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typedef
Quote: No Man’s Sky is a game about exploration and survival in an infinite procedurally generated galaxy. http://www.nomanssky.com/ 

28 Oct 2015, 05:32 

Trinitek
That's cool I guess...but is it written with FASM?


28 Oct 2015, 07:59 

MHajduk
When I'm fed up with foggy autumn days I create sunny landscapes that serve me as a background for mathematical problems and their solutions.


29 Oct 2015, 11:33 

MHajduk
Just for the sake of completeness (every question should have corresponding answer ):
Use of inequality between weighted arithmetic mean and weighted geometric mean: 

30 Oct 2015, 22:17 

YONG
Bro, you need to prove Inequality (1) in your first solution before applying it!
(Yeah, I know the "Arithmetic Mean >= Geometric Mean" inequality. But many forum members may not.) 

31 Oct 2015, 01:24 

MHajduk


31 Oct 2015, 23:25 

YONG
To keep the proof simple, I would start from
[sqrt(a)  sqrt(b)]^2 >= 0 where a & b are nonnegative real numbers. Then we have a  2 sqrt(ab) + b >= 0 a + b >= 2 sqrt(ab) (a + b)/2 >= sqrt(ab) So, A.M. >= G.M. BTW, the background images of your solutions are really nice. 

01 Nov 2015, 06:29 

MHajduk
My proof is quite simple too. The only thing that makes it longer (visually) is that I show everything stepbystep and have added some descriptive explanations in English.
BTW, in the middle of the proof we get the inequality "(a + b)^2 >= 4ab" for every real a,b that is frequently used in solutions of other inequalities. 

01 Nov 2015, 11:52 

MHajduk
A graph presenting a kind of "genetic relationship" between basic inequalities.
The symbols of a form "/<operator> f(a,b)" next to the arrows symbolize the operation that is to be done on the both sides of the given inequality to transform it into another inequality. For example, symbol "/ + 4ab" means that we have to add 4ab to both sides of inequality. 

01 Nov 2015, 20:56 

YONG
Yeah, your proof gives some spinoff inequalities which are very useful.
BTW, I think you should ask a moderator to extract all these math posts and keep them in a general math thread. You started one some time ago, right? 

02 Nov 2015, 01:28 

revolution
Where are the mods when you need them?


02 Nov 2015, 06:50 

YONG
Well, I guess one of them is on a fictional planet appearing in Frank Herbert's Dune universe.


02 Nov 2015, 07:00 

revolution
YONG wrote: Well, I guess one of them is on a fictional planet appearing in Frank Herbert's Dune universe. Well at least I made an attempt to get it back on topic. 

02 Nov 2015, 07:10 

YONG
revolution wrote: Well at least I made an attempt to get it back on topic. 

02 Nov 2015, 09:43 

MHajduk
YONG wrote: Yeah, your proof gives some spinoff inequalities which are very useful. 

03 Nov 2015, 14:38 

YONG
MHajduk wrote:
Some of the mods live in fictional worlds  we can't count on them to fix problems in the real world! 

07 Nov 2015, 03:03 

revolution
YONG wrote: Some of the mods live in fictional worlds  we can't count on them to fix problems in the real world! 

07 Nov 2015, 12:47 

TheRaven
Stimulus^2 (visual & intellectual)
Neat way of managing your sets. Inequalities, scientific process of elimination; fascinating and quite unexpected. I remember avoiding these in high school, but I'm older now and more stupid. Nice stuff, seriously. _________________ Nothing so sought and avoided more than the truth. I'm not insane, I know the voices in my head aren't real! 

20 Oct 2016, 05:22 

MHajduk
Yeah, one picture is worth a thousand words, really. But it's not easy to enclose a given subject only in one page of text; in order to achieve that goal and to compress information you have to assume some things as widely known (or describe them somewhere else, also in onepage document).


20 Oct 2016, 21:06 

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