Pascal's Triangle

by **Environmentalist** on Wed Jan 07, 2009 7:51 pm

one possible bonus, the hockey stick, is formed in many ways, so long as the numbers add up, like in the image below, where

1 + 12 = 13
1 + 6 + 26 + 56 = 84
1 + 7 + 28 + 84 + 210 + 462 + 924 = 1716

and another bonus, Fibonnacci's numbers (can begin from left side or right side, which is nice)

1, 2
1, 3, 1
1, 4, 3
1 ,5, 6, 1
1, 6, 10, 4
1, 7, 15, 10, 1
etc.

and here is a way to make it even more interesting....3D. note that the yellow and purple coloring corresponds to odd and even numbers, respectively

an alternative appearance of the triangle, also showing odds and evens in different colors. one could easily make a square using 2 triangles with the shape below, which would be effectively the same as the 3D image above.

this could be made either a simple map, or complex. personally, i say the more complex the better.
ok, i'll stop now and wait to see what people think before saying any more.

by **zeros** on Fri Jan 09, 2009 6:14 am

Very interesting. I'm pleased I visited this page! Thanks. I'll be back…

by **MrBenn** on Fri Jan 09, 2009 6:24 am

Sierpinski's Gasket... It's interesting from a Number Theory point of view, but I'm not convinced how attractive it would become as a CC map?

by **Barack_Obama** on Sun Jan 11, 2009 6:04 am

well, its sounds nice but not everyones a mathematician

by **Joodoo** on Sun Jan 11, 2009 6:06 am

Interesting idea...

by **Environmentalist** on Tue Jan 20, 2009 7:42 pm

Barack_Obama wrote:well, its sounds nice but not everyones a mathematician

it doesn't take a mathematician to play a map such as i've proposed. it'd require knowing how to add sometimes, perhaps. but its really all about patterns, and simple diagrams could accompany the map to show people those patterns. anyway, does it really matter? everybody has maps they don't play, for whatever reason.

the real strength of this idea, which i believe is what sets it apart from all the others, is the way that the region bonuses are extensively interconnected, not to mention the shear number of obtainable bonuses. its kind of like connect four on steroids. but there's more....take a look at this following picture again:

consider the possibility of having attack restrictions, such as along the spine where the 2 sides meet (what would be the row of 1's along the side of Pascal's triangle). and don't forget about the additional regional bonuses there (purple triangles/even numbers). lines of attack could be, at least in part, dictated by that pattern.

--------------------------------------------------------------------------------

i suppose if i had a choice, i would make 2 maps. the first would be a strictly 2 dimensional map based on the traditional Pascal's Triangle. i'd wait and do a 2nd, more complex map based on the above pyramid.

and this isn't anywhere near as complex as the idea i'm still working on. this just crossed my mind along the way, so i figured i'd post it. imo, its a pretty simple concept that could be developed fairly quickly. i guess the biggest problem is finding people to develop it....

by **zeros** on Mon Jan 26, 2009 9:51 am

I like your idea.

In my opinion further complication would make it less appealing to many people, perhaps myself included! If your maps require extensive explanation, that could put people off.

An important philosophy of mathematics is that the most beautiful ideas are often the simplest.

by **Environmentalist** on Mon Jan 26, 2009 10:59 am

zeros wrote:I like your idea.

In my opinion further complication would make it less appealing to many people, perhaps myself included! If your maps require extensive explanation, that could put people off.

An important philosophy of mathematics is that the most beautiful ideas are often the simplest.

no argument there. perhaps starting with a simple map would help to generate more interest in a more complex version further down the road.

by **zeros** on Mon Jan 26, 2009 11:35 am

Yes, that's a good idea.

There can be no better example of that thinking than Conquer Club itself, which sits somewhere in the complexity of on line gaming of this immense world wide web. Conquer Club; a relative jungle of variations of its great but comparatively simple ancestor: Risk. Risk is itself a variation on the concept of the board game. And all board games are variations on the idea of playing games, which includes such diversity as soccer, golf, hangman, Formula 1 and even dancing!

How many people would be here if it weren't for the original Risk?

Generate interest first with simplicity. Once interest is properly established, people will be more likely to accept your brilliant ideas.

Understanding the apparently complex requires a thorough grasp of the basics.

That's why I know you understand my first complicated paragraph. -You have the interest already!

by **sailorseal** on Mon Jan 26, 2009 4:44 pm

I enjoy the idea but you need to figure out how to put a territory number in with a number for the armies also try and keep it 2-D

by **Victor Sullivan** on Thu Sep 30, 2010 11:08 pm

I know this is dead, but this is... AMAZING. Of course, I'm a math guy, so... yeah. I wonder how the bonuses would work...? I'd be willing to pick this one back up, if anyone's interested in the idea.

-Sully

by **tokle** on Fri Oct 01, 2010 5:43 pm

I think you should. It looks promising.

by **Victor Sullivan** on Fri Oct 01, 2010 6:19 pm

Shweet! I can make a draft if I get a couple more supporters

by **kengyin** on Fri Oct 01, 2010 7:35 pm

i support you, i love maths

by **rdsrds2120** on Mon Oct 04, 2010 12:06 am

kengyin wrote:i support you, i love maths

Me too, and I like English!
I think this would be ok as a map to play on, it's the demand, however, that worries me.

by **Victor Sullivan** on Mon Oct 04, 2010 12:58 am

rdsrds2120 wrote:
kengyin wrote:i support you, i love maths

Me too, and I like English!
I think this would be ok as a map to play on, it's the demand, however, that worries me.

Ah, yes. Abstract maps tend to not go over well, I'm afraid. But I do have a fantastic idea as to how this will work and I've even thought of some problems I'll run into and have fixed them!

Hopefully I can get a draft up for everyone soon.

by **RedFlyingGolf** on Mon Oct 04, 2010 2:44 pm

I just don't see this becoming a map.

by **army of nobunaga** on Mon Oct 04, 2010 2:54 pm

I dont see if becoming a map only because of the immense time and hurdles involved. The Idea could work. And god knows there are enough geeks in CC that this would have a following.

gl if you try it.

by **ManBungalow** on Tue Oct 05, 2010 2:15 pm

If somebody is seriously considering making a mathematical map, try looking Fibonacci up.

You could draw a pineapple with an interesting bonus structure.

by **Victor Sullivan** on Tue Oct 05, 2010 8:30 pm

I assume you are referring to the Fibonacci sequence? I don't fully understand what you mean by the whole pineapple thing.

by **Victor Sullivan** on Tue Oct 05, 2010 10:28 pm

Please redirect your comments here:
http://www.conquerclub.com/forum/viewtopic.php?f=63&t=128268
I started a new thread so I could update things easier.

-Sully