PYRAMIDAL NUMBERS Meaning and
Definition
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Pyramidal numbers are a series of numbers that form a pyramid-like shape when displayed in a visual representation. These numbers are obtained by arranging objects or elements in the form of stacked layers, with each layer containing a specific number of elements. The name "pyramidal" is derived from the characteristic shape that resembles a pyramid, with each subsequent layer having one more element than the layer above.
Mathematically, pyramidal numbers are defined in terms of a formula. The nth pyramidal number, denoted as P(n), can be calculated by summing the first n triangular numbers. A triangular number represents the sum of consecutive positive integers, starting from 1. Hence, the formula for pyramidal numbers can be written as P(n) = 1 + 2 + 3 + ... + (n-1) + n.
For example, the first few pyramidal numbers are 1, 4, 10, 20, 35, 56, and so on. Visually, these numbers can be represented by arranging objects in a triangular shape, where the number of objects in each row corresponds to the respective pyramidal number. The sum of the objects in each layer forms the pyramidal number.
Pyramidal numbers have various applications in mathematics, including number theory, combinatorics, and geometric patterns. They also find applications in real-world scenarios, such as calculating the number of balls required to build a stacked pyramid or determining the arrangements of objects in a pyramidal shape.
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Numbers resulting from the successive sums of polygonal numbers.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.
Common Misspellings for PYRAMIDAL NUMBERS
- oyramidal numbers
- lyramidal numbers
- -yramidal numbers
- 0yramidal numbers
- ptramidal numbers
- pgramidal numbers
- phramidal numbers
- puramidal numbers
- p7ramidal numbers
- p6ramidal numbers
- pyeamidal numbers
- pydamidal numbers
- pyfamidal numbers
- pytamidal numbers
- py5amidal numbers
- py4amidal numbers
- pyrzmidal numbers
- pyrsmidal numbers
- pyrwmidal numbers
- pyrqmidal numbers
Etymology of PYRAMIDAL NUMBERS
The term "pyramidal numbers" comes from the geometric shape of a pyramid. In mathematics, pyramidal numbers refer to a sequence of numbers that can be arranged in the shape of a pyramid. The base of the pyramid consists of a row of consecutive numbers, and each successive layer is formed by adding an extra number to the base. The word "pyramidal" is derived from the Latin word "pyramis" which means pyramid.
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