Area of a circle inscribe a hexagon. Cut the hexagon into six triangles by splitting it from the center. Two opposite triangles both touch two common diameters; slide them along one so the radial edges are adjacent. They now form a parallelogram, with the hexagon sides making two opposite edges, one of which is the base, "s". Two radial edges form slanted sides, and the height, "h" is equal to its apothem (as in the Archimedes proof). In fact, we can assemble all the triangles into one big parallelogram by putting successive pairs next to each other. The same is true if we increase
Peptide plane flipping Peptide plane flipping Peptide plane flipping is a type of conformational change that can occur in proteins by which the dihedral angles of adjacent amino acids undergo large-scale rotations with little displacement of the side chains. The plane flip is defined as a rotation of the dihedral angles φ,ψ at amino acids "i" and "i+1" such that the resulting angles remain in structurally stable regions of Ramachandran space. The key requirement is that the "sum" of the ψ angle of residue "i" and the φ angle of residue "i+1" remain roughly constant; in effect, the flip is a crankshaft move