05-13-2017, 07:15 PM (This post was last modified: 05-13-2017 08:22 PM by Vtile.)
Post: #26
 Vtile Senior Member Posts: 406 Joined: Oct 2015
(05-13-2017 01:33 PM)Dieter Wrote:
(05-12-2017 11:58 PM)Vtile Wrote:  I now understand what the 3/5 does with floor, as 3 changes in five,

?!?
I'm just trying to understand how this behaviour is written on the fraction numbers. I have not had much exposure of "algorithm math" and I haven't though the system from this point of view before.
Code:
 1 *(3/5)=0    (1. State change) 2 *(3/5)=1 3 *(3/5)=1    (2. State change) 4 *(3/5)=2    (3. State change) 5 *(3/5)=3 --- 6 *(3/5)=3     (1. State change) 7 *(3/5)=4 8 *(3/5)=4     (2. State change) 9 *(3/5)=5     (3. State change) 10*(3/5)=6
Floor("no. of state changes"/"Length of sequence")
It is obvious as it is the same a 1/4 mentioned earlier, but 1/4 is simpler as is 1/10 etc. to internalise from other common uses of fractions. Of course this is also same case without floor operator, the sequence have exactly same number of integer changes, I just have not though it from this point of view as said.

With CEIL operator the nominator gives "no. of different numbers" in sequence length.

Above is not entirely universal, ie. 1/5 if you start look 0 to 4 it doesn't have any change, but.. I'm working on this (self-evidence). Actually this relates also to one oldish topic in here, how the math is written/spoken in different languages, if there is difference how one interpret a fraction if you say one per five or if you say 1 part of five, which atleast here the first case is what I commonly see (conception I have ) in older books while the latter is the more seen on modern books (x per y is almost non-existent .. again conception what I have while thinking of it).

(05-13-2017 01:33 PM)Dieter Wrote:
(05-12-2017 11:58 PM)Vtile Wrote:  but I can still not figure out the other parts.

What parts exactly?

Dieter
[/quote]
How it then sums up to 31-30-31-31... sequence (I _think_ I know the mechanics in this case, but I still don't understand it intuitively). It does something to do with odd and even summation and and the pattern the fraction creates (the pattern part I need to dive next, to see if there is any common denominator between fractions). But I'm getting there, I just had some unexpected appointments and work in last few days.
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