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Sum of consecutive (triangular) cubes (Nicomachus's theorem)

In number theory, the sum of the first n cubes is the square of the nth triangular number. The sequence of squared triangular numbers is

0, 1, 9, ... more

Sum of natural numbers raised to the fifth power

he formula is a special case of general Faulhaber’s formula and gives the sum of natural consecutive numbers raised to the fifth power,(starting with 1), ... more

Triangular Prism Volume

A triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.
... more

Geometric progression (nth term)

A geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous ... more

Arithmetic progression

An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant and is ... more

Geometric series (sum of the numbers)

A geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous ... more

Volume of a tetrahedron

A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. It has six edges and four ... more

Regular Icosahedron (Surface Area)

An icosahedron is a polyhedron with 20 triangular faces, 30 edges and 12 vertices. A regular icosahedron has 20 identical equilateral faces, with five of ... more

Regular Icosahedron (Volume)

An icosahedron is a polyhedron with 20 triangular faces, 30 edges and 12 vertices. A regular icosahedron has 20 identical equilateral faces, with five of ... more

Regular Icosahedron ( circumscribed sphere radius)

An icosahedron is a polyhedron with 20 triangular faces, 30 edges and 12 vertices. A regular icosahedron has 20 identical equilateral faces, with five of ... more

Regular Icosahedron ( midscribed sphere radius)

An icosahedron is a polyhedron with 20 triangular faces, 30 edges and 12 vertices. A regular icosahedron has 20 identical equilateral faces, with five of ... more

Regular Icosahedron ( inscribed sphere radius)

An icosahedron is a polyhedron with 20 triangular faces, 30 edges and 12 vertices. A regular icosahedron has 20 identical equilateral faces, with five of ... more

Triangle wave (in trigonometric terms)

A triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function. Like a square ... more

Standard deviation of any arithmetic progression

An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant and is ... more

Triangle Wave

A triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function.
Like a ... more

Height of a regular tetrahedron

The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. A ... more

Surface area of a regular tetrahedron

The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. A ... more

Regular Octahedron Area

An octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at ... more

Regular Octahedron Volume

An octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at ... more

Sum of natural numbers raised to the fourth power

The formula is a special case of general Faulhaber’s formula and gives the sum of natural consecutive numbers raised to the fourth power,(starting ... more

Wiswesser's rule

The Wiswesser rule gives a simple method to determine the energetic sequence of the atomic subshells (n,l). n is the principal quantum number and l is the ... more

Metcalfe’s Law

Metcalfe’s law states that the value of a telecommunications network is proportional to the square of the number of connected users of the system ... more

Fibonacci numbers

A recurrence relation is an equation that recursively defines a sequence, once one or more initial terms are given: each further term of the sequence is ... more

Permutation ( k-permutations of n)

Informally, a permutation of a set of objects is an arrangement of those objects into a particular order. The notion of permutation relates to the act of ... more

Sum of the infinite terms

A geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous ... more

Sum of consecutive (pyramidal) squares

In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square ... more

Resonant frequency of string

Acoustic resonance is the tendency of an acoustic system to absorb more energy when it is forced or driven at a frequency that matches one of its own ... more

Binomial distribution

Binomial distribution, with parameters n and p, is the discrete probability distribution of the number of successes in a sequence of n independent yes/no ... more

Weighted power mean

The weighted mean is similar to an arithmetic mean (the most common type of average), where instead of each of the data points contributing equally to the ... more

Heronian mean

The Heronian mean of two non-negative real numbers is a weighted mean of their arithmetic and geometric means.The weighted mean is similar to an ... more

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