Area of a circle order to arrive at the formula for the area of a disk. Consider unwrapping the concentric circles to straight strips. This will form a right angled triangle with r as its height and 2r (being the outer slice of onion) as its base. Finding the area of this triangle will give the area of the disk The opposite and adjacent angles for this triangle are respectively in degrees 9.0430611..., 80.956939... and in radians 0.1578311... , 1.4129651... Explicitly, we imagine dividing up a circle into triangles, each with a height equal to the circle's radius and a base that is infinitesimally
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