In this youtube video Coding Challenge #81.1: Circle Morphing there is this guy solving a Javascript code challenge about morphing an equilateral triangle into a circle. Here is a one-line Wolfram expression written in a pure functional style that returns the solution using only built-in function.

{Interpolation[#2, InterpolationOrder -> 1], Most@Array[# &, 50, {#1, #2}] & @@ #1} &~MapThread~(
Partition[#, 2, 1] & /@ {First@Transpose@#, #} &@Table[{Cos@x, Sin@x}, {x, -Pi/6, 2 Pi - Pi/6, 2 Pi/3}]) // 
       Join @@ MapThread[Transpose@{#2, #1@#2} &, Transpose@#] & // 
      Transpose@{#, Most@N@Table[{Cos@x, Sin@x}, {x, -Pi/6, 2 Pi - Pi/6, 2 Pi/(Length@#)}]} & // 
     Animate[.5 (Sin@k First@# + (1 - Sin@k) Last@#) & /@ Append[#, First@#] // Graphics[{Thickness@.01, Line@#},
     PlotRange -> {{-.5, .5}, {-.6, .6}}] &, {k, 0, Pi/2}, AnimationDirection -> ForwardBackward, AnimationRate -> .5] &