The history of Euler's number e in 3 minutes! #mathfacts

The complete history of Euler's number e, detailing how the great mathematicians discovered the marvelous constant e=2.17.. over the ages!

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Timestamps:

0:00 - Intro
0:34 - The first reference to e
0:59 - How e was first discovered
1:20 - e was used to be called 'b'
1:32 - How the use of e was popularized
2:23 - How e became Euler's number

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[BoBoNUto]

I feel the fact that video isn't 2.71 minutes long is a missed opportunity

[theoriginalchefboyoboy]

Fun Fact: Euler, besides being a brilliant mathematician, was also an incurable coupon clipper. Yes, they had them way back when, and, upon his death more than 15 shoeboxes full of coupons for various merchants were discovered in his house, some as many as 5 years past expiration...

[sayandas]

That's not Goldbachs photo it's Reimann

[dinosaric]

One tip: don't use so much audio effects

[sanjayj]

PUK PUK sound is very much disturbing.

[Ruddigore]

A 3-minute video and I only made it halfway before switching off. It's not that the subject matter wasn't interesting, it was the barrage of very, VERY annoying sound effects. Sorry my friend but you really do need to have a re-think on your video presentation.

[JayTemple]

I only learned a few years ago that Euler did not name the number "e" after himself.

[JimCoder]

How can a video about Euler's number be made without mentioning that f(x)=eˣ is both its own derivative and its own integral?

[Zane_Alto]

Was about to lookup some videos to practice Double Integrals with Polar Coordinates but had to make a quick pitstop

[davidjohnston]

The decimals going on to infinity is not what makes it irratioanl. The decimals of 1/3 go on to infinity, but it's definitily not irrational.

[stevekerp]

Good content, my friend, but very annoying presentation. Next time, avoid the distracting sound effects that add nothing of value to the video.

[rsassine]

That would have been a wonderful video unfortunately those pops took the charms away.

[mtmdesigns]

I would have liked to continue watching, but the audio effects drove me away.

[donsena]

The natural base e can be derived implicitly from the development of the natural-growth function, describing the continuous growth of a mass like a bacterial colony over time.
You would start with step-wise growth, as in the case of bank interest, and eventually take the limit as the number of times compounded within a general time unit, like a year, approached infinity.
Then, with application of the general statement of the binomial theorem for positive integers, you would arrive at Sigma[1/n!], n=0 to n=infinity, = 1/0! + 1/1! + 1 /2! + 1/3! + …, a value to which symbol ‘e’ is assigned.
A reexamination of the development of this number would show that
e^x = x^0 / 0! + x^1 /1! + x^2 / 2! + x^3 / 3! + …
which would quickly lead to d(e^x)/dx = e^x. from which it can then be shown that the area under y= 1/x, from x=1 to x=n, = log/e (n) <= ln (n).

[apburner]

So, Bernoulli stumbled upon a calculus equation that didn't exist for another how many years? Wow, that is talent.

[JaimeGutierrezSalazar]

There's a General Analytic Solution Method to solve the Knight's Tour Problem which can be applied on (4xm) boards for m > 4. To know more about it you may look for the 9 minutes video "YouTube · The Knight's Tour Problem: A Geometric Approach".
In 1759, Euler gave a presentation addressing this subject stating it did not seem to be subject to any analysis ... but it was, although most of the further attempts have been based on trial and error strategies, except the one I'm referring to ...

[lawrencejelsma]

He forgot the was defined in Integrals Calculus. For the function f(x) = 1/x the area under that function curve in a defined x>0 since 1/0 and Integrals of x > 0 to x<0 could not have a finite limit, especially at x= 0. Someone picked a lower bound x= 1 to an upper bound x>1 and needed to find the area of 1 unit under the f(x) = 1/x curve. Through delta summations to an x > 1 the area under the integral from 1 to this upper bound of 1 unit was calculated as x = e or approximately the 2.718... value students in modern life accept. Notice the Integral of Euler's of f(x) = 0^0/0! + 1^1/1! + 2^2! + 3^3/3! + ... also found this upper limit Integral value 2.718 ... that the integral of 1 to e formed an area of 1 unit.

[garrywright]

Good info, but the popping sounds and grunts are unnecessary and distracting.

[charlessupp]

Goldbach transformed into Bsrnhard Riemann somehow.😊

[KerrySoileau]

Very nice work. Just one correction: when you presented an image of Goldbach, you mistakenly used the face of Riemann.