This constant provides an approximate value for the square root of two (`sqrt(2)`). The `sqrt(2)` is an irrational number and appears very often in many scientific and mathematical applications.
An irrational number is anythat cannot be expressed as a ratio of . Irrational numbers are those real numbers that cannot be represented as terminating or . As a consequence of that the real numbers are and the rationals countable, it follows that real numbers are irrational.
When theof lengths of two line segments is irrational, the line segments are also described as being , meaning they share no measure in common.
Numbers which are irrational include the ratio of a circle's circumference to its diameter, Euler's number , the golden ratio , and the , in fact all square roots of natural numbers not being a are irrational.
It would seem that taking the square root of a number we have all know since childhood should result in something simple -- just because the number 2 is so close to our daily thoughts. We grab a couple of cookies from the cookie jar, I give Brutus (my golden) a couple of treats when he comes in out of the snow, I am in a relationship which makes me a partner in a "couple". Two is commonplace and I was at an early age capable of doubling just about any number within my grasp. So, it is a little magical and surprising to find that the `sqrt(2)` is irrational.
There is elegance in many simple mathematical concepts and no more elegant proof exists than the proof by contradiction. And no more representative application of such a proof-by-contradiction exists than that which proves the `sqrt(2)` is irrational. John Phillip Jones ofgives a thorough and . This video is worth watching for all those entering high school and college mathematics where proof-by-contradiction will enter into your mathematical tool box.