0.66666… = 1 (in base 7)

Рет қаралды 136,092

26 күн бұрын

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
To learn more about animating with manim, check out:
manim.community

Пікірлер: 132

@tylosenpai6920 25 күн бұрын

...At this rate, you should be using a hexagon...

@wyattstevens8574 25 күн бұрын

Wouldn't a heptagon (because it has 7 sides) be even better?

@tylosenpai6920 24 күн бұрын

@@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 ?

@gabekrieck6772 4 күн бұрын

It is the bestagon

@Grimmmmmmmy 3 күн бұрын

Best reference@@gabekrieck6772

@HueNguyen-jo4fi 2 күн бұрын

@@gabekrieck6772 true

@notmynameaaaaaaaaaaaaaaa 24 күн бұрын

0.nnnnn... = 1 in base (n+1)

@RandyKing314 24 күн бұрын

is this always true?

@cccexestarted 24 күн бұрын

@@RandyKing314 yes, always true

@taylormarinescu805 22 күн бұрын

@@cccexestartedwhat about base 1

@saginur4380 21 күн бұрын

Oh yeah I forgot about that rule

@alesonbrjk 18 күн бұрын

@@taylormarinescu805 also true

@christiandeaver789 24 күн бұрын

I thought it was Pink Floyd at first

@h-ye7um 3 күн бұрын

By reading the title, I was gobsmacked, collaterally dumbfounded and rendering my prime knowledge of math into shreds.

@mysteriousecurb1791 3 күн бұрын

This is why i hate supertasks

@mauschen_gaming 23 күн бұрын

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

@justanothergirl__ 24 күн бұрын

Love this! I only wish KZfaq didn't cover the bottom of the video

@MathVisualProofs 24 күн бұрын

Longer version on my channel (wordless) doesn’t have as much covering it

@justanothergirl__ 24 күн бұрын

@@MathVisualProofs I'll have to give it a watch!

@aceofanimation4325 4 күн бұрын

If you go into comments and hold the bar near the bottom you can see it without obstruction.

@musicofficial6924 6 күн бұрын

By using infinity you can prove any number equal to any another number

@kkupsky6321 10 күн бұрын

Sigma means sum? If that’s all I learned today…

@thiennhanvo2591 3 күн бұрын

Yes

@1leon000 2 күн бұрын

You mean that your teacher didn't mention sigma meaning sum in passing in your 7th grade math class?

@kkupsky6321 10 күн бұрын

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.

@bharath2768 25 күн бұрын

Best representation

@BR0SK1X 4 күн бұрын

New Roblox logo just got leaked

@Wiesto1 10 күн бұрын

7 is very weard

@wolfscraft8501 2 күн бұрын

Bruh, I'm in holidays rn stop overloading my mind

@evanlandis990 7 күн бұрын

It seems more like the infinite sum is like a sub-atomic rounding up principal

@finpin2622 17 күн бұрын

Love listening to these videos. I don’t learn or retain any of it but it seems pretty interesting.

@Tqvh Күн бұрын

I lost you at “equilateral triangle”

@konstantindrumev8036 24 күн бұрын

Hi, can you please recommend any books you found useful in your journey of math? Ty❤

@ET_CostaLotta 4 күн бұрын

It doesnt fill in the triangle completely do yk what a fraction is and how it works?

@polarisukyc1204 22 күн бұрын

I always wondered how to prove that 1/(x-1) can be represented by an infinite sum of 1/(x^n)

@neitoxotien2258 24 күн бұрын

What software do you use for animation? Thank you

@Dalroc 24 күн бұрын

Pretty sure it's manim

@MathVisualProofs 24 күн бұрын

manim

@blu-birb 2 күн бұрын

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.

@DQFozz 24 күн бұрын

Nice !

@matthewbell4273 24 күн бұрын

This video has me all sixes and sevens

@Lunawithcheese 8 күн бұрын

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* ]

@KaliFissure 25 күн бұрын

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.

@alex_ramjiawan 25 күн бұрын

1/n < 1/n+1. Therefore, it's not one below.

@alex_ramjiawan 25 күн бұрын

1/n < 1/n-1. Therefore, it's not one below.

@KaliFissure 25 күн бұрын

@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

@jackscourage 6 күн бұрын

I'm confused but I feel enlightened

@p1xelat3d 7 күн бұрын

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)

@chrisrodriguezm13 3 күн бұрын

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)

@p1xelat3d 3 күн бұрын

@@chrisrodriguezm13 yeah that works too

@JaphethThomas-um9gw 14 күн бұрын

I allways thought u would have 1/ inf not shaded but i think it means the same thing

@sasho_b. 15 күн бұрын

For all sums of the type m*(1/n+1/n*n+...), the sum is equal to m*1/(n-1)

@jaredadkinson 24 күн бұрын

Wow. He did it again. The infinite sum of 1/n is always equal to 1/(n-1)

@BaronSterling 5 күн бұрын

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.

@user-jk1rk3xz4f 17 күн бұрын

sum of 1/n from n to infinity always equals 1/n-1

@bharath2768 25 күн бұрын

Niceee sir

@lucasbetterman165 Күн бұрын

Isn’t 6/7 more than .6

@lucgagnon7169 24 күн бұрын

0,66666 periodic in base 7 equal 1, just like 0,999 periodic in base 10 = 1

@drazyxm5386 24 күн бұрын

Easy maths proof using telescopic sum

@r4e3xx 7 күн бұрын

its the same thing as 0.99999...=1

@kinshuksinghania4289 23 күн бұрын

0.k repeating in base (k+1) is 1

@Swingylad Күн бұрын

Idk seems like some type of fractal to me.

@travelbhksc 23 күн бұрын

This figure made by which software. Kindly informed me. Thanks

@MathVisualProofs 23 күн бұрын

manim. It is in every video description and on my main channel page.

@hyoominoid01 Күн бұрын

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

@equilibrochu 24 күн бұрын

Not quite. But sounded very convincing. Nice try.

@mathhead4975 14 күн бұрын

routh's theorem?

@wscamel226 22 күн бұрын

in base 7.... 😡

@budakgame4506 6 күн бұрын

So basically if it's hexadecimal, 0.FFFFF... is 1 right?

@chrisrodriguezm13 3 күн бұрын

Maybe

@Errordemon001 4 күн бұрын

All I understood was 1 7th

@c1-math12 23 күн бұрын

There is something ambiguous about number

@mutafyanny 6 күн бұрын

Now do 0.111111111111111111111111111111111111111111111111111111111... = 1 (in base 2)

@MathVisualProofs 6 күн бұрын

It’s on the channel… 😀

@BloodTheGamer 21 күн бұрын

☠️☠️☠️

@avaneeshtungar3291 25 күн бұрын

😢

@0303maf 24 күн бұрын

6/7⁶⁹⁴²⁰=1

@johncheshirsky8822 25 күн бұрын

What

@pr3zelman 2 күн бұрын

I’m nodding my head in agreement as I have no clue what’s going on

@Peppet490 2 күн бұрын

Basicly its like saying 0.9999999999999999_ = 1

@NicleT 22 күн бұрын

But it will never be all shaded. Even if you reach the Planck's limit.

@mrfancyshmancy 18 күн бұрын

In real life not, but in math it will...

@paulosullivan3472 25 күн бұрын

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.

@TurtleBoi-lg4rw 25 күн бұрын

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.

@paulosullivan3472 25 күн бұрын

@@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.

@Rando2101 25 күн бұрын

Just call it 1- Problem solved

@TurtleBoi-lg4rw 25 күн бұрын

@paulosullivan3472 then prove that my statement is wrong, do 1-0.999... and tell me the answer

@TurtleBoi-lg4rw 25 күн бұрын

@paulosullivan3472 and if I am wrong that means 3/3 =/= 1