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Spacing in a lined document

TeX - LaTeX Asked on June 23, 2021

I have the following document:

documentclass[12pt,a4paper,fleqn]{article}
usepackage[utf8]{inputenc}
usepackage{tikz,amsmath}
usepackage{amsfonts}
 usepackage[left=2cm,right=1.7cm,top=2cm,bottom=2cm,headheight=1cm, headsep=1cm]{geometry} 
pagestyle{empty}
setlength{parindent}{10ex}
usepackage{lipsum}
%~~~~~~~~~~~~~~~
usepackage[default]{frcursive}
usepackage[eulergreek,noplusnominus,noequal,nohbar,nolessnomore,noasterisk]{mathastext}

usepackage{atbegshi} % added
usepackage{enumitem}  % added

usepackage{tikz,tkz-euclide}
usepackage{setspace}
usetkzobj{all}
usetikzlibrary{arrows}
usepackage{amsmath}
usetikzlibrary{quotes,angles}
usepackage{pgfplots}
usepgfplotslibrary{fillbetween}
usetikzlibrary{shapes,shadings}
usetikzlibrary{arrows.meta}
usepgfplotslibrary{polar}
    
AtBeginShipout{AtBeginShipoutUpperLeft{%
        begin{tikzpicture}[remember picture,overlay] 
        %foreach i in{2.1,2.2,...,28}  % not needed
        foreach x in{2,3,...,28}
        draw[line width=1pt,gray!40!white]([shift={(-1,x)}]current page.south west)--([shift={(0,x)}]current page.south east);
        foreach t in{4,5,...,25}
        draw[line width=1pt,red!80!black]([shift={(1.8,-1)}]current page.south west)--([shift={(1.8,1)}]current page.north west);
        end{tikzpicture}   
            }}
        
setlength{topmargin}{-81pt}  % needed to set right every page 
begin{document}

setlength{baselineskip}{1cm}
setlength{topskip}{baselineskip}

 
color{blue}


textbf{ Nome: Rafael Pinheiro }  

vspace*{baselineskip}

Exercício: Encontre a área do plano $rtheta$ tal que $theta^2 leq r leq theta$.

underline{Resolução:} 

A área procurada é a hachurada a seguir.


Note que, $theta = theta^2$ se e somente se $theta=0$ ou $theta=1$. Ou seja, os pontos de intersecção destas duas curvas se dão nestes ângulos ($alpha = theta=0$ e $beta = theta=1$). Este é o limite de integração a ser considerado.

Agora, sabemos da teoria que a área entre duas curvas polares de equações $r=f_1(theta)$ e $r=f_2(theta)$ é dada por:

$$boxed{A = frac{1}{2} int_{alpha}^beta left[ f_2(theta)right]^2 - left[ f_1(theta)right]^2   , dtheta}$$

Aplicando em nosso exemplo, temos que $f_1(theta) = theta^2$ e $f_2(theta) = theta$ (pois $theta geq theta^2$ para $0 leq theta leq 1$), e assim:


end{document}

when compiled produces
Compiled document

My question is: after an equation, the text are not in the baseline. I need to adjust by vspace{} all time, try and try. How can I fix this?

One Answer

Define

newcountlnum
longdeffittolines#1{par
   vskip-prevdepth
   setbox0=vbox{#1}
   lnum=ht0 dividelnum bybaselineskip advancelnum by1
   nointerlineskip
   vbox tothelnumbaselineskip{vskip.5baselineskipvssbox0vss}
}

and use

fittolines{
   $$boxed{A = frac{1}{2} ... }$$
}

Answered by wipet on June 23, 2021

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