskip
\noindent
\textbf{Applications.} 

\begin{enumerate}
    \item Design of a calendar : A year is the orbital period of the earth moving in its orbit  around the Sun.  For an observer on Earth, this corresponds to the period it takes to the Sun to complete one rotation, which is approximately 365.2422 days whose continued fraction expression is 
            $$365.2422=[365,4,7,1,3,4,1]~.$$         
The second convergent is  $\displaystyle{365.25=365+\frac{1}{4}}$, which means a calendar of 365 days per year but a leap year every 4 years. The fourth convergent gives a better approximation
$$365.2424 \dots  =[ 365,4,7,1 ]= 365+\frac{8}{33}~.$$ 
%\begin{wrapfigure}{R}{5.5cm}
%\caption{A wrapped figure going nicely inside the text.}\label{wrap-fig:1}
%\includegraphics[width=8.6cm]{Greg.jpg}
%\end{wrapfigure}
The most commonly used civil calendar today is known as the \textbf{Gregorian calendar}, which is also called the Western calendar, or the Christian calendar. This calendar was named after Pope Gregory XIII, who introduced it in 1582. Today, the Gregorian calendar is part of our everyday lives, and most of us use it without really knowing its backstory, the reasons for its introduction, and the effects that it had on the world.

\begin{center}
   \includegraphics[width=84 mm, height=64 mm]{Greg.jpg}
\end{center}

This is based on a cycle of 400 years: there is one leap year every year which is a multiple of 4 but not of 100 unless it is a multiple of 400. 


\item Design of a planetarium : Christiaan Huygens (1629–1695) among being a mathematician was an astronomer, 
physicist, probabilist, and was also a great horologist. He
designed more accurate clocks then the ones available at his time. In particular, his invention of the pendulum clock was a breakthrough in timekeeping. Huygens also built a mechanical model of the solar system. He wanted to design the gear ratios in order to produce a proper scaled version of the planetary orbits. He knew that the time required for the planet Saturn to orbit around the Sun is about

\end{enumerate}

\end{document}
  • The commented code is the one I used but it still appeared below the text. – Eureka Aug 15 '18 at 8:18
  • Sorry, I only check commented code if explicitly mentioned in the post. – TeXnician Aug 15 '18 at 8:19
4

Inserting images near list environment doesn't work well with the usual packages (wrapfig, floatflt). Here is a solution with the plain TeX macro package insbox, combined with enumitem, more powerful than enumerate. In particular, you can set the right margin of a list, and stop a list, then resume it, continuing the counter from the value for the previous list, with a different right margin (and changing other parameters if you wish).

Unrelated: I simplified your preamble, removing repeated package loading.

\documentclass[12 pt]{article}
\usepackage{geometry}
\geometry{%
  letterpaper,
  margin=1 cm,
  footskip=20 pt,
  headheight=12pt}
\usepackage[demo]{graphicx}
\usepackage{epstopdf}
\usepackage[shortlabels]{enumitem}
\usepackage{amsmath, amssymb}
\usepackage{relsize}
\usepackage{textcomp}
\usepackage{tcolorbox}

\input{insbox}

\begin{document}

\begin{center}
    \textbf{Continued Fraction}
\end{center}

This is a very efficient method of finding the best rational approximations of a real number. Continued fractions are written as fractions within fractions which are added up in a special way, and which may go on indefinitely. Every number can be written as a continued fraction and the finite continued fractions are sometimes used to give approximations to numbers like $\sqrt{2}$ and $\pi$.
\bigskip

\InsertBoxR{1}{\raisebox{0pt}[\dimexpr\height+2.5ex]{\includegraphics[width=84 mm, height=64 mm]{Greg.jpg}}}
\noindent
\textbf{Applications.}
\begin{enumerate}[rightmargin=88mm]
    \item Design of a calendar : A year is the orbital period of the earth moving in its orbit around the Sun. For an observer on Earth, this corresponds to the period it takes to the Sun to complete one rotation, which is approximately 365.2422 days whose continued fraction expression is
            $$365.2422=[365,4,7,1,3,4,1]~.$$
The second convergent is $\displaystyle{365.25=365+\frac{1}{4}}$, which means a calendar of 365 days per year but a leap year every 4 years. The fourth convergent gives a better approximation
\[ 365.2424 \dots =[ 365,4,7,1 ]= 365+\frac{8}{33}~. \]
\end{enumerate}
\begin{enumerate}[resume]
\item[]
The most commonly used civil calendar today is known as the \textbf{Gregorian calendar}, which is also called the Western calendar, or the Christian calendar. This calendar was named after Pope Gregory XIII, who introduced it in 1582. Today, the Gregorian calendar is part of our everyday lives, and most of us use it without really knowing its backstory, the reasons for its introduction, and the effects that it had on the world.

This is based on a cycle of 400 years: there is one leap year every year which is a multiple of 4 but not of 100 unless it is a multiple of 400.

\item Design of a planetarium : Christiaan Huygens (1629–1695) among being a mathematician was an astronomer,
physicist, probabilist, and was also a great horologist. He
designed more accurate clocks then the ones available at his time. In particular, his invention of the pendulum clock was a breakthrough in timekeeping. Huygens also built a mechanical model of the solar system. He wanted to design the gear ratios in order to produce a proper scaled version of the planetary orbits. He knew that the time required for the planet Saturn to orbit around the Sun is about

\end{enumerate}

\end{document} 

enter image description here

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