In Euclidean geometry, the right triangle altitude theorem or geometric mean theorem is a relation between the altitude on the hypotenuse in a right triangle...

In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the...

the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers...

"arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps to distinguish it from other types of means, such as geometric and...

Arithmetic-geometric mean Arithmetic-harmonic mean Cesàro mean Chisini mean Contraharmonic mean Elementary symmetric mean Geometric-harmonic mean Grand mean Heinz...

Euclid's first theorem, on the prime factors of products The Euclid–Euler theorem characterizing the even perfect numbers Geometric mean theorem about right...

arithmetic–geometric mean (AGM or agM) of two positive real numbers x and y is the mutual limit of a sequence of arithmetic means and a sequence of geometric means...

q {\displaystyle h_{c}={\sqrt {pq}}}   (Geometric mean theorem; see Special Cases, inverse Pythagorean theorem) For acute triangles, the feet of the altitudes...

In mathematics, the mean value theorem (or Lagrange's mean value theorem) states, roughly, that for a given planar arc between two endpoints, there is...

are: the angle bisector theorem, the geometric mean theorem, Ceva's theorem, Menelaus's theorem and the Pythagorean theorem. Similar triangles also provide...

mathematics, the geometric–harmonic mean M(x, y) of two positive real numbers x and y is defined as follows: we form the geometric mean of g0 = x and h0...

Greeks, along the way inventing the concept of geometric proof and proving various geometric theorems. However, there is no direct evidence for any of...

length of the resulting segment is the geometric mean. This can be proven by applying the Pythagorean theorem to three similar right triangles, each having...

(circles) Gauss–Wantzel theorem (geometry) Geometric mean theorem (geometry) Hinge theorem (geometry) Hjelmslev's theorem (geometry) Impossibility of angle trisection...

based on the intercept theorem. A slightly less elementary construction using these tools is based on the geometric mean theorem and will construct a segment...

goes with the arithmetic mean, is the geometric mean to the power n. Thus the n-th harmonic mean is related to the n-th geometric and arithmetic means. The...

In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that the sum of the...

arithmetic-logarithmic-geometric mean inequality. To see this, consider the case where n = 0 {\displaystyle n=0} . From the mean value theorem, there exists a...

the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard...

fundamental theorem of calculus. The first published statement and proof of a rudimentary form of the fundamental theorem, strongly geometric in character...

the theorem and the inverse-square law imply that the light intensity at C is the same as when a single lamp is placed at D. Geometric mean theorem – Theorem...

algebraic theorems to accompany various geometric shapes. It focuses on the area of rectangles and squares (see Quadrature), and leads up to a geometric precursor...

classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a compass. The idealized ruler...

soap bubble theorem is a mathematical theorem from geometric analysis that characterizes a sphere through the mean curvature. The theorem was proven in...

within time-velocity space. These geometric procedures anticipated the Oxford Calculators, including the mean speed theorem, by 14 centuries. South of Egypt...

transformed into a square of the same area with the help of Euclid's geometric mean theorem. One extends the side O N ¯ {\displaystyle {\overline {ON}}} by...

of arithmetic and geometric means. For any real vector a = ( a 1 , … , a n ) {\displaystyle a=(a_{1},\dots ,a_{n})} define the "a-mean" [a] of positive...

symmetries of field extensions, provides an elegant proof of the Abel–Ruffini theorem that general quintic equations cannot be solved in radicals. Fields serve...

converges to the sum of ⁠ 1 {\displaystyle 1} ⁠. Each term in a geometric series is the geometric mean of the term before it and the term after it, in the same...

theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem,...