Circle a triangle whose base has the length of the circle's circumference and whose height equals the circle's radius, which comes to multiplied by the radius squared: Equivalently, denoting diameter by "d", that is, approximately 79% of the circumscribing square (whose side is of length "d"). The circle is the plane curve enclosing the maximum area for a given arc length. This relates the circle to a problem in the calculus of variations, namely the isoperimetric inequality. Equation of a circle<br> In an "x"–"y" Cartesian coordinate system, the circle with centre coordinates ("a", "b") and radius "r" is the set of
Earth's circumference Rhodes was 5,000 stadia due north of Alexandria, and the difference in the star's elevation indicated the distance between the two locales was 1/48 of the circle, he multiplied 5,000 by 48 to arrive at a figure of 240,000 stadia for the circumference of the earth. It is generally thought that the stadion used by Posidonius was almost exactly 1/10 of a modern statute mile. Thus Posidonius's measure of 240,000 stadia translates to , not much short of the actual circumference of .<ref name="fragment 202"/ Strabo noted that the distance between Rhodes and Alexandria is 3,750 stadia, and reported Posidonius's