How to Count in Fractional and Irrational Bases

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An interesting companion to base phi is Zeckendorf representation, where each position is the next fibonacci number. It also has the property that 11=100, but it's easier to count: 0, 1, 10, 100, 101, 1000, 1001, 1010...

ok but how do you count in base square root of 100, checkmate librel

Thank you for the video. By the the way, in germany the name from the late mid age about the number 1.5 survived since today. Its the single number name today that name a fraction. We called the number 3/2 or 1.5 between 1 and 2:" "anderthalb" (which comes from "(the) other half").

This answers the question I've been wondering about for years, but whenever I looked them up the answers felt completely unapproachable! Thank You! Is there another video describing ways in which these bases end up being useful? I'm sure they are, I just trust that Combo Class is where I'll grok it fastest.

Trying to genarilize your dice method with any fraction, let's say x/y
If you have x/y dices in a case, you have enough dices to throw them all and put a 1 in the case on the left. However, you can't throw them all, since you can't cut your dices. And since you only want to move an integer amount of dices, you'll move x dices to the left case. Once you've moved your x dices: since you're supposed to remove (x/y)-1 dices for x/y dices moved, here you'll remove y((x/y)-1) dices (if you move x dices to the left instead of x/y, you have to remove y times what you would have removed for x/y dices, I like to make everything explicit)

That is to say, if you're in base x/y, for each set of x dices in a case, you can move these x dices to the case that is on the left, and remove y((x/y)-1) dices per set of x dices you've moved

0.5 in base 1/3 = ...1110

So 10.01 (2) = 1.11?

What about like base 10+sqrt(2)

What about if the base is a generic solution to quintin equation?
It's algebraic and yet cannot be represented as square root expression and isn't rational either.

Love the production. Very crisp math presented in highly informative and entertaining manner in the dystopian environment of backyard trash and bloody white coat of a psycho scientist. <3

1 2 3 0.1 1.1 2.1 3.1 0.2 1.2 2.2
Can you guess which base I counted to 10 in

I like the vibe from this homeless guy. It is so soothing

11111111111111111111111...111111111111111111 (Infinitely) in Base 1/2 = 0.1 in Base 1/2

That looks messy.

Based video

nice video

Base Phi is my new favorite thing

WAIT, you might get to it, but I wonder if interesting things will happen in base phi, since phi^2 = phi +1 and 1/phi = phi -1

I read the title as "Fictional and Irrational" and it was so funny

bootleg Bill nye

I didn't even know bases on non-integers was even a thing, let alone irrational or even transcendental numbers!

I am in the process of recreating a big number library in C, That I did years ago for 32 bits. No I'm trying for 64-bit.

During golden ratio his head was blocking the board

there is no way this guy films sober

Start watching as a joke, kept watching while looking like the thinking man and stayed for the whole thing. Prepare world, for now I can fuck with your minds que magic fingers

How about base i?

I'm not going to lie. Base Root 10 actually sounds hella useful for logarithmic scales and anything involving exponentials. You can even stretch it out more with 4th root letting you get evenly inbetween factors of root 10s. Or Root 8, 16... all the way to any Root (2 to the n) base. Depending on how stretched out you need it.

I know the golden ratio is your personal favorite. But in terms of sheer real life applications and practical utility, root 10, root 2 and root 16 (or just base 4) bases show huge potential.

Hell, if we want to approximate Pi in Base (2 to the n) root 10, we can just say that Pi roughly equals 10 in Base Root 10. Or 1000 in Base 4th Root 10. 10 in Base Root 10 is a LOT closer to the true value of Pi than 3 in Base 10.

Your two channels are 100% my favorites. You never fail to make me smile while learning something new.

Slight disappointment in the digits selection. Using digits 0-9 in base sqrt(10) is silly when all real numbers can be represented using only the digits 0-3.

φ=phi
Δ=delta
π=pi
Π=something in math
Σ=the "E" looking thing in math
Ω=absolute infinity
ω=omega
τ=tau
μ=micro
μs=microsecs
η=nano
ηs=nanosecs
S=secs
Ms=millisecs
Η=henry in electronics
β=beta
ζ=zeta
ξ=eta
θ=??????

My god, this channel is amazing.

Damn. I'm impressed by how you found that "take three, throw one"-game. Cool!

Fractional and irrational bases make no sense. The 1/2 and sqrt(2) examples were just plain old binary. The golden ratio base was just flawed. You showed one way to display 2 in that base, but there are infinite other ways to display it.
The number of symbols is what matters and that can only ever be a natural number.

Love it... and love where you imagination runs!!!! Someone who definitely thinks outside the square... I'd even say lives outside the box!!! What about various complex bases? Oh, you touched on it at the end!!! What about Base 0? Base 1? I am tired so probably they don't exist!

What about base 1000? the -Illions series becomes the place values.

IIRC isn't the root of 2 the foundation of the 'Imaginary' numbers, or was it root of 1, if so base root 2 would include 'imaginary' numbers

Goldbach's Conjecture, the insane part of me in hubris thinks I can prove, sees value in this.

Do a video on phi(GR)

Oh boy the base 3/2 system should be interesting for thinking about ratios of musical notes

I ate an amogus 🦶.