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Supergolden ratio, the Glossary

In mathematics, the supergolden ratio is a geometrical proportion close to.^[1]

44 relations: Almost integer, Aspect ratio, Binomial coefficient, Characteristic equation (calculus), Combinatorics on words, Compact space, Composition (combinatorics), Conjugate element (field theory), Constant-recursive sequence, Continued fraction, Cubic equation, Dedekind eta function, Discriminant, Fermat's little theorem, Fibonacci sequence, Fixed-point iteration, Generating function, Geometric series, Golden ratio, Golden rectangle, Hilbert class field, Incidence matrix, L-system, Matrix (mathematics), Minimal polynomial (field theory), Narayana Pandita (mathematician), Padovan sequence, Permutation, Perrin number, Phase (waves), Pisot–Vijayaraghavan number, Plastic ratio, Pseudoprime, Quadratic field, Rauzy fractal, Recurrence relation, Ring of integers, Self-similarity, Semi-Thue system, Supersilver ratio, Symmetry (journal), The Mathematical Gazette, Weber modular function, Zero of a function.
Cubic irrational numbers
History of geometry

Almost integer

In recreational mathematics, an almost integer (or near-integer) is any number that is not an integer but is very close to one.

See Supergolden ratio and Almost integer

Aspect ratio

The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions.

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Binomial coefficient

In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Supergolden ratio and binomial coefficient are integer sequences.

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Characteristic equation (calculus)

In mathematics, the characteristic equation (or auxiliary equation) is an algebraic equation of degree upon which depends the solution of a given th-order differential equation or difference equation.

See Supergolden ratio and Characteristic equation (calculus)

Combinatorics on words

Combinatorics on words is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages.

See Supergolden ratio and Combinatorics on words

Compact space

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space.

See Supergolden ratio and Compact space

Composition (combinatorics)

In mathematics, a composition of an integer n is a way of writing n as the sum of a sequence of (strictly) positive integers.

See Supergolden ratio and Composition (combinatorics)

Conjugate element (field theory)

In mathematics, in particular field theory, the conjugate elements or algebraic conjugates of an algebraic element, over a field extension, are the roots of the minimal polynomial of over.

See Supergolden ratio and Conjugate element (field theory)

Constant-recursive sequence

In mathematics, an infinite sequence of numbers s_0, s_1, s_2, s_3, \ldots is called constant-recursive if it satisfies an equation of the form for all n \ge d, where c_i are constants. Supergolden ratio and constant-recursive sequence are integer sequences.

See Supergolden ratio and Constant-recursive sequence

Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.

See Supergolden ratio and Continued fraction

Cubic equation

In algebra, a cubic equation in one variable is an equation of the form ax^3+bx^2+cx+d.

See Supergolden ratio and Cubic equation

Dedekind eta function

In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane of complex numbers, where the imaginary part is positive.

See Supergolden ratio and Dedekind eta function

Discriminant

In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them.

See Supergolden ratio and Discriminant

Fermat's little theorem

In number theory, Fermat's little theorem states that if is a prime number, then for any integer, the number is an integer multiple of.

See Supergolden ratio and Fermat's little theorem

Fibonacci sequence

In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Supergolden ratio and Fibonacci sequence are integer sequences.

See Supergolden ratio and Fibonacci sequence

Fixed-point iteration

In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.

See Supergolden ratio and Fixed-point iteration

Generating function

In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series.

See Supergolden ratio and Generating function

Geometric series

In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms.

See Supergolden ratio and Geometric series

Golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Supergolden ratio and golden ratio are history of geometry and mathematical constants.

See Supergolden ratio and Golden ratio

Golden rectangle

In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, 1: \tfrac, which is 1:\varphi (the Greek letter phi), where \varphi is approximately 1.618.

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Hilbert class field

In algebraic number theory, the Hilbert class field E of a number field K is the maximal abelian unramified extension of K. Its degree over K equals the class number of K and the Galois group of E over K is canonically isomorphic to the ideal class group of K using Frobenius elements for prime ideals in K.

See Supergolden ratio and Hilbert class field

Incidence matrix

In mathematics, an incidence matrix is a logical matrix that shows the relationship between two classes of objects, usually called an incidence relation.

See Supergolden ratio and Incidence matrix

L-system

An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar.

See Supergolden ratio and L-system

Matrix (mathematics)

In mathematics, a matrix (matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.

See Supergolden ratio and Matrix (mathematics)

Minimal polynomial (field theory)

In field theory, a branch of mathematics, the minimal polynomial of an element of an extension field of a field is, roughly speaking, the polynomial of lowest degree having coefficients in the smaller field, such that is a root of the polynomial.

See Supergolden ratio and Minimal polynomial (field theory)

Narayana Pandita (mathematician)

Nārāyaṇa Paṇḍita (नारायण पण्डित) (1340–1400) was an Indian mathematician.

See Supergolden ratio and Narayana Pandita (mathematician)

Padovan sequence

In number theory, the Padovan sequence is the sequence of integers P(n) defined. Supergolden ratio and Padovan sequence are integer sequences.

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Permutation

In mathematics, a permutation of a set can mean one of two different things.

See Supergolden ratio and Permutation

Perrin number

In mathematics, the Perrin numbers are a doubly infinite constant-recursive integer sequence with characteristic equation. Supergolden ratio and Perrin number are integer sequences.

See Supergolden ratio and Perrin number

Phase (waves)

In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is expressed in such a scale that it varies by one full turn as the variable t goes through each period (and F(t) goes through each complete cycle).

See Supergolden ratio and Phase (waves)

Pisot–Vijayaraghavan number

In mathematics, a Pisot–Vijayaraghavan number, also called simply a Pisot number or a PV number, is a real algebraic integer greater than 1, all of whose Galois conjugates are less than 1 in absolute value.

See Supergolden ratio and Pisot–Vijayaraghavan number

Plastic ratio

In mathematics, the plastic ratio is a geometrical proportion close to. Supergolden ratio and plastic ratio are cubic irrational numbers, history of geometry, integer sequences and mathematical constants.

See Supergolden ratio and Plastic ratio

Pseudoprime

A pseudoprime is a probable prime (an integer that shares a property common to all prime numbers) that is not actually prime.

See Supergolden ratio and Pseudoprime

Quadratic field

In algebraic number theory, a quadratic field is an algebraic number field of degree two over \mathbf, the rational numbers.

See Supergolden ratio and Quadratic field

Rauzy fractal

In mathematics, the Rauzy fractal is a fractal set associated with the Tribonacci substitution It was studied in 1981 by Gérard Rauzy, with the idea of generalizing the dynamic properties of the Fibonacci morphism.

See Supergolden ratio and Rauzy fractal

Recurrence relation

In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms.

See Supergolden ratio and Recurrence relation

Ring of integers

In mathematics, the ring of integers of an algebraic number field K is the ring of all algebraic integers contained in K. An algebraic integer is a root of a monic polynomial with integer coefficients: x^n+c_x^+\cdots+c_0.

See Supergolden ratio and Ring of integers

Self-similarity

In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts).

See Supergolden ratio and Self-similarity

Semi-Thue system

In theoretical computer science and mathematical logic a string rewriting system (SRS), historically called a semi-Thue system, is a rewriting system over strings from a (usually finite) alphabet.

See Supergolden ratio and Semi-Thue system

Supersilver ratio

In mathematics, the supersilver ratio is a geometrical proportion close to. Supergolden ratio and supersilver ratio are cubic irrational numbers, history of geometry, integer sequences and mathematical constants.

See Supergolden ratio and Supersilver ratio

Symmetry (journal)

Symmetry is a monthly peer-reviewed open access scientific journal published by MDPI covering several aspects of theories and applications related to symmetry/asymmetry phenomena in the natural sciences.

See Supergolden ratio and Symmetry (journal)

The Mathematical Gazette

The Mathematical Gazette is a triannual peer-reviewed academic journal published by Cambridge University Press on behalf of the Mathematical Association.

See Supergolden ratio and The Mathematical Gazette

Weber modular function

In mathematics, the Weber modular functions are a family of three functions f, f1, and f2,f, f1 and f2 are not modular functions (per the Wikipedia definition), but every modular function is a rational function in f, f1 and f2.

See Supergolden ratio and Weber modular function

Zero of a function

In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is a solution to the equation f(x).

See Supergolden ratio and Zero of a function

References

[1] https://en.wikipedia.org/wiki/Supergolden_ratio

Also known as Base psi, Base ψ, Base-psi, Base-ψ, Cows sequence, Narayana sequence, Super-golden ratio, Super-phi, Supergolden base, Supergolden ratio base, Supergolden rectangle, Superphi.

Supergolden ratio, the Glossary

Table of Contents

See also

Cubic irrational numbers

History of geometry

References