Forming Areas with a Given Length: A(n) Function

[husseinshimal]

I`ve been reviewing the list of special functions and i guess i came up with anew special function. i also need your opinions about it. this function is about the area we can form by agiven length. Assume we have alength,s, and we want to start generating different areas by closing this length by keeping all the SUBLENGTHS WE CUT EQUAL.Oviously we will start with atriangle where each sublength=(s\3).The function,A(numbers of sublengths) has aminumium value at the triangle, A(3)=[(s^2)\36](3)^(1\2),and amaximum value at the circle,A(n)=(s^2)\4pi,where,n→infinity.in general,we may put,A(n)=nA(3).thank you

 

[HallsofIvy]

Did you mean A(n,s) or A_n(s)? As you wrote it, this is not a function of n.