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 theory Lie theory In mathematics, the researcher Sophus Lie ( ) initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject is Lie sphere geometry. This article addresses his approach to transformation groups, which is one of the areas of mathematics, and was worked out by Wilhelm Killing and Élie Cartan. The foundation of Lie theory is the exponential map relating Lie algebras to Lie groups which is called the Lie group–Lie algebra correspondence. The subject is part of differential geometry since Lie