Euler's Exponentials - Professor Raymond Flood

Leonhard Euler was the most prolific mathematician of all time. He introduced the symbols e for the exponential number f for a function and i for √-1. He discovered what many mathematicians consider to be the most beautiful expression in mathematics, e ix = cosx + i sinx: a relation connecting the exponential and trigonometric functions. The exponential function and its inverse the logarithm function appear throughout mathematics and its applications, in physics, engineering, mathematical biology, chemistry and economics.

[NoActuallyGo-KCUF-Yourself]

I can't get enough of Prof. Flood.
These are so good!

[kevinobrien]

Quote "We have not the slightest idea of what this equation means, but we may be certain that it means something very important"

This is why we love this stuff! That quote to my mind, sums up the mystery and excitement of the pursuit of knowledge. Superb quote.

[alastairbateman]

Euler discovered the identity 158^4 = 134^4 + 133^4 - 59^4 . Checking it out on my calculator from memory I input 159^4 -134^4 -133^4 = 3810304 which is 1952^2. Removing the two common terms from both equations gives 159^4 = 158^4 +59^4 +1952^2. So there you have it, a trio of interrelated quadruples I have called Euler - Bateman quadruples. They are in fact Pythagorean quadruples. Many similarly related trios are also found in cubic quadruples.
At the time I had this strange feeling that Euler was whispering in my ear but alas I didn't know what he was saying as I can't speak German.
An excellent lecture that was easy to follow and listen to.

[qcislander]

About that Irish Coffee question: the trick to keeping the cup/glass warm the longest is to WHIP the cream just enough to incorporate air at 20-25% by volume, and let the cream integrate slowly into the coffee as its whipping fails.

While it still sits atop the coffee with air emulsified in it, the cream will greatly slow heat loss from the entire top surface of the coffee. :-)

[Ratsonic]

Any engineering student will agree that Euler is the go to dude in structural support column acceptable load to prevent catastrophe.

[dnickaroo]

Yes, he brilliantly brought back the mystery with i^i

[sloaiza]

Anybody know where to get the full version of the image shown at the 8 min mark?

[andywander]

What if you took the milk out of the refrigerator, and either added it immediately, or left the milk out for 30 minutes and then added it?

[shuvamghosh]

thank you, sir, for your great lecture

[MagruderSpoots]

39:30 more detail at this point would have been helpful for me, such as some additional terms in the cos n(theta) series.

[DaveGeelen]

24.40 Now we come to the most important part, witch is, :p

[providedrailroad]

United States here - had no issues with the dialect. Quite enjoyed the lecture.

[WahranRai]

Euler, the swiss quality.
The father of russian mathematics school

[Imaginose]

What if you put in milk before you put in coffee?

[raulariza]

Profesor your voice goes away, i cannot understand the end of your sentences.

[rahul]

great video..i think it was north east of england accent.

[Timmmmartin]

"... one of histories greatest mathematicians" should read "... one of history's greatest mathematicians" or rather "... history's greatest mathematician".

[drbonesshow]

Not being an Englishman, it was not easy to follow the dialect.