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The Koch snowflake is a fractal curve, also known as the Koch island, which was first described by Helge von Koch in 1904. It is built by starting with an equilateral ...

While some authors define "circumference" as distance around an arbitrary closed object (sometimes restricted to a closed curved object), in the work, the term "perimeter" is ...

A lattice polygon consisting of a closed self-avoiding walk on a square lattice. The perimeter, horizontal perimeter, vertical perimeter, and area are all well-defined for ...

A perimeter-bisecting segment of a polygon originating from the midpoint of one side. Each cleaver M_1C_1, M_2C_2, and M_3C_3 in a triangle DeltaA_1A_2A_3 is parallel to an ...

Find a closed plane curve of a given perimeter which encloses the greatest area. The solution is a circle. If the class of curves to be considered is limited to smooth ...

Define the minimal bounding rectangle as the smallest rectangle containing a given lattice polygon. If the perimeter of the lattice polygon is equal to that of its minimal ...

A lattice polygon formed by a three-choice walk. The anisotropic perimeter and area generating function G(x,y,q)=sum_(m>=1)sum_(n>=1)sum_(a>=a)C(m,n,a)x^my^nq^a, where ...

A right triangle is triangle with an angle of 90 degrees (pi/2 radians). The sides a, b, and c of such a triangle satisfy the Pythagorean theorem a^2+b^2=c^2, (1) where the ...

A convex polyomino containing at least one edge of its minimal bounding rectangle. The perimeter and area generating function for directed polygons of width m, height n, and ...

Let T_1 be the point at which the J_1-excircle meets the side A_2A_3 of a triangle DeltaA_1A_2A_3, and define T_2 and T_3 similarly. Then the lines A_1T_1, A_2T_2, and A_3T_3 ...