Mantel's theorem states that the maximum number of edges in an n-vertex graph without these objects is the floor of "n squared over 4". These objects, which are sometimes referred to as 2-simplices ["SIMP-li-sees"], name a construction where the value at the n-th row and k-th column is equal to "n choose k". Successively removing subsets from one of these results in a Sierpinski ["sir-PIN-ski"] gasket. They name and satisfy an inequality which states that the sum of the lengths of two of their sides is greater than or equal to the length of a third side. For 10 points, name these geometric fig
Mantel's theorem states that the maximum number of edges in an n-vertex graph without these objects is the floor of "n squared over 4". These objects, which are sometimes referred to as 2-simplices ["SIMP-li-sees"], name a construction where the value at the n-th row and k-th column is equal to "n choose k". Successively removing subsets from one of these results in a Sierpinski ["sir-PIN-ski"] gasket. They name and satisfy an inequality which states that the sum of the lengths of two of their sides is greater than or equal to the length of a third side. For 10 points, name these geometric figures which obey the Law of Cosines and have three sides.