0.bbbb... = 1 (in base b+1) | 9 geometric series dissection proofs without words

This is a compilation of nine shorts (most with words). If you want to see those, the links are below (along with attribution to the original ``proof without words" author).

00:38 Infinite sum of powers of 1/3 (0.222... = 1 in base 3):

01:20 Infinite sum of powers of 1/4 (0.333... = 1 in base 4):

01:55 Infinite sum of powers of 1/5 (0.444... = 1 in base 5):

02:40 Infinite sum of powers of 1/6 (0.555... = 1 in base 6):

03:20 Infinite sum of powers of 1/7 (0.666... = 1 in base 7):

04:15 Infinite sum of powers of 1/8 (0.777... = 1 in base 8):

05:00 Infinite sum of powers of 1/9 (0.888... = 1 in base 9):

05:50 Infinite sum of powers of 1/10 (0.999... = 1 in base 10):

To learn more about animating with manim, check out:
___________________________________
Music:
Creative Commons / Attribution 4.0 International (CC BY 4.0)

[vijaylaxmi]

Love your videos since the channel has started

[binbots]

Math is just counting an infinite amount of zeros.

[KinuTheDragon]

For an arithmetic proof of this same proposition:
Let S = the sum from n=1 to infinity of (b/(b+1))^n.
Therefore, S = b * sum from n=1 to infinity of (1/(b+1))^n.
Multiply by b + 1:
(b+1)S = b(sum from n=0 to inf of (1/(b+1))^n)
= b(1 + sum from n=1 to inf of (1/(b+1))^n)
= b(1 + S/b) = b + S
(b+1)S = b + S
bS = b
S = 1

[jakobthomsen]

The base-7 visualization is especially nice :)

[STEAMerBear]

Thank you for all you do!!

As a math, science and engineering teacher, I would absolutely love to acquire the knowledge and skills needed to produce this kind of video. I’ve explored it extensively and sadly the time required would cost me too much in terms of planning, grading, and actually teaching my classes (and of course attending so many meetings about matters of vital importance—to someone—though the school board and administration can’t seem to figure out who). 🤪

[pugzas]

*me curious as to which system they'll use for 11, 12, 13 and up.*
*they don't show them*
*sad*

[Sergey-Primak]

6:12 - универсальная визуализация с любой базой)

[JaxEntersEvasion]

You can just do the circle one for every number

[MisterSnail]

Question: what is the equivalent to the sum of reciprocals of n up to x?

[jpopelish]

The last example is not as satisfying as the first 8, because it does not demonstrate how the smaller area is 1/10th if the whole. That same method would also work for all the other examples, by also being less satisfying. Is there not a geometric shape that can intuitively be divided into 10 equal areas?

[toferg.]

Why don’t we write base numbers in Roman numerals? Like “Base 10” really could mean anything.

[justarandomdood]

(0.6...)₇ = 1 was definitely my favorite, that one was so wild

[TKN]

Hello sir good afternoon

I extremely sorry sir I will remove all your videos in my channel after some days, please 🙏 don’t be angry, its my humble request to you please don’t give me any copyright strike, Please sir

[barnowlcom]

There is an art to geometry that I love to see in math. And my late wife loved to see it in artwork. In 9 days I'll cross a threshold where I'm a widower as long as I was married to her. And I see this video as a beautiful representation of those 9 days … always getting closer to 1 but never truly wanting to cross the threshold. Thank you for the beautiful representation! 🥲