How To Multiply Dog × Tree?! A Dimensional Analysis Primer

To try everything Brilliant has to offer—free—for a full 30 days, visit https://brilliant.org/zhuli . The first 200 of you will get 20% off Brilliant’s annual premium subscription.

How can we multiply all of these different things together? What does it mean? In this video, we will take a detailed dive into dimensional analysis, to better understand how we can do arithmetic with units, and how it is applied to solving problems. Can you come up with any other interesting ways to apply dimensional analysis?

My Patreon:   / zhulimath  

0:05 Introduction and Outline
1:18 What is a unit / dimension?
1:50 Add/Subtract Commensurable Units
2:38 Dividing Units
3:13 Multiplying Units
4:54 Part I Summary
5:36 Base and Derived Units
6:10 Conversion Factors
8:30 Example Problem 1
10:07 Example Problem 2
11:09 Example Problem 3
12:57 Sanity Check
13:56 Special Insights: Percents
14:46 Special Insights: Degrees
16:36 Fuel Economy as... area??
18:11 Arbitrary Analysis
20:03 Conclusion

Joseph Newton's video, Cursed Units:    • Cursed Units  
Kieran Borovac's video, Seven Dimensions:    • Seven Dimensions  

Intro riff taken from: Nikolai Kapustin - 8 Concert Etudes, Op. 40: III. Toccatina

Music Credit:
Seeking Song / American Legion
Aligned / Hara Noda
Blues for the Lonesome / Rikard From
The First Fall of Snow / Johannes Bornlof
Winter Is upon Us / Sayuri Hayashi Egnell
Blank Stare Happy / American Legion
Forest Moon / Gavin Luke
Groove Retrospective / Will Harrison
courtesy of www.epidemicsound.com

This video was sponsored by Brilliant.