Area of a circle to eight sides and so on. For a polygon with 2"n" sides, the parallelogram will have a base of length "ns", and a height "h". As the number of sides increases, the length of the parallelogram base approaches half the circle circumference, and its height approaches the circle radius. In the limit, the parallelogram becomes a rectangle with width "r" and height "r". There are various equivalent definitions of the constant π. The conventional definition in pre-calculus geometry is the ratio of the circumference of a circle to its diameter: However, because the circumference of a circle is not a
Straight-line grammar minimal size that generates a given string is called the smallest grammar problem. Straight-line grammars (more precisely: straight-line context-free string grammars) can be generalized to "Straight-line context-free tree grammars". The latter can be used conveniently to compress trees. A context-free grammar "G" is an SLG if: 1. for every non-terminal "N", there is at most one production rule that has "N" as its left-hand side, and 2. the directed graph "G"=<"V","E">, defined by "V" being the set of non-terminals and ("A","B") ∈ "E" whenever "B" appears at the right-hand side of a production rule for "A", is acyclic. A mathematical