Amazing video! One interesting note is that the right rule on a fraction x can be stated as x+1. And the left rule has a similarly concise statement: x || 1, where "||" is the "parallel combination" operator, famously used in electric circuit analysis to find the total resistance of two resistors in parallel. By extension, m consecutive right moves can be stated as x + m, and m consecutive left moves as x || (1/m).
I'm dizzy after watching this, you are explaining it so well that i being 15yr old can understand it, this is lot of information to hold, i actually feel like it will spill out of my brain
10:12, I believe that the last remainder before you get a remainder of zero is the gcd. In your example, the gcd is one but you pointed to the wrong ‘1’. Sorry to point out an error but I hope it helps.
11:41 You could make your list spiral around if you wanted all-positive indexing. Also, if you just want to find the next term you can do this: take twice the integer part, add 1, subtract the current term, and invert the result.
hm, i dont remember the video totally but if its abt listing rationals u can use this prolly, f(x,n)=n+\frac{n + (x - n - 1)mod(x - 1)}{x - 1} - 1 for x eq 1 and n for x=1 with x,n in N and then the fraction will be x/f(x.n) and u can get the nth fraction with numerator x by iterating n, naturally to get negative ones u can simly put a - in front of the fraction, idk if what i had sent back then worked but this should
![[SoME1] Listing the Rationals Using Continued Fractions](http://i.ytimg.com/vi/cSD3moYu3cs/mqdefault.jpg)
Amazing video! One interesting note is that the right rule on a fraction x can be stated as x+1. And the left rule has a similarly concise statement: x || 1, where "||" is the "parallel combination" operator, famously used in electric circuit analysis to find the total resistance of two resistors in parallel. By extension, m consecutive right moves can be stated as x + m, and m consecutive left moves as x || (1/m).
Excellent presentation: thank you Ben. Very much enjoying your work.
This is awesome! Thank you so much for making this series Ben
I'm dizzy after watching this, you are explaining it so well that i being 15yr old can understand it, this is lot of information to hold, i actually feel like it will spill out of my brain
10:12, I believe that the last remainder before you get a remainder of zero is the gcd. In your example, the gcd is one but you pointed to the wrong ‘1’. Sorry to point out an error but I hope it helps.
Amazing! Your videos are excellent!
11:41 You could make your list spiral around if you wanted all-positive indexing.
Also, if you just want to find the next term you can do this: take twice the integer part, add 1, subtract the current term, and invert the result.
next video please
But to list all the rational numbers without repeatings cant we use x/xn+mod(m,x) ???
I don't know- does x/(xn+(m mod x) ever have the same ratio of x to xn+(m mod x) show up twice? More importantly, does *every* ratio show up?
hm, i dont remember the video totally but if its abt listing rationals u can use this prolly, f(x,n)=n+\frac{n + (x - n - 1)mod(x - 1)}{x - 1} - 1 for x
eq 1 and n for x=1 with x,n in N and then the fraction will be x/f(x.n) and u can get the nth fraction with numerator x by iterating n, naturally to get negative ones u can simly put a - in front of the fraction, idk if what i had sent back then worked but this should
too lazy to check the other
The title is missing a capital "U" for Using. All your other titles formatted it like that
Thanks! Fixed.