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was thought to have infinitely many solutions that were called geometrically real. These solutions are the unit vectors that form the surface of a unit sphere. A geometrically real quaternion is one that can be written as a linear combination of i, j and k, such that the squares of the coefficients add up to one. Hamilton demonstrated that ...
Its two equal sides are in the golden ratio to its base. [46] The triangle formed by two sides and a diagonal of a regular pentagon is called a golden gnomon . It is an obtuse isosceles triangle with apex angle 108 ∘ {\displaystyle 108^{\circ }} and base angle 36 ∘ {\displaystyle 36^{\circ }\!} .
[13] [14] These three ways of combining two numbers were all studied in ancient Greek mathematics, and are called the Pythagorean means. [15] Conversely, this can be taken as an alternative definition of the Kepler triangle: it is a right triangle whose edge lengths are the three Pythagorean means of some two numbers.
A proportion is a mathematical statement expressing equality of two ratios. [1] [2]: =: a and d are called extremes, b and c are called means. Proportion can be written as =, where ratios are expressed as fractions.
Fair division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share. . That problem arises in various real-world settings such as division of inheritance, partnership dissolutions, divorce settlements, electronic frequency allocation, airport traffic management, and exploitation of Earth ...
The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun.
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In mathematics, the silver ratio is a geometrical proportion close to 70/29. Its exact value is 1 + √2, the positive solution of the equation x 2 = 2x + 1. The name silver ratio results from analogy with the golden ratio, the positive solution of the equation x 2 = x + 1.