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Tent function, often used in signal processing
A triangular function (also known as a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle. Often
Triangular_function
Figurate number
The triangular numbers or triangle numbers are the sequence of positive integers that can be represented as a lattice of points arranged in an equilateral
Triangular_number
Probability distribution
The symmetric triangular distribution is commonly used in audio dithering, where it is called TPDF (triangular probability density function). Trapezoidal
Triangular_distribution
Function whose graph is 0, then 1, then 0 again, in an almost-everywhere continuous way
The rectangular function (also known as the rectangle function, rect function, Pi function, Heaviside Pi function, gate function, unit pulse, or the normalized
Rectangular_function
Non-sinusoidal waveform
playing this file? See media help. A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise
Triangle_wave
Topics referred to by the same term
Tri or El Tricolor, nicknames of the Mexico national football team Triangular function, tri(t) Trichloroethylene Triple reuptake inhibitors Trisakti University
Tri
Type of mathematical function
piecewise constant function Boxcar function, Heaviside step function Sign function Triangular function An approximation to a known curve can be found by sampling
Piecewise_linear_function
Electronic test equipment used to generate electrical waveforms
of the most common waveforms produced by the function generator are the sine wave, square wave, triangular wave and sawtooth shapes. These waveforms can
Function_generator
Model in digital signal processing
{rect} (x)\ } is the rectangular function and t r i ( x ) {\displaystyle \mathrm {tri} (x)\ } is the triangular function. The effective frequency response
First-order_hold
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
Type of figurate number
properties of oblong, triangular, and square numbers. The number 10 for example, can be arranged as a triangle (see triangular number): But 10 cannot
Polygonal_number
Centered figurate number that represents a triangle with a dot in the center
OEIS). If the centered triangular numbers are treated as the coefficients of the McLaurin series of a function, that function converges for all | x |
Centered_triangular_number
Anatomical feature in the wrist
The triangular fibrocartilage complex (TFCC) is formed by the triangular fibrocartilage discus (TFC), the radioulnar ligaments (RULs) and the ulnocarpal
Triangular_fibrocartilage
Psychological theory by Robert Sternberg
The triangular theory of love is a theory of love developed by Robert Sternberg. In the context of interpersonal relationships, "the three components of
Triangular_theory_of_love
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Natural number
is the 46th triangular number and a member of Padovan sequence. 1086 = 2 × 3 × 181. It is a Smith number and the sum of totient function for the first
1000_(number)
Square of a triangular number
number theory, the sum of the first n cubes is the square of the nth triangular number. That is, 1 3 + 2 3 + 3 3 + ⋯ + n 3 = ( 1 + 2 + 3 + ⋯ + n ) 2
Squared_triangular_number
Result of repeatedly applying a mathematical function
In mathematics, an iterated function is a function that is obtained by composing another function with itself two or several times. The process of repeatedly
Iterated_function
Integer that is both a perfect square and a triangular number
In mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a square number, in other words
Square_triangular_number
Recursive integer sequence
binomial coefficients, by Stirling's approximation for n!, or via generating functions. The only Catalan numbers Cn that are odd are those for which n = 2k −
Catalan_number
Product of an integer with itself
integer Quadratic function – Polynomial function of degree two Square triangular number – Integer that is both a perfect square and a triangular number Some
Square_number
Ten raised to an integer power
Centered nonagonal Centered decagonal Star non-centered Triangular Square Square triangular Pentagonal Hexagonal Heptagonal Octagonal Nonagonal Decagonal
Power_of_10
Method of representing curves and surfaces in computer graphics
non-zero. As mentioned before, N i , 1 {\displaystyle N_{i,1}} is a triangular function, nonzero over two knot spans rising from zero to one on the first
Non-uniform_rational_B-spline
Numbers with a certain property involving recursive summation
eventually reaches 1 when iterated over the perfect digital invariant function for p = 2 {\displaystyle p=2} . The origin of happy numbers is not clear
Happy_number
Integer having a non-trivial divisor
Sieve of Eratosthenes Table of prime factors Divisor function Prime omega function Möbius function Pettofrezzo & Byrkit 1970, pp. 23–24. Long 1972, p. 16
Composite_number
speed, -w. Assuming the fundamental diagram (flow-density) is a triangular function, a traffic state A with speed vA and density kA can be assumed in
Newell's_car-following_model
Number used for counting
a list of objects in a specific order. More precisely, a sequence is a function that assigns an object to each position in that list. The positions themselves
Natural_number
Coordinate system that is defined by points instead of vectors
coordinates are extremely useful in engineering applications involving triangular subdomains. These make analytic integrals often easier to evaluate, and
Barycentric_coordinate_system
Natural number
prime 2699 – Sophie Germain prime 2701 – triangular number, super-Poulet number 2702 – sum of the totient function for the first 94 integers 2707 – strong
2000_(number)
Number divisible only by 1 and itself
the zeros of the Riemann zeta function ζ ( s ) {\displaystyle \zeta (s)} are located. This function is an analytic function on the complex numbers. For
Prime_number
Special function in the physical sciences
mathematics, the Airy function (or Airy function of the first kind) A i ( x ) {\displaystyle \mathbf {Ai({\boldsymbol {x}})} } is a special function named after
Airy_function
Class of natural numbers with many divisors
{d(n)}{n^{\varepsilon }}}\geq {\frac {d(k)}{k^{\varepsilon }}}} where d(n), the divisor function, denotes the number of divisors of n. The term was coined by Ramanujan
Superior highly composite number
Superior_highly_composite_number
{\displaystyle {\frac {1}{2^{n+1}}}\cdot \delta } . The triangular function is a refinable function. B-spline functions with successive integral nodes are refinable
Refinable_function
Spline function
ranges. For example, B i , 1 ( x ) {\displaystyle B_{i,1}(x)} is a triangular function that is zero below x = t i {\displaystyle x=t_{i}} , ramps to one
B-spline
Function whose domain is the positive integers
prime-counting functions. This article provides links to functions of both classes. An example of an arithmetic function is the divisor function whose value
Arithmetic_function
y}}} . So the derivation of triangular codes of a function F ( x ) {\displaystyle F(x)} consists in determining the triangular code of the partial derivative
Computer for operations with functions
Computer_for_operations_with_functions
Polyhedral number representing a tetrahedron
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a
Tetrahedral_number
Numbers arranged in a triangle
In mathematics and computing, a triangular array of numbers, polynomials, or the like, is a doubly indexed sequence in which each row is only as long as
Triangular_array
Mathematical form
convolution. Under the Fourier transform, convolution becomes point-wise function multiplication. The product of two polynomials is given by the following:
Product_(mathematics)
Integers occurring in the coefficients of the Taylor series of 1/cosh t
Taylor series expansions of the secant and hyperbolic secant functions. The latter is the function in the definition. They also occur in combinatorics, specifically
Euler_number
Topics referred to by the same term
statistics Hat operator, notation used in mathematics Hat function, alternate name for the triangular function The hat tile, a solution to the einstein problem
Hat_(disambiguation)
Integer filtered out using a sieve similar to that of Eratosthenes
Centered nonagonal Centered decagonal Star non-centered Triangular Square Square triangular Pentagonal Hexagonal Heptagonal Octagonal Nonagonal Decagonal
Lucky_number
Scale-free network generation algorithm
spectral density is not an exact triangular function by analyzing the moments of the spectral density as a function of the power-law exponent. Model A
Barabási–Albert_model
Description of continuous random distribution
probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function whose value at any given
Probability_density_function
Main external rotator of the shoulder
thick triangular muscle which occupies the chief part of the infraspinatous fossa. As one of the four muscles of the rotator cuff, the main function of the
Infraspinatus_muscle
Formal power series
generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often
Generating_function
Repeated sum of a number's digits
which allows it to be used as a divisibility rule. The formula for the function d r b : N → ⋃ k = 0 b − 1 { k } , b ∈ N ⩾ 2 {\displaystyle \mathrm {dr}
Digital_root
Number equal to the sum of its proper divisors
_{1}(n)=2n} where σ 1 {\displaystyle \sigma _{1}} is the sum-of-divisors function. This definition is ancient, appearing as early as Euclid's Elements (Book
Perfect_number
Arithmetic operation
example, if f is a function whose valued can be multiplied, f ∘ n {\displaystyle f^{\circ n}} denotes exponentiation with respect to function composition, whereas
Exponentiation
Numbers obtained by adding the two previous ones
that 8 and 144 are the only such non-trivial perfect powers. The only triangular Fibonacci numbers are 1, 3, 21, and 55, which was conjectured by Vern
Fibonacci_sequence
Type of symmetric key cipher
function. Instead of a linear driving device, one may use a nonlinear update function. For example, Klimov and Shamir proposed triangular functions (T-functions)
Stream_cipher
Count of permutations by cycles
factorial function, n ! = n ( n − 1 ) ( n − 2 ) ⋯ 2 ⋅ 1 {\displaystyle n!=n(n-1)(n-2)\cdots 2\cdot 1} , we may extend this notion to define triangular recurrence
Stirling numbers of the first kind
Stirling_numbers_of_the_first_kind
Centered figurate number that represents a decagon with a dot in the center
centered decagonal number can be reckoned by multiplying the (n − 1)th triangular number by k, 10 in this case, then adding 1. As a consequence of performing
Centered_decagonal_number
Number that represents a hexagon with a dot in the center
centered hexagonal number for n is 1 more than 6 times the (n − 1)th triangular number. In the opposite direction, the index n corresponding to the centered
Centered_hexagonal_number
Number used to approximate the square root of 2
approximate the square root of two, Pell numbers can be used to find square triangular numbers, to construct integer approximations to the right isosceles triangle
Pell_number
Iterative algorithm on numbers
sequence. Repeat step 2. The sequence is called a Kaprekar sequence and the function K b ( n ) = α − β {\displaystyle K_{b}(n)=\alpha -\beta } is the Kaprekar
Kaprekar's_routine
Product of the first "n" prime numbers
# {\displaystyle p_{n}\#} ", is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying
Primorial
Mathematical function used in cryptography
a T-function is called triangular. Thanks to their bijectivity (no collisions, therefore no entropy loss) regardless of the used Boolean functions and
T-function
Concept in combinatorics
Centered nonagonal Centered decagonal Star non-centered Triangular Square Square triangular Pentagonal Hexagonal Heptagonal Octagonal Nonagonal Decagonal
Cake_number
Type of figurate number
number is a triangular number, but only every other triangular number (the 1st, 3rd, 5th, 7th, etc.) is a hexagonal number. Like a triangular number, the
Hexagonal_number
Sum of a number's digits
Encyclopedia of Integer Sequences. Borwein & Borwein (1992) use the generating function of this integer sequence (and of the analogous sequence for binary digit
Digit_sum
Numbers that evenly divide powers of 60
the harmonic whole numbers. Wikifunctions has a regular number checking function. Algorithms for calculating the regular numbers in ascending order were
Regular_number
Infinite integer series where the next number is the sum of the two preceding it
− 4 ( 18 ) + 6 {\displaystyle 256=322-4(18)+6} The ordinary generating function of the sequence of Lucas numbers is the power series Φ ( x ) = ∑ k = 0
Lucas_number
Number raised to the third power
n × n × n. The cube function is the function x ↦ x3 (often denoted y = x3) that maps a number to its cube. It is an odd function, as (−n)3 = −(n3). The
Cube_(algebra)
Two raised to an integer power
Centered nonagonal Centered decagonal Star non-centered Triangular Square Square triangular Pentagonal Hexagonal Heptagonal Octagonal Nonagonal Decagonal
Power_of_two
Triangular array of the binomial coefficients
7\quad 1\end{array}}} In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability
Pascal's_triangle
Mathematical approximation of a function
of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the
Taylor_series
Numbers parameterizing ways to partition a set
second kind can be understood as inverses of one another when viewed as triangular matrices. This article is devoted to specifics of Stirling numbers of
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
Product of two prime numbers
where π ( x ) {\displaystyle \pi (x)} is the prime-counting function and p k {\displaystyle p_{k}} denotes the kth prime. To see this, take
Semiprime
Product of numbers from 1 to n
The superfactorials are continuously interpolated by the Barnes G-function. Triangular number Just as the n {\displaystyle n} th factorial is the product
Factorial
Mathematical transform that expresses a function of time as a function of frequency
takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output
Fourier_transform
Figurate number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns
Pentagonal_number
Upper bound on intersecting set families
through any single point. A signed set consists of a set together with sign function that maps each element to { 1 , − 1 } {\displaystyle \{1,-1\}} . Two signed
Erdős–Ko–Rado_theorem
Natural number
preceding 232. 231 is a sphenic number. 231 is the 21st triangular number, a doubly triangular number, a hexagonal number, an octahedral number and a centered
231_(number)
Mathematical sequences in combinatorics
understood to be matrix inverse relationships. That is, let s be the lower triangular matrix of Stirling numbers of the first kind, whose matrix elements s
Stirling_number
Mathematical proportionality to a square
polynomial. Certain integer sequences such as the triangular numbers. The n {\displaystyle n} th triangular number has value n ( n + 1 ) / 2 {\displaystyle
Quadratic_growth
Number that remains the same when its digits are reversed
Centered nonagonal Centered decagonal Star non-centered Triangular Square Square triangular Pentagonal Hexagonal Heptagonal Octagonal Nonagonal Decagonal
Palindromic_number
Material used to support a medical dressing or injured body part
the patient is in a resting position. Also known as a cravat bandage, a triangular bandage is a piece of cloth put into a right-angled triangle, and often
Bandage
Shape with three sides
generalized notion of triangles known as the simplex, and the polytopes with triangular facets known as the simplicial polytopes. Each triangle has many special
Triangle
Result of multiplying four instances of a number together
v t e Figurate numbers 2-dimensional centered Centered triangular numbers Centered square numbers Centered pentagonal numbers Centered hexagonal numbers
Fourth_power
Odd number with specific properties
Centered nonagonal Centered decagonal Star non-centered Triangular Square Square triangular Pentagonal Hexagonal Heptagonal Octagonal Nonagonal Decagonal
Sierpiński_number
Size of a geometric arrangement of points
different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions
Figurate_number
Number that is the result of operation on its own digits
Centered nonagonal Centered decagonal Star non-centered Triangular Square Square triangular Pentagonal Hexagonal Heptagonal Octagonal Nonagonal Decagonal
Friedman_number
Composite number in number theory
{\displaystyle m} if and only if the n {\displaystyle n} th-power-raising function p n {\displaystyle p_{n}} is an endomorphism on every ( Z / n Z ) {\displaystyle
Carmichael_number
Type of matrix factorization
decomposition which decomposes a matrix into a lower triangular matrix (L), an upper triangular matrix (U) and, although not always needed, a permutation
Crout_matrix_decomposition
Number of form 2^(2^p-1)-1 with prime exponent
number is known as a "Martian prime". Cunningham chain Double exponential function Fermat number Perfect number Wieferich prime Chris Caldwell, Mersenne Primes:
Double_Mersenne_number
Counts pieces of a disk cut by lines
{n}{0}}+{\dbinom {n}{1}}+{\dbinom {n}{2}}.} Simply put, each number equals a triangular number plus 1. These are the first number on each row of Floyd's triangle
Lazy_caterer's_sequence
Concept in number theory
Let n {\displaystyle n} be a natural number. We define the narcissistic function for base b > 1 {\displaystyle b>1} F b : N → N {\displaystyle F_{b}:\mathbb
Narcissistic_number
Rare neurodevelopmental disorder
Many individuals exhibit distinctive craniofacial features such as a triangular or elongated face, high anterior hairline, almond‑shaped or deep‑set eyes
Chopra–Amiel–Gordon_syndrome
Natural number, composite number
vertices and 14 triangular faces, respectively. Steffen's polyhedron, the simplest flexible polyhedron without self-crossings, has 14 triangular faces. A regular
14_(number)
Number in the 5th cell of any row of Pascal's triangle
number theory, a pentatope number (or hypertetrahedral number or triangulo-triangular number) is a number in the fifth cell of any row of Pascal's triangle
Pentatope_number
Number, non-palindrome after repeated sum with reverse
number. Let n {\displaystyle n} be a natural number. We define the Lychrel function for a number base b > 1, F b : N → N {\displaystyle F_{b}:\mathbb {N} \rightarrow
Lychrel_number
Polynomial sequence
{\textstyle n-1} for n > 0 {\textstyle n>0} . A tabulation of the numbers in a triangular array is called the Euler triangle or Euler's triangle. It shares some
Eulerian_number
Mathematical function
In mathematics, Hooley's delta function, also called Erdős--Hooley delta-function, defines the maximum number of divisors of n {\displaystyle n} in [ u
Hooley's_delta_function
Natural number
a zero of Mertens function, and the smallest number that is the product of an emirp pair. 404 = 22 × 101, a zero of Mertens function, a nontotient and
400_(number)
Arithmetic function related to the divisors of an integer
theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number
Divisor_function
Natural number
the eighth triangular number or the sum of the first eight non-zero positive integers, which makes 36 the first non-trivial square triangular number. Aside
36_(number)
in idealizations studied by geometers, or in triangular arrays such as Pascal's triangle or triangular matrices, or concretely in physical space. It
List_of_triangle_topics
Count of the possible partitions of a set
exponential function and the nonemptiness constraint ≥1 into subtraction by one. An alternative method for deriving the same generating function uses the
Bell_number
Chinese national flag (1889–1912)
Banners hierarchy, he instead removed one corner to create a triangular flag. The triangular version of the yellow dragon flag was restricted to naval and
Flag_of_the_Qing_dynasty
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