What is an irrational number between 3 1/7 and 3 1/6?


An irrational number is one that cannot be expressed as a fraction. Pi is a famous irrational number. People have calculated Pi to over one million decimal places and still there is no pattern.

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A mathematical constant is a special number, usually a real number, that is "significantly interesting in some way". Constants arise in many different areas of mathematics, with constants such as e and π occurring in such diverse contexts as geometry, number theory and calculus.

What it means for a constant to arise "naturally", and what makes a constant "interesting", is ultimately a matter of taste, and some mathematical constants are notable more for historical reasons than for their intrinsic mathematical interest. The more popular constants have been studied throughout the ages and computed to many decimal places.

In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers and b is non-zero.

Informally, this means that an irrational number cannot be represented as a simple fraction. Irrational numbers are those real numbers that cannot be represented as terminating or repeating decimals. As a consequence of Cantor's proof that the real numbers are uncountable (and the rationals countable) it follows that almost all real numbers are irrational.

Pi Fraction E

This page is about the history of approximations for the mathematical constant pi (π). There is a table summarizing the πchronology of computation of . See also the πhistory of for other aspects of the evolution of our knowledge about mathematical properties of π.

The square root of 2, often known as root 2, radical 2, or Pythagoras's constant, and written as \sqrt{2}, is the positive algebraic number that, when multiplied by itself, gives the number 2. It is more precisely 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. Its numerical value truncated to 65 decimal places is:

Mathematics Numbers




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