Concept
Square root of 2
Overview
The square root of 2 (approximately 1.4142) is the positive real number that, when multiplied by itself or squared, equals the number 2. It may be written as
2
{\displaystyle {\sqrt {2}}}
or
2
1
/
2
{\displaystyle 2^{1/2}}
. It is an algebraic number, and therefore not a transcendental number. Technically, it should be called the principal square root of 2, to distinguish it from the negative number with the same property.
Geometrically, the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. The fraction 99/70 (≈ 1.4142857) is sometimes used as a good rational approximation with a reasonably small denominator.
Sequence A002193 in the On-Line Encyclopedia of Integer Sequences consists of the digits in the decimal expansion of the square root of 2, here truncated to 30 decimal places:
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
Thus, a habit is a habit of something, knowledge is knowledge of something, attitude is the attitude of something. So it is with all other relatives that have been mentioned. Those terms, then, are called relative, the nature of which is explained by reference to something else, the preposition 'of' or some other preposition being used to indicate the relation. Thus, one mountain is called great in comparison with…
Aristotle, The Categories
States what Square root of 2 is; the author is tied to Square root of 2 in the knowledge graph.
Very true. But is this the only thing which is called odd? Are there not other things which have their own name, and yet are 104 called odd, because, although not the same as oddness, they are never without oddness?—that is what I mean to ask—whether numbers such as the number three are not of the class of odd. And there are many other examples: would you not say, for example, that three may be called by its proper…
Plato, The dialogues of Plato in five volumes, Vol. 2
States what Square root of 2 is; the author is tied to Square root of 2 in the knowledge graph.
In union with itself, it does not by its nature produce anything imperfect or foreign. All its changes are defined; it either produces itself or the Decad, either the homogeneous or the perfect.
Plutarch, Selected Essays of Plutarch, Vol. II.
States what Square root of 2 is.
Philosophers who discussed Square root of 2
Related ideas
- Golden ratio
- History of India
- Integer
- Law of excluded middle
- Geometry
- Real number
- Natural number
- Reductio ad absurdum
- Plato
- Euclid's Elements
- Recursion
- Pythagorean theorem
- Pythagoreanism
- Triangle
- Aristotle
- Berlin
- Babylonia
- Prior Analytics
- Complex number
- Algorithm
- Decimal
- Ratio
- Euclid
- Hippasus
Place in the tradition
Part of Philosophy of mathematics.