Title: What every student of math or cs should know about
        Euclidean constructions

 Abstract:

    Historically, the first extensive family of algorithms
    was Euclid's constructions with ruler and compass. Also
    the first (and still the most famous) impossibility results
    in mathematics (like "squaring the circle") were connected
    with Euclidean constructions.
       In this talk we shall review what should have been taught
    (and once upon a time was indeed taught) in high school
    about this topic. We shall also discuss it from the
    following five modern perspectives:

     1) The logical content and complexity of Euclidean "construction problems"
     2) Euclidean constructions as constructive existence proofs
     3) Euclidean constructions as algorithms/programs
     4) Euclidean constructions from an algebraic point of view
     5) Euclidean constructions  and the axioms of Euclidean Geometry