Pacific Ocean width at about 5°N latitude, where it stretches approximately from Indonesia to the coast of Colombia—halfway around the world, and more than five times the diameter of the Moon. The lowest known point on Earth—the Mariana Trench—lies below sea level. Its average depth is , putting the total water volume at roughly . Due to the effects of plate tectonics, the Pacific Ocean is currently shrinking by roughly per year on three sides, roughly averaging a year. By contrast, the Atlantic Ocean is increasing in size. Along the Pacific Ocean's irregular western margins lie many seas, the largest of which
Lie group Lie groups are called "isomorphic" if there exists a bijective homomorphism between them whose inverse is also a Lie group homomorphism. Equivalently, it is a diffeomorphism which is also a group homomorphism. Isomorphic Lie groups necessarily have isomorphic Lie algebras; it is then reasonable to ask how isomorphism classes of Lie groups relate to isomorphism classes of Lie algebras. The first result in this direction is Lie's third theorem, which states that every finite-dimensional, real Lie algebra is the Lie algebra of some (linear) Lie group. One way to prove Lie's third theorem is to use Ado's theorem, which says