parskip 行为异常；更改字母会占用大量空间

Question

这个问题只是出于好奇。在纠正了一个拼写错误（“ad”改成了“at”）后，我注意到更改一个字母会完全改变输出（在第一种情况下，编译器无法在两行中完成，而在第二种情况下，它只需要两行即可完成。

梅威瑟：

\documentclass[11pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[parfill]{parskip}
\usepackage[top=3.5cm,bottom=3.5cm,left=3.5cm,right=3.5cm]{geometry}

\begin{document}
    Hint: for a fixed $y$, let $f(x):=\sin(x+y)-\sin(x)\cos(y)-\cos(x)\sin(y)$; prove that $f''=-f$ (so that $f$ equals its Taylor series centered ad $0$) and $f(0)=f'(0)=0$.

    Hint: for a fixed $y$, let $f(x):=\sin(x+y)-\sin(x)\cos(y)-\cos(x)\sin(y)$; prove that $f''=-f$ (so that $f$ equals its Taylor series centered at $0$) and $f(0)=f'(0)=0$.
\end{document}

输出：

谁能解释为什么会发生这种情况？

Answer 1

parfill 选项强制在段落末尾留出 30pt 的自由空间，现在刚好低于这个限制。通过稍微减少该值，您也可以在第一个版本中避免换行（我删除了inputenc，因为当前的 LaTeX 中不再需要它）：

\documentclass[11pt,a4paper]{article}
\usepackage[parfill=29.1pt]{parskip}
\usepackage[top=3.5cm,bottom=3.5cm,left=3.5cm,right=3.5cm]{geometry}

\begin{document}
    Hint: for a fixed $y$, let $f(x):=\sin(x+y)-\sin(x)\cos(y)-\cos(x)\sin(y)$; prove that $f''=-f$ (so that $f$ equals its Taylor series centered ad $0$) and $f(0)=f'(0)=0$.

    Hint: for a fixed $y$, let $f(x):=\sin(x+y)-\sin(x)\cos(y)-\cos(x)\sin(y)$; prove that $f''=-f$ (so that $f$ equals its Taylor series centered at $0$) and $f(0)=f'(0)=0$.
\end{document}