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typedef



Joined: 25 Jul 2010
Posts: 2913
Location: 0x77760000
typedef
Quote:
No Man’s Sky is a game about exploration and survival in an infinite procedurally generated galaxy.


http://www.no-mans-sky.com/
Post 28 Oct 2015, 05:32
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Trinitek



Joined: 06 Nov 2011
Posts: 257
Trinitek
That's cool I guess...but is it written with FASM? Wink
Post 28 Oct 2015, 07:59
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typedef



Joined: 25 Jul 2010
Posts: 2913
Location: 0x77760000
typedef
No. I was simply amazed by the way the world is generated. It's infinitely vast indeed and it's all happening as you play. Contrast that with other games where they spend hours just to manually design the world.
Post 28 Oct 2015, 20:19
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MHajduk



Joined: 30 Mar 2006
Posts: 6034
Location: Poland
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. Wink

Image

Image
Post 29 Oct 2015, 11:33
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MHajduk



Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
Just for the sake of completeness (every question should have corresponding answer Wink ):

Image

Image

Use of inequality between weighted arithmetic mean and weighted geometric mean:

Image
Post 30 Oct 2015, 22:17
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YONG



Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
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.)

Wink
Post 31 Oct 2015, 01:24
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MHajduk



Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
Image
Post 31 Oct 2015, 23:25
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YONG



Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
To keep the proof simple, I would start from

[sqrt(a) - sqrt(b)]^2 >= 0

where a & b are non-negative 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.

Wink
Post 01 Nov 2015, 06:29
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MHajduk



Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
My proof is quite simple too. The only thing that makes it longer (visually) is that I show everything step-by-step 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.

Smile
Post 01 Nov 2015, 11:52
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MHajduk



Joined: 30 Mar 2006
Posts: 6034
Location: Poland
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.

Image
Post 01 Nov 2015, 20:56
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YONG



Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
Yeah, your proof gives some spin-off 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?

Wink
Post 02 Nov 2015, 01:28
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revolution
When all else fails, read the source


Joined: 24 Aug 2004
Posts: 17284
Location: In your JS exploiting you and your system
revolution
Where are the mods when you need them?
Post 02 Nov 2015, 06:50
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YONG



Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
Well, I guess one of them is on a fictional planet appearing in Frank Herbert's Dune universe.

Wink
Post 02 Nov 2015, 07:00
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revolution
When all else fails, read the source


Joined: 24 Aug 2004
Posts: 17284
Location: In your JS exploiting you and your system
revolution
YONG wrote:
Well, I guess one of them is on a fictional planet appearing in Frank Herbert's Dune universe.
I wonder if it was procedurally generated?

Well at least I made an attempt to get it back on topic.
Post 02 Nov 2015, 07:10
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YONG



Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
revolution wrote:
Well at least I made an attempt to get it back on topic.
That's why I said it would be a good idea to extract the math posts in this thread and put them in a general math thread started by MHajduk.
Post 02 Nov 2015, 09:43
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MHajduk



Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
YONG wrote:
Yeah, your proof gives some spin-off 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?

Wink
I have copied most of the posts to the thread mentioned by you. Smile
Post 03 Nov 2015, 14:38
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YONG



Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
MHajduk wrote:
YONG wrote:
Yeah, your proof gives some spin-off 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?

Wink
I have copied most of the posts to the thread mentioned by you. Smile
Good for you. Wink

Some of the mods live in fictional worlds -- we can't count on them to fix problems in the real world! Evil or Very Mad Wink
Post 07 Nov 2015, 03:03
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revolution
When all else fails, read the source


Joined: 24 Aug 2004
Posts: 17284
Location: In your JS exploiting you and your system
revolution
YONG wrote:
Some of the mods live in fictional worlds -- we can't count on them to fix problems in the real world! Evil or Very Mad Wink
Razz
Post 07 Nov 2015, 12:47
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TheRaven



Joined: 22 Apr 2008
Posts: 89
Location: U.S.A.
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!
Post 20 Oct 2016, 05:22
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MHajduk



Joined: 30 Mar 2006
Posts: 6034
Location: Poland
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 one-page document). Smile

Image
Post 20 Oct 2016, 21:06
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