Imaginary interest rates | Ep. 5 Lockdown live math

Compound interest, e, and how it relates to circles. Full playlist:    • Lockdown math   Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Great Mathologer video:    • e to the pi i for dummies   Beautiful pictorial summary by @ThuyNganVu:   / 1258221677990703105     / 1258222002889875457   My other videos on imaginary exponents:    • e^(iπ) in 3.14 minutes, using dynamics | DE5      • Euler's formula with introductory group th...   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. ------------------ 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 ------------------ The live question setup with stats on-screen is powered by Itempool. https://itempool.com/ Curious about other animations? https://www.3blue1brown.com/faq#manim Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/a... Stream the music on Spotify: https://open.spotify.com/album/1dVyjw... If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter:   / 3blue1brown   Reddit:   / 3blue1brown   Instagram:   / 3blue1brown_animations   Patreon:   / 3blue1brown   Facebook:   / 3blue1brown