Constants

[noz92]

I have already made a post for this, but that was in early October, and would be hard to find in all of the more recent posts. I wanted to know what the uses of the mathematical constants [math]\pi[/math], [math]e[/math], [math]y[/math], and [math]\phi[/math] are for, and what there uses are. For example, I know that [math]C=\pi r2[/math], and that [math]A= \pi r^2[/math], and that [math]\pi[/math] is aproximatly equal to [math]3.1415[/math]. So, I guess I understand [math]\pi[/math] pretty well. But I have no idea about [math]y[/math] [math]e[/math] or [math]\phi[/math].

[NSX]

I'm not sure what y is myself.

 

e is the natural log.

It's defined as the area under curve of y=1/x, bounded 1 and some number, e, such that the area is 1.

 

phi is the golden ratio.

I haven't applied phi anywhere in my studies yet, but I remember a SFN thread talking about it.

[noz92]

Do you remember what thread it was, maybee I can look it up?

[bloodhound]

hmm. if u think pi is all about area and circumference of a cricle, then you arent that familiar with it after all.

 

Pi is a important constatnt that crops up, once you try to define an angle and length in an euclidian space..

[JaKiri]

e is a number which is invariant in certain differal and integral calculus calculations.

 

Int e^x dx = e^x, de^x/dx = e^x.

[noz92]

Well, yes, I knew that [math]\pi[/math] was used for that, but I didn't exactly understand how it's used. I've done a thread on [math]\sin[/math] and [math]\cos[/math], and noticed that [math]\pi[/math] was used there a few times, but I didn't understand it (it would also help if Irken_Link would give me back my calculator [laugh]). That's why I did put [math]\pi[/math] up there with [math]e[/math], [math]y[/math], and [math]\phi[/math], because all I know about [math]\pi[/math] is that it helps in the circunfrence and area of a circle.

[noz92]

But what does [math]e[/math] equal? I think (I don't know if I'm correct, that's why I'm asking) [math]e[/math] is aproximatly equal to [math]2.17[/math]. Is that right. And does anybody know how to do aproximatly in [math]$L^AT^EX$[/math]?

[bloodhound]

there are vairous forms of writing e.

the infinite series

[math]\sum_{n=0}^{\infty}\frac{1}{n!}[/math]

 

or in terms of limit

 

[math]\lim_{n\to \infty}(1+\frac{1}{n})^n[/math]

 

more stuff on e can be found here

 

http://mathworld.wolfram.com/e.html

[noz92]

deleted

[CPL.Luke]

I thought lowercase theta was used as a counterpart to the uppercase theta, in relation to angles

 

Pi comes up in trigonometry (sin,cos,tan etc.) because a common way of measuring angles is in radians. basicly a radian is an angle where the angle measure is lage enough that the arc length is equal to the radius. since Pi is the ratio of a circles diameter to its circumference, there are 2Pi radians in a circle. an angle measured at 180 degrees is equal to Pi radians, an angle measured at 90 degrees is equal to Pi/2 radians. you will never see a decimal approximation when working with radians and you will always see them measured with units of pi. this is partially to do with accuracy because any decimal of Pi is an approximation, so if you continually converted radians into decimals you would lose accuracy.

 

also just wondering but I had heard that a method of calculating pie was by using inscribed polygons, and this led to it being an irrational number. has anyone ever tried to use integral calculus to find an exact value of it?

 

or is there more to its irrationality than that?

also its C=Pi r squared not Pi r 2 (just in case that wasn't a typo)

 

Ps. how do you make it write out the formulas properly?

[Dave]

also just wondering but I had heard that a method of calculating pie was by using inscribed polygons' date=' and this led to it being an irrational number. has anyone ever tried to use integral calculus to find an exact value of it?

 

or is there more to its irrationality than that?

also its C=Pi r squared not Pi r 2 (just in case that wasn't a typo)

 

Ps. how do you make it write out the formulas properly?[/quote']

 

I think the method used to calculate pi originally was to use circumscribed and inscribed polygons, but I can't remember the specifics. You can't find an "exact" value for pi because it's irrational: it's like trying to find a exact value for [math]\sqrt{2}[/math].

 

As far as the formulae go, take a look at the quick latex tutorial in General Mathematics.

[CPL.Luke]

I was asking because that method seems flawed, using inscribed polygons with ever increasing numbers of sides would forever be trying to approximate it, it would seem that if you tried using integral calculus on it you would get an exact value

or even if the numbers irrational value was native it would seem that integral calculus would provide a more accurate value

oh yeah I was mistaken in believing that the greek letter was a lowercase theta it really was an uppercase phi here is the wikipedia article on it and its many uses in mathmatics and physics

http://en.wikipedia.org/wiki/Phi_%28letter%29

http://en.wikipedia.org/wiki/Golden_ratio#Definition_of_the_Golden_Ratio

[bloodhound]

the polygon method is just reimann integration, thats how must of the integration is done for simple curves.

[noz92]

also its C=Pi r squared not Pi r 2 (just in case that wasn't a typo)

 

No' date=' here's what my algebra book says:

 

The perimiter of a circle is given a special name, circumference, C, and

 

[math]C=\pi d[/math],

 

where [math]\pi[/math] stands for a number that is aproximately equal to ([math]\doteq[/math]) [math]\frac{22}{7}[/math] and [math]d[/math] is the measure of the diameter.

down to another section of the book

[math]C=2\pi r[/math], [math]r[/math] is the mesure of the radius

[math]\pi r^2[/math] is the measurment of the area.

 

And why isn't my italic working properly?

[CPL.Luke]

why not use integration by the fundamental theorem? isn't that simpler and more accurate?

[bloodhound]

that probably cos u will just get [math]\pi[/math] instead of the number ur looking for

[noz92]

So, how is [math]\pi[/math] used in trigonometry?

[CPL.Luke]

as a unit of measure (radians)

 

there are 2Pi radians in a circle

 

360 degrees is equal to 2Pi radians

180 degrees is equal to Pi radians

90 degrees is equal to Pi/2 radians

45 degrees is equal to Pi/4 radians

etc.

http://en.wikipedia.org/wiki/Radians

more on radians

 

but in trig radians are basicly used to measure angles

[bloodhound]

bit embarassing to say that I honestly dont know much about how pi is used in trigonometry.

[CPL.Luke]

oh yeah sorry about that I'm just used to hearing it C=2Pi r rather than C=Pi r2 and I converted it to the area equation in my head.

[noz92]

So, what exactly is a radian? And how do they help us?

[JaKiri]

It's a measure of rotation, as is the degree.

 

They're used because they make some triganometric calculations infinitely easier.

[noz92]

So, what does [math]\pi[/math] have to do with it? I understand what you guys were saying before, but I just don't understand what [math]\pi[/math] has to do with radians.

[jordan]

Pi is used in radians because the circumfrence of a circle is found by the equation C=2(pi)r. Sub in 1 for the radius and the circumfrence of the cirle is 2 pi (thus 180 ⁰) is pi radians. This is known as the unit cirle. Angles in any circle of larger or smaller diameter can simply be found by multiplying the measure of the angle in this unit circle by the new radius.

[noz92]

Oh.