0.66666… = 1 (in base 7)
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- Опубликовано: 16 июн 2024
- This is a short, animated visual proof showing the sum of the infinite geometric series with first term 6/7 and ratio 1/7, which in turn allows us to compute the sum of the series of powers of 1/7 and determine an interesting base 7 representation of 1.
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualPr.... Thanks!
For a longer, wordless version of this animation with two other proofs, see • Three Geometric Series...
Also, check out my playlist on geometric sums/series: • Geometric Sums
This animation is based on a proof by Stephan Berendonk (2020) from the November 2020 issue of The College Mathematics Journal, (doi.org/10.1080/07468342.2020... p. 385)
#mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricsums #series #infinitesums #infiniteseries #geometric #geometricseries #equilateraltriangle
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...At this rate, you should be using a hexagon...
Wouldn't a heptagon (because it has 7 sides) be even better?
@@wyattstevens8574 No, it's like using a triangle to figure out a sum of 1/4^n (Which will become 1/3)
Why ? You'll get 6 sides and a central piece that is a smaller version of the entire shape that is 1/7 of the area, making this visual proof possible
In a heptagon, what visual representation can be made about such a thing ?
It is the bestagon
Best reference@@gabekrieck6772
@@gabekrieck6772 true
0.nnnnn... = 1 in base (n+1)
is this always true?
@@RandyKing314 yes, always true
@@cccexestartedwhat about base 1
Oh yeah I forgot about that rule
@@taylormarinescu805 also true
I thought it was Pink Floyd at first
By reading the title, I was gobsmacked, collaterally dumbfounded and rendering my prime knowledge of math into shreds.
Usually we use the formula
S = a_1 / (1 - r) but the visual proof makes it much easier to understand with the eye and I'm glad you can help others understand it more easily
Love this! I only wish RUclips didn't cover the bottom of the video
Longer version on my channel (wordless) doesn’t have as much covering it
@@MathVisualProofs I'll have to give it a watch!
If you go into comments and hold the bar near the bottom you can see it without obstruction.
This is why i hate supertasks
Omg I love these. I always was a visual learner. Numbers just are language I don’t speak. Awesome. I’ll maybe learn a bit too.
Sigma means sum? If that’s all I learned today…
Yes
You mean that your teacher didn't mention sigma meaning sum in passing in your 7th grade math class?
By using infinity you can prove any number equal to any another number
Best representation
Love listening to these videos. I don’t learn or retain any of it but it seems pretty interesting.
New Roblox logo just got leaked
Hi, can you please recommend any books you found useful in your journey of math? Ty❤
Bruh, I'm in holidays rn stop overloading my mind
Oh no, fractal
What software do you use for animation? Thank you
Pretty sure it's manim
manim
It’s always the black magic of the concept of infinity….
7 is very weard
I always wondered how to prove that 1/(x-1) can be represented by an infinite sum of 1/(x^n)
So, polydivide (my preferred way of saying divide multiple times) by 2 and 3, then connect opposing trisectors and vertices, then connect the remaining trisectors with the midpoints, and then repeat the process with the middle triangle indefinitely, which will *precisely* give you [ *1* ]
Nice !
The infinite sum of a single simple fraction is the one below. 1/3+1/9+1/27... = 1/2
And 5/6+5/36+5/6³ = 1 ?
In all configurations.
So cool.
1/n < 1/n+1. Therefore, it's not one below.
1/n < 1/n-1. Therefore, it's not one below.
@alex_ramjiawan I mean that the sum of thirds gives 1/2, the number as denominator gets smaller, making the portion get larger.
1/5+1/5²+1/5³.....=1/4
I lost you at “equilateral triangle”
It's Not Art
It's Not Math
It's Both
Depends on how accurate you really wanna be.
I mean, if youre buying a car and youre a dime short, chances are you can still buy the car, but if youre trying to buy a soda and youre a dime short, chances are you wont be able to buy the soda.
Does that mean that (price of a car-a dime)=price of a car?
No, but in most cases, the dime is not as important as the rest of the price.
This video has me all sixes and sevens
I'm confused but I feel enlightened
YOOOO MY COMMENT WAS RIGHT DIDN'T KNOW THERE WAS A VISUALIZATION FOR THIS ONE AS WELL
n being a digit
0.nnnnnnn... = 1 in base (n+1)
Well, meaning 0.99999999999… = 1 (in base 10) is true?
Well, for bases higher than 10, maybe HEXAdecimal might be 0.FFFFFFFFFFF…….. = 1 (in hexadecimal)
@@chrisrodriguezm13 yeah that works too
For all sums of the type m*(1/n+1/n*n+...), the sum is equal to m*1/(n-1)
Wow. He did it again. The infinite sum of 1/n is always equal to 1/(n-1)
This figure made by which software. Kindly informed me. Thanks
manim. It is in every video description and on my main channel page.
its the same thing as 0.99999...=1
Niceee sir
…and so on and so forth…
I allways thought u would have 1/ inf not shaded but i think it means the same thing
0,66666 periodic in base 7 equal 1, just like 0,999 periodic in base 10 = 1
sum of 1/n from n to infinity always equals 1/n-1
Easy maths proof using
telescopic sum
0.k repeating in base (k+1) is 1
Well, two minutes into the video and already the objectively incorrect take of "Heavy Blade is really bad" has appeared. Not giving me confidence in the rest of this video.
routh's theorem?
Idk seems like some type of fractal to me.
So basically if it's hexadecimal, 0.FFFFF... is 1 right?
Maybe
All I understood was 1 7th
Now do 0.111111111111111111111111111111111111111111111111111111111... = 1 (in base 2)
It’s on the channel… 😀
☠️☠️☠️
😢
in base 7.... 😡
Huh
6/7⁶⁹⁴²⁰=1
What
No there won't, there will alsways he a missing 1/7!
I’m nodding my head in agreement as I have no clue what’s going on
It doesnt fill in the triangle completely do yk what a fraction is and how it works?
Basicly its like saying 0.9999999999999999_ = 1
It seems more like the infinite sum is like a sub-atomic rounding up principal
by definition of the construction, a void always remains at the center. so, it is not equal.
Not quite. But sounded very convincing. Nice try.
Isn’t 6/7 more than .6
Not even, this is an asymptote, no matter how many parts you fill in unless you fill it in fully it will not be equal to one, also 6/7 isn't .666, that's for the 1/3
There is something ambiguous about number
But it will never be all shaded. Even if you reach the Planck's limit.
In real life not, but in math it will...
I have heard this many times from very well educated sources but it is false, infinite means it goes on for ever and therefore consists of a constant repetition forever of the same process. Each process always leaves a small part unaccounted for, therefore an infinite process APPROACHES 1 but never reaches it. It does not equal 1, it approximately equals 1, that may sound small but its a very big difference when this incorrect proof is used in certain ways to state that it equals 1.
Convert this same thing into base 10 with an infinity repeating fraction that approaches 1 (0.999...) is equal to 1. Convert it into a fraction and you get 3/3=0.999...=1.
@@TurtleBoi-lg4rw No this proof is what people use to justify the statement that 0.9 recurring equals 1. You cannot use a false proof to make a statement and then claim the statement proves the false proof.
Just call it 1-
Problem solved
@paulosullivan3472 then prove that my statement is wrong, do 1-0.999... and tell me the answer
@paulosullivan3472 and if I am wrong that means 3/3 =/= 1