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The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles.In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...
In geometry, a nonagon (/ ˈ n ɒ n ə ɡ ɒ n /) or enneagon (/ ˈ ɛ n i ə ɡ ɒ n /) is a nine-sided polygon or 9-gon. The name nonagon is a prefix hybrid formation , from Latin ( nonus , "ninth" + gonon ), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century.
Close approximations to the regular hendecagon can be constructed. For instance, the ancient Greek mathematicians approximated the side length of a hendecagon inscribed in a unit circle as being 14/25 units long. [7] The hendecagon can be constructed exactly via neusis construction [8] and also via two-fold origami. [9]
The most common example is the pentagram, which has the same vertices as a pentagon, but connects alternating vertices. For an n-sided star polygon, the Schläfli symbol is modified to indicate the density or "starriness" m of the polygon, as {n/m}. If m is 2, for example, then every second point is
A centered nonagonal number (or centered enneagonal number) is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers. The centered nonagonal number for n layers is given by the formula [1]
Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to ...
The mass of an object of known density that varies incrementally, the moment of inertia of such objects, as well as the total energy of an object within a discrete conservative field can be found by the use of discrete calculus. An example of the use of discrete calculus in mechanics is Newton's second law of motion: historically stated it ...
An example of a concave polygon. A simple polygon that is not convex is called concave , [ 1 ] non-convex [ 2 ] or reentrant . [ 3 ] A concave polygon will always have at least one reflex interior angle —that is, an angle with a measure that is between 180 degrees and 360 degrees exclusive.