This week you were introduced to the natural number e 2.718. In mathematics ther

Question

This week you were introduced to the natural number e 2.718. In mathematics there are several important numbers similar to e. You are likely familiar with the constant pi 3.14. For example: You are likely familiar with the constant pi 3.14. Do some research on either one of these two numbers, or, better yet, find another very important number in mathematics. Share with us what you have found out about the number, for example, its history, some trivial facts about the number, and/or how it is applied 150 words only

Explanation / Answer

The constant (pi) has a natural definition in Euclidean geometry (the ratio between circumference and diameter of a circle), but may be found in many places in mathematics e.g. the Gaussian integral in complex analysis, the roots of unity in number theory, and Cauchy distributions in probability. However, its universality is not limited to pure mathematics alone. Indeed, various formulae in physics, such as the cosmological constant include the constant . The presence of in physical principles, laws and formulae can have very simple explanations. The numeric value of is approximately 3.14159. Memorizing increasingly precise digits of is a world record pursuit.

The imaginary unit or unit imaginary number, denoted as i, is a mathematical concept which extends the real number system R to the complex number system C, which in turn provides at least one root for every polynomial . The imaginary unit's core property is that i2 = 1. The term "imaginary" is used because there is no real number having a negative square.

There are in fact two complex square roots of 1, namely i and i, just as there are two complex square roots of every other real number, except zero, which has one double square root.

At first, imaginary numbers were considered useless (an imaginary number is a number that, when squared, gives a negative result; e.g. 5i2= -25). But by the Enlightenment Era, thinkers began to demonstrate its value in math and geometry, including Leonhard Euler, Carl Gauss, and Caspar Wessel (who used it when working with complex planes). i is used to find the square root of a real negative number. Today, i is used in signal processing, control theory, electromagnetism, fluid dynamics, quantum mechanics, cartography, and vibration analysis.

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