The value of 1/sqrt(2)/2 is equal to 0.7071..., which can also be represented as 0.707 or as a fraction 710.
This expression is a type of irrational number, specifically, a non-terminating, non-repeating decimal. This means that the number will continue on after the decimal point without the digits ever repeating. Although the number is not exact, the rounded value of 1/sqrt(2)/2 is 0.707.
What is sqrt(2)?
Sqrt(2) is the square root of 2, or the number which, when multiplied by itself, equals 2. In mathematical terms, this is written as sqrt(2) or √2.
The square root of 2 is an irrational number, meaning that it cannot be expressed in terms of a fraction or repeated decimals. Its decimal expansion is non-terminating and non-repeating, shown here as 1.414213562…
How did mathematicians calculate 1/sqrt(2)/2?
Mathematicians were able to calculate the value of 1/sqrt(2)/2 by realising that the inverse (or opposite) of the square root of two would result in a multiplication by itself.
In mathematical terms, this is written as follows:
1/sqrt(2)/2 = (1*sqrt(2))/2 = (sqrt(2))/2
From here, one can further simplify the equation by dividing sqrt(2) by two, which results in the final value 1/sqrt(2)/2 = 0.707...
Why is 1/sqrt(2)/2 important?
The value of 1/sqrt(2)/2 is a well-known numerical constant with many interesting properties. Most notably, this value is used in many areas of mathematics including geometry, trigonometry, calculus, probability, and in the construction of mathematical models.
In particular, this value is important for computational geometry, which involves the crafting of geometric shapes and images using manipulation of numerical linear algebraic equations.
FAQs
What is the square root of two?
The square root of two is an irrational number (1.414213562...) which, when multiplied by itself, equals two. It is written mathematically as sqrt(2) or √2.
What is an irrational number?
An irrational number is a number that can not be expressed in terms of a fraction or repeated decimals. Its decimal expansion is non-terminating and non-repeating, meaning it continues on infinitely.
What is the inverse of sqrt(2)?
The inverse (opposite) of the square root of two is 1/sqrt(2).
How did mathematicians calculate 1/sqrt(2)/2?
To calculate the value of 1/sqrt(2)/2, mathematicians utilised the inverse (opposite) of the square root of two which resulted in a multiplication by itself. This led to the equation 1/sqrt(2)/2 = (1*sqrt(2))/2 = (sqrt(2))/2. Further simplification by dividing sqrt(2) by two resulted in the final value 1/sqrt(2)/2 = 0.707...
What is the value of 1/sqrt(2)/2?
The value of 1/sqrt(2)/2 is equal to 0.7071..., which can also be represented as 0.707 or as a fraction 710.