# Would you say e, pi and i are the most important non-integer numbers in mathematics?

• Elbobo
In summary, The conversation discusses the importance of various mathematical constants such as Euler's constants e^gamma and gamma, the golden ratio, zeta(3), zeta(2), Brun's constant, W(1), Catalan's G, and the imaginary unit i. The participants have different opinions on the importance of these constants, with some saying 1/2 is more important and others arguing for other numbers like 7/13. The conversation also touches on the use of these constants in different branches of mathematics such as calculus and quantum mechanics. Ultimately, the conversation ends with a discussion on the combination of these constants in the form of e^{i\pi} = -1.
Elbobo
That's what my Precal teacher said, and so far I agree with him (though that's not saying much as I've only been exposed up to Precal mathematics).

Do all of you mathematicians agree?

Yes.

Also important are Euler's constants e^gamma and gamma, the golden ratio, zeta(3), zeta(2), Brun's constant, W(1), Catalan's G, ...

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I'm pretty sure 1/2 is more important than any of those.

Elbobo said:
That's what my Precal teacher said, and so far I agree with him (though that's not saying much as I've only been exposed up to Precal mathematics).

Do all of you mathematicians agree?

I would say kind of because what they represent in words is important, but the number value they hold is arbitrary.

In the world of quantum mechanics this is certainly true, I would say that the order is:

1) e
2) i
3) pi

In precal math you often use e to solve financial problems of calculating continually compounding interest. In calculus you find that e is present anytime that the rate of growth of something is proportional to the current amount e.g. money, population, etc. In advanced group theory you find that the exponential e is involved with compounding the infinitesimal generators of the lie algebra (the tangent space at the identity) into the finite elements of the lie group (the entire manifold).

Pi is found everywhere because spheres and circles are the most symmetrical objects (they are defined to be that way).

The imaginary unit i is of similar importance as the real unit 1. In quantum mechanics i is more important than 1, but 1 is also more important than Pi.

Of course, the decimal representations of pi and e are of no importance.

Werg22 said:
I'm pretty sure 1/2 is more important than any of those.
I totally disagree. 7/13 is much more important than any of the above-mentioned numbers.

I thought 22/7 was pi?

The primes are important since they can be regarded as the basic building blocks of all integers

arildno said:
I totally disagree. 7/13 is much more important than any of the above-mentioned numbers.

I haven't seen 7/13 in many applications or mathematical/scientific literature. 1/2 on the other hand...

arildno why do you think 7/13 is important?

arildno why do you think 7/13 is important?

Because 6+7=13, whereas 6*7=42!
I thought that would have been obvious.

Oh thanks.Nice one.I used to drive a Ford Prefect.

The extended real numbers $\pm \infty$ are pretty darned important, as is projective infinity. Aleph-null too.

(0.1)^n are pretty important, at least if you consider the decimal representations we use every day to be a part of math!

Isn't there a better way to combine these?

$$e^{i\pi} = -1$$

waht said:
Isn't there a better way to combine these?

$$e^{i\pi} = -1$$

Yeah, that's the reason why he was discussing that in class =P

uman said:
(0.1)^n are pretty important, at least if you consider the decimal representations we use every day to be a part of math!

No, not really. :)

## 1. What is the significance of the numbers e, pi, and i in mathematics?

The numbers e, pi, and i are considered the most important non-integer numbers in mathematics because they have numerous applications in various fields of mathematics, science, and engineering. They also have unique properties that make them essential in many mathematical equations and concepts.

## 2. How is the number e related to exponential growth and decay?

The number e, also known as Euler's number, is commonly used to represent exponential growth and decay. It is the base of the natural logarithm and is used to model continuous growth or decay in various real-world scenarios, such as population growth, radioactive decay, and financial growth.

## 3. Why is pi often referred to as the "most famous" irrational number?

Pi, denoted by the Greek letter π, is the ratio of a circle's circumference to its diameter. It is an irrational number, meaning it cannot be expressed as a finite decimal or fraction. Pi has been studied for thousands of years and has numerous applications in geometry, trigonometry, and calculus, making it one of the most well-known and studied non-integer numbers in mathematics.

## 4. How is the imaginary number i used in mathematics?

The imaginary number i is defined as the square root of -1 and is used to represent complex numbers in mathematics. Complex numbers have both a real and imaginary part and are used in many fields, such as electrical engineering, quantum mechanics, and signal processing.

## 5. Are there any real-life applications of the numbers e, pi, and i?

Yes, there are numerous real-life applications of e, pi, and i in various fields. For example, e is used in compound interest calculations, pi is used in architecture and engineering to calculate the circumference and area of circles, and i is used in electrical engineering to analyze AC circuits. These numbers also have applications in physics, chemistry, and economics.

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