In the new curricula that are now gradually being implemented in secondary schools in Flanders, the Dutch-speaking part of Belgium, there is a shift towards mathematics as a part of STEM (Science, Technology, Engineering, Mathematics) and towards computational thinking in mathematics: programming, logic and electronic gates, graph theory, and for some pupils linear programming. Meanwhile, the new curricula contain less geometry and fewer references to history and art. As a first reaction, I welcome the introduction of graph theory, but I regret the loss of some beautiful parts of geometry. Instead of complaining, I try to relate the new subjects with geometry and the history of mathematics. There have always been algorithms in mathematics, long before there were electronic computers that could be programmed. Moreover, geometrical and visual thinking can be used to discover many algorithms. In this article, I would like to illustrate historical and geometrical aspects ofalgorithms with some examples: the calculation by hand of the digits of a square root and the algorithm for constructing a Eulerian circuit in a multigraph in which the degree of each vertex is even.