Area of a circle of Cnidus in the fifth century B.C. had found that the area of a disk is proportional to its radius squared. Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius in his book "Measurement of a Circle". The circumference is 2"r", and the area of a triangle is half the base times the height, yielding the area "r" for the disk. Prior to Archimedes, Hippocrates of Chios was the first
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