Name: Problems Plus 12: Can You Stack Books Infinitely Far Away from the Table?
Uploaded: 2023-09-22T02:39:11+00:00
Duration: 20 min 49 s
Description: In this video I go over the famous Book Stacking Problem, and show that it is possible to stack books that extend infinitely far away from the table! To do this you have to stack such that the first b

2 years ago

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math calculus science book stacking problem stacking books math series sequences and series harmonic series p-series divergent series stacking infinite books

In this video I go over the famous Book Stacking Problem, and show that it is possible to stack books that extend infinitely far away from the table! To do this you have to stack such that the first book extends 1/2 from the second book which extends 1/4 from the third which extends 1/6 from the 4th, and so one. Then the center of mass of the stack of books can be determined and shown to be still above the table, which means the books won't tip over. Lastly, I show that the series of distances 1/2 + 1/4 + 1/6 + ... etc. is a divergent Harmonic series, which means that the distance keeps extending out to infinity as we add more books. Try this yourself and let me know how many books, or playing cards, you can stack up!

The timestamps of key parts of the video are listed below:

- Problem 12: Book Stacking Problem: 0:00
- Solution: Book extending completely off the table: 1:57
- Center of mass of the stack of books: 7:20
- Center of mass doesn't extend past the table: 17:02
- Books can extend infinitely far via the divergent Harmonic series: 18:42

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P