Why e Is Everywhere | Euler’s Number Explained
Aion
23,563 views
In this video, we build Euler’s number *e* from first principles, starting with compound interest and continuous growth. Then we see why the exponential function \(e^x\) is unique, why its derivative equals itself, and why the same mathematical structure keeps appearing across seemingly unrelated problems.
By the end, you’ll see why *π naturally belongs to circles, while e naturally belongs to change itself.*
Chapters
00:00 — Why Does e Appear Everywhere?
00:27 — Building e From Compound Interest
01:20 — Continuous Compounding
01:35 — The Limit That Creates e
01:44 — Why e Represents Continuous Growth
01:55 — Population Growth & Calculus
02:18 — Why the Derivative of eˣ Is eˣ
02:57 — Exponential Decay
03:29 — e in Probability
04:03 — e in Statistics & the Bell Curve
04:29 — Euler’s Identity: eⁱπ + 1 = 0
04:49 — Why e Really Appears Everywhere
05:10 — e Is the Number of Change
#Mathematics #EulerNumber #Calculus #MathExplained #ExponentialGrowth #Probability
4 Comments
Why e Is Everywhere | Euler’s Number Explained
Aion
23,563 views
In this video, we build Euler’s number *e* from first principles, starting with compound interest and continuous growth. Then we see why the exponential function \(e^x\) is unique, why its derivative equals itself, and why the same mathematical structure keeps appearing across seemingly unrelated problems.
By the end, you’ll see why *π naturally belongs to circles, while e naturally belongs to change itself.*
Chapters
00:00 — Why Does e Appear Everywhere?
00:27 — Building e From Compound Interest
01:20 — Continuous Compounding
01:35 — The Limit That Creates e
01:44 — Why e Represents Continuous Growth
01:55 — Population Growth & Calculus
02:18 — Why the Derivative of eˣ Is eˣ
02:57 — Exponential Decay
03:29 — e in Probability
04:03 — e in Statistics & the Bell Curve
04:29 — Euler’s Identity: eⁱπ + 1 = 0
04:49 — Why e Really Appears Everywhere
05:10 — e Is the Number of Change
#Mathematics #EulerNumber #Calculus #MathExplained #ExponentialGrowth #Probability