Linear scaleA linear scale, also called a bar scale, scale bar, graphic scale, or graphical scale, is a means of visually showing the scale of a map, nautical chart, engineering drawing, or architectural drawing. A scale bar is common element of map layouts. On large scale maps and charts, those covering a small area, and engineering and architectural drawings, the linear scale can be very simple, a line marked at intervals to show the distance on the earth or object which the distance on the scale represents.
Brouwer fixed-point theoremBrouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function mapping a nonempty compact convex set to itself there is a point such that . The simplest forms of Brouwer's theorem are for continuous functions from a closed interval in the real numbers to itself or from a closed disk to itself. A more general form than the latter is for continuous functions from a nonempty convex compact subset of Euclidean space to itself.
