Sphenic Acres of Space
In number theory, a sphenic number (from Ancient Greek: σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because of there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definition[edit source]
A sphenic number is a product pqr where p, q, and r are three distinct prime numbers. In other words, the sphenic numbers are the square-free 3-almost primes.
Examples[edit source]
The smallest sphenic number is 30 = 2 × 3 × 5, the product of the smallest three primes. The first few sphenic numbers are
As of October 2020 the largest known sphenic number is
- (282,589,933 − 1) × (277,232,917 − 1) × (274,207,281 − 1).
Acre
acre 
Comparison of some Imperial and metric units of areaGeneral information Unit system US customary units, Imperial units Unit of Area Symbol ac or acre Conversions 1 ac in ... ... is equal to ... SI units ≈ 4,046.9 m2 US customary, Imperial ≡ 4,840 sq yd
≡ 1⁄640 sq mi
The acre is a unit of land area used in the imperial and US customary systems. It is traditionally defined as the area of one chain by one furlong (66 by 660 feet), which is exactly equal to 10 square chains, 1⁄640 of a square mile, 4,840 square yards, or 43,560 square feet, and approximately 4,047 m2, or about 40% of a hectare. Based upon the international yard and pound agreement of 1959, an acre may be declared as exactly 4,046.8564224 square metres. The acre is sometimes abbreviated ac[1] but is usually spelled out as the word "acre".[2]
Traditionally, in the Middle Ages, an acre was conceived of as the area of land that could be ploughed by one man using a team of oxen in one day.[3]
The acre is still a statutory measure in the United States. Both the international acre and the US survey acre are in use, but they differ by only four parts per million (see below). The most common use of the acre is to measure tracts of land.
The acre is commonly used in a number of current and former British Commonwealth countries by custom only. In a few, it continues as a statute measure, although since 2010 not in the UK itself, and not since decades ago in Australia, New Zealand and South Africa. In many of those where it is not a statute measure, it is still lawful to "use for trade" if given as supplementary information and is not used for land registration.
| acre | |
|---|---|
 Comparison of some Imperial and metric units of area | |
| General information | |
| Unit system | US customary units, Imperial units |
| Unit of | Area |
| Symbol | ac or acre |
| Conversions | |
| 1 ac in ... | ... is equal to ... |
| SI units | ≈ 4,046.9 m2 |
| US customary, Imperial | ≡ 4,840 sq yd ≡ 1⁄640 sq mi |
The acre is a unit of land area used in the imperial and US customary systems. It is traditionally defined as the area of one chain by one furlong (66 by 660 feet), which is exactly equal to 10 square chains, 1⁄640 of a square mile, 4,840 square yards, or 43,560 square feet, and approximately 4,047 m2, or about 40% of a hectare. Based upon the international yard and pound agreement of 1959, an acre may be declared as exactly 4,046.8564224 square metres. The acre is sometimes abbreviated ac[1] but is usually spelled out as the word "acre".[2]
Traditionally, in the Middle Ages, an acre was conceived of as the area of land that could be ploughed by one man using a team of oxen in one day.[3]
The acre is still a statutory measure in the United States. Both the international acre and the US survey acre are in use, but they differ by only four parts per million (see below). The most common use of the acre is to measure tracts of land.
The acre is commonly used in a number of current and former British Commonwealth countries by custom only. In a few, it continues as a statute measure, although since 2010 not in the UK itself, and not since decades ago in Australia, New Zealand and South Africa. In many of those where it is not a statute measure, it is still lawful to "use for trade" if given as supplementary information and is not used for land registration.
Contents
Basis (linear algebra)
In mathematics, a set B of vectors in a vector space V is called a basis if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called basis vectors.
Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.[1] In other words, a basis is a linearly independent spanning set.
A vector space can have several bases; however all the bases have the same number of elements, called the dimension of the vector space.
This article deals mainly with finite-dimensional vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces.
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