Alternating Geometric Series Sum
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- Опубликовано: 12 июн 2024
- This is a short, animated visual proof demonstrating the infinite alternating geometric series formula for any positive ratio r with r less than 1 and with positive first term a. This series is important for many results in calculus, discrete mathematics, and combinatorics.
To buy me a coffee, head over to www.buymeacoffee.com/VisualPr...
Thanks!
For a slower, wide format version of this video (without words), see • Alternating Geometric ...
Also, check out my playlist on geometric sums/series: • Geometric Sums
This animation is based on a proof by The Viewpoints 2000 group from the October 2001 issue of Mathematics Magazine page 320 (www.jstor.org/stable/2691106 ).
#mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricsums #series #infinitesums #infiniteseries #geometric #geometricseries
To learn more about animating with manim, check out:
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When people say "math is beautiful," things like this are what they mean.
Exactly!
Nope. Not always.
Depends on who you mean when you say "people". A lot of mathematicians would disagree with you
What about "ugly math". I wanna see some abominations.
Ja se ne slazem, ja je uopste ne razumem!
The isosceles triangle is so underrated LOL
That was your best one yet. Brilliant.
I'll be really honest. I have no idea what you're talking about, but I like listening to you talk about it
This left me with mouth wide open
Probably the best visual proof of this channel so far!
You sir are a genius, this explanation was a masterclass
My analysis book had a picture of this for the cover
this is an awesome proof
Great work!
wow this is good.
Good good thanks for the information brother
That's wild
Chat is this real?
nah bro u accidentaly took some funny mushrooms this morning :(
Yes it is, I was the convergence point
Yes, under the condition that -1
@NitronBeam can I have an autograph?
@@LumaSloth
Yeah sure, wait a...
Oh ... , I forgot points don't even have arms to sign one :(
As pirates are wont to say, "Arrrrr!"
Does this correspond to r being a negative number? This is a beautiful animation, is it manim
Yes. Manim. This is a geometric series with negative ratio. Or you can make r positive and alternate as I have here.
so nice
Sweet
Wow!
HOW DO YOU FIGURE ALL THAT OUT
All proofs have citations in the description :)
@@MathVisualProofs now that's pretty cool
People get paid to do this. Cool job!
Wowzers
Looks like it forms a hallway 😮
this is so useful in my daily life.
Are those animations made in Python (Manim)?
Yes. Made with manim
How bro how you imagine all this stuff 😮😂😂
not all me. I provide citations for each visual proof in the descriptions.
@MathVisualProofs who helps u with such beautiful ideas?
@@Sara-ns3lq As mentioned, I just use the citations given (which are typically static diagrams) and then animate them in a way that I want to see them unfold. I don't have any help producing the animations or videos.
@MathVisualProofs
Can u recommend any books which has such visual proofs
@@Sara-ns3lq Check out any of the books by Roger B. Nelsen (he has a lot). At some point I had thought about doing a video about the books I use... maybe that's a good idea... :)
Can you do a visual of talet theorem?
Basically
Summation to infinity n=0 of
A×(-r)^n
§ is stand in for summation because no symbol in keypad :(
Or just Aק-r^n
the fazbear sum
Substituit u=-r and you will get a+au+au²+....=a÷(1-u)
No, it would be (a/1+r)/2 since the final result you showed was half
i can't see why the distance between the purple line with length ar and the line y=-rx+a is ar^2, can anyone help
This takes some work. You first want to use the previous information to find the x-coordinate of that line, which is a-ar (because it is obtained by first traveling distance a and then back ar. Now when you plug x=a-ar into the two lines you get -r(a-ar)+a and a-ar. When you subtract these you get (-ar+ar^2+a) - (a-ar), which is ar^2. Same type of thing goes for the next vertical line and so on.
All i know is a and r are lines at an x coordinate so yeah im smart
The piece I’m unclear about is why we can be sure it’s an isosceles triangle if the absolute value of the slopes of the lines ( +1 and
The line of interest is y=x. If you draw from any point on y=x and draw a vertical distance z, then a horizontal distance of z will put you back at y=c (because you changed the c and y coordinates both by z)
Why didn’t you divide them by a 😔
how do you come up with these proofs
All the videos have citations in the description to the original published static diagrams. I don’t come up with them, I just animate them so they can get wider exposure.
Curves??
Sort of like a lerp function 🤔
My first thought was - who tf uses y=-rx+a rther than y=-mx+c
what's this useful for?
ok
💀
*ratio of -r
Huh?
you lost me when you started using the alphabet
Bruh
Ok wtf