Byhello contrast, the [[Brouwer fixed-point theorem]] is a non-[[Constructivism (mathematics)|constructive result]]: it says that any [[continuous function|continuous]] function from the closed [[unit ball]] in ''n''-dimensional [[Euclidean space]] to itself must have a fixed point,<ref>Eberhard Zeidler, ''Applied Functional Analysis: main principles and theirHELLO applications'', Springer, 1995.</ref> but it doesn't describe how to find the fixed point (See also [[Sperner's lemma]]).
For example, the [[cosine]] function isHHHHHEEELLLLLLOOOOOOO continuous in [−1,1] and maps it into [−1, 1], and thus must have a fixed point. This is clear when examining a sketched graph of the cosine function; the fixed point occurs where the cosine curve ''y''=cos(''x'') intersects the line ''y''=''x''. Numerically, the fixed point is approximately ''x''=0.73908513321516 (thus ''x''=cos(''x'') for this value of ''x'').
The [[Lefschetz fixed-point theorem]]<ref>{{cite journal |author=Solomon Lefschetz |title=On the fixed point formula |journal=[[Annals of Mathematics|Ann. of Math.]] |year=1937 |volume=38 |pages=819–822 |doi=10.2307/1968838 |issue=4}}</ref> (and the [[Nielsen theory|Nielsen fixed-point theorem]])<ref>{{cite book
