e to the i pi

After (yet another) false start I present my corrected attempt to explain why e to the i pi = -1

Category:

Entertainment

Tags:

• e
• i
• pi
• imaginary
• number
• differentiation

[AMarsden95]

wehn x=3, then 2x=6, not 3!!

[Frege100]

You know about typo's then. Thanks for pointing it out, though.

[lewbloch]

@FlorPerezLascano No, it couldn't. The definition of "rational" is "expressible as the quotient of two integers. There are no such integers that yield the exact value of pi. Thus, by definition, pi is irrational.

[sk8rdman]

@FlorPerezLascano You can't find pi simply by measuring the circumference and diameter of circular objects and dividing. No object is perfectly circular, and measurement would never be exactly correct, at least not with any tools we could use at home. The methods used to find the value of pi often use what we know about other theorems and equations. We find it not by trial and error, but by mathematical proofs. I know of one equation to find pi using trig functions, but it can only approximate.

[JoeJoeTater]

Is pi within the intervals of convergence of the power series expansions of e^x, sin(x), and cos(x)? I am being lazy i will go check...

[FlorPerezLascano]

Couldn't it be that pi is rational but all methods to calculate it are prone to give us irrationals? Please reply if you can explain this... I'm dying to know!!

[FlorPerezLascano]

Afterwards I read different ways of calculating pi but of all of them tend to find an irrational. So I wonder: is pi really irrational or are the formulas just taking us there? I was told by an advanced maths student that Niven's demontration of pi's irrationality is not related at all to the circumference. So, may be there is an irrational pi, but how can we be certain that the circumference divided by it's diameter is that same irrational number?

[FlorPerezLascano]

IF PI = CIRCUMFERENCE / DIAMETER, WHY IS PI IRRATIONAL?(I'm not a mathematician). If pi is irrational, then the circumference or the diameter or both are irrational. But if I imagine the historic process by which the concept pi was born, it's impossible to get an irrational pi by taking meassures of circumferences and diameters at home (unless there are simple ways of getting irrational numbers when meassuring).

[jakehr3]

good video. i'm taking AP Calculus BC and this is probably one of the most fascinating formulas, when x= pi for e((i)(x))=cos(x) + isin(x), then e^((i)(pi)) + 1 = 0. Just beautiful.

[AMarsden95]

this better be good!!