In this video, we explore the fascinating mathematical constant known as “e,” and try to answer the burning question on many students’ minds, “Why is e the natural number?” We’ll dive into the history and significance of e, and explore its relationship to calculus, and exponential growth.
Whether you’re a seasoned mathematician or just curious about the world of numbers, this video is sure to be an enlightening and entertaining journey into the world of e. So sit back, relax, and join us as we explore the math behind this incredible mathematical constant.
Thank you to: Mind Your Decision, Syber Math, and Zach Star. For years they’ve been making math interesting and inspired me to bring you the math behind interesting problems! 😁
#maths #calculus #naturalnumber
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3:06 The way you arranged nulbers is the singlemost diabolical thing any youtuber has ever done
I don't believe that e shows up everywhere. It certainly shows up in a lot of videos claiming that it shows up everywhere. It probably shows up a lot in numerical computation, for example in banking the computation required is (1+r)^N, e may become involved when a numerical answer is required, which may involve natural logarithms. What does show up everywhere is multiplicative growth and decay (b^x), but the chosen base b is seldom if ever e.
e always comes with i in physics
so technically pi is a natural number since it also shows everywhere in circles?
"The secret of the Universe is the Number e." – by Douglas Adams in The Hitchhiker's Guide to the Galaxy [Reviewed]. 😅
Best video about e I've seen. Thanks!
Dyk any natural phenomenon that progresses by a rhythm of exp curve?
becouse its Natural ?? Naturaly ?
what blew my mind is that SIN X CAN BE WRITTEN IN TERMS OF e
AND SO CAN SINH X
and therefore, all trigonometric and hyperbolic functions
(sin x = e^ix – e^-ix / 2i)
(sinhx= e^x-e^-x/2)
I believe it's because of how you can express complex numbers in cartesian form and polar form, polar form also involving… e
why is e there too
it's just annoying that it's that value. Just a random value with that property.
🤔
I rarely commented on youtube, but this video alone finally helps me understand what exactly e is. This was a thing I've avoided for years, and today, your video gives me crystal clear of clarity. Thank you so muchh!
i like this explanation for Euler's number. but i wish you had explained that part why we can express any exponential function in terms of e
get a different video editor. it's stupid how you move operators and numbers around into irrelevant steps
2:07 im sorry how do all the h variables cancel out? Like, wouldnt there be one left since theres a h ^2?
face reveal
Go algorithm
I’m a bit confused on how (2^h – 1) / h became .69314
Even simpler, $1.00 at 100% interest per year is $2.00
If the interest is calculated quarterly, it's $2.44
If the interest is calculated daily, it's $2.71
1 to 2 is a discreet doubling at the END of a time interval – while 1 to 2.71828… is a smooth compounded type of doubling when the growth happens continuously DURING the time interval. The number e is therefore "natural" because real world growth/change can be considered smooth processes.
I'm really hooked on this topic…can you make a video starting from the basics to everything covering 'e'?
Commenting for the algorithm
fire
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