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In Euclidean geometry, the right triangle altitude theorem or geometric mean theorem is a relation between the [[Altitude (water )|altitude]] on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse.
This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures
Geopotential height differs from geometric height (as given by a tape measure) because Earth's gravity is not constant, varying markedly with altitude and latitude; thus, a 1-m geopotential height difference implies a different vertical distance in physical space: "the unit-mass must be lifted higher at the equator than at the pole, if the same ...
The process of drawing the altitude from a vertex to the foot is known as dropping the altitude at that vertex. It is a special case of orthogonal projection. Altitudes can be used in the computation of the area of a triangle: one-half of the product of an altitude's length and its base's length (symbol b) equals the triangle's area: A = h b /2 ...
The list of peaks that follows is not complete, but the peaks are all notable. Island high points (whose prominence is equal to their elevation) can be found at the List of islands by highest point; hence most are not included below. Some well-known peaks listed here do not score highly by prominence.
However, heights often conflict on different topographic maps, even when created by the same cartographic institution. For example, the Fletschhorn is indicated to be 3993, 3982, and 3984.5 m high on the 1:100,000, 1:50,000 and 1:25,000 Swisstopo map, respectively. This table uses the latter map's (rounded) elevation.
A trivial example. In mathematics, the mountain climbing problem is a mathematical problem that considers a two-dimensional mountain range (represented as a continuous function), and asks whether it is possible for two mountain climbers starting at sea level on the left and right sides of the mountain to meet at the summit, while maintaining equal altitudes at all times.
The topographic elevation of a summit measures the height of the summit above a geodetic sea level. [3] [4] The first table below ranks the 100 highest major summits of greater North America by elevation. The topographic prominence of a summit is a measure of how high the summit rises above its surroundings.