Imaginary interest rates | Lockdown math ep. 5

2020-05-01

[public] 358K views, 15.2K likes, 135 dislikes audio only

Compound interest, e, and how it relates to circles.

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Great Mathologer video:

/youtube/video/-dhHrg-KbJ0

Beautiful pictorial summary by @ThuyNganVu:

https://twitter.com/ThuyNganVu/status/1258221677990703105

https://twitter.com/ThuyNganVu/status/1258222002889875457

My other videos on imaginary exponents:

/youtube/video/v0YEaeIClKY

/youtube/video/mvmuCPvRoWQ

Mistakes:

In the off-handed remarks on quaternions, I mentioned rotation in 4d would require 10 degrees of freedom. That's wrong, what I should have said was it requires 6 degrees of freedom, and rotation in 5D is what requires 10 degrees of freedom.

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Video Timeline (Thanks to user "Just TIEriffic")

0:00:00 Welcome

0:00:55 Q1: Prompt (Would you take an imaginary interest rate)

0:02:05 "e to the pi i for dummies" video shoutout

0:02:45 Q1: Results

0:03:30 Q2: Prompt (two banks, two rates)

0:04:55 Ask: Beauty of connections in math

0:06:00 Q2: Results

0:07:05 Desmos for Q2

0:09:10 Q3: Prompt (savings growth rate, 6% every 6mo)

0:10:35 Q3: Results

0:12:35 Desmos graph explored

0:14:45 Breaking down an interest rate

0:18:00 An interesting interest equation

0:19:20 Q4: Prompt (100*(1+0.12/n)^2 as n → ∞)

0:21:05 Ask: Quaternions

0:22:35 Q4: Results

0:24:50 Explaining Q4

0:26:40 Defining e

0:28:40 The definition of e from previous lectures

0:30:45 The imaginary interest rate

0:32:35 Graphing this relationship

0:33:50 The imaginary interest rate animation

0:37:55 Compounding continuously with i

0:40:45 The spring & Hooke's law

0:43:20 Q5: Prompt (Δx & Δv for a spring)

0:44:50 Ask: Rotation in for multiple dimensions

0:47:45 Q5: Results

0:49:50 Rewriting the spring's position

0:55:00 Bringing it all together

0:59:00 Ask: Hints on last lecture's homework

1:03:25 Closing Remarks

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