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In typography, a page header (or simply header) is text that is separated from the main body of text and appears at the top of a printed page. Word processing programs usually provide for the creation and maintenance of page headers, which are often the same from page to page, with merely small differences in information, such as page number.
In publishing and certain types of academic writing, a running header or running headline is a header that appears on each page. Typical running heads in a book might consist of the book title on the left-hand (verso) page, and the chapter title on ...
Every year TeX Live provides a new version. My recollection is that soon after a new version is released, the old version's tlmgr stops fetching updates to packages. They provide upgrading instructions with the disclaimer
This procedure is not bullet-proof, or especially recommended
There i...
I'm having a weird vertical gap in one of my documents, which only is there when I use multicol together with \documentclass[parskip=half]{scrreprt}.
Minimal example
\documentclass[parskip=half]{scrreprt}
\usepackage{multicol}
\begin{document}
\begin{multicols}{2}
\subsubsection{title}...
It does this but it uses a computer and so requires less manual labour.
(image from Wikipedia)
In non-Euclidean geometry, the Poincaré half-plane model is the upper half-plane (denoted below as H), together with a metric, the Poincaré metric, that makes it a model of two-dimensional hyperbolic geometry.
It is named after Henri Poincaré, but originated with Eugenio Beltrami, who used it, along with the Klein model and the Poincaré disk model (due to Riemann),
to show that hyperbolic geometry was equiconsistent with Euclidean geometry. The disk model and the half-plane model are isomorphic under a conformal mapping.
Metric
The metric of the model on the half-plane
:\{ \langle x, y ...
In geometry, the Poincaré disk model or Poincaré ball model, also called the conformal disk model, is a model of n-dimensional hyperbolic geometry in which the points of the geometry are in an n-dimensional disk, or unit ball, and the straight lines consist of all segments of circles contained within the disk that are orthogonal to the boundary of the disk, plus all diameters of the disk. Along with the Klein model and the Poincaré half-space model, it was proposed by Eugenio Beltrami who used these models to show hyperbolic geometry was equiconsistent with Euclidean geometry.
Metric
If...
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.
In this context, "almost surely" is a mathematical term with a precise meaning, and the "monkey" is not an actual monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. The relevance of the theory is questionable—the probability of a monkey exactly typing a complete work such as Shakespeare's Hamlet is so tiny that th...
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