Katabatak Math-An Exploration In Pure Number Theory

[TheBigDog]

:)

:hyper:

 

:beer: :beer: :beer: B) :beer: :beer: :beer:

 

Bill

[Queso]

Full page work in progress; feel free to point out any error(s)

Triangular Table Tiling

 

I love this, Turtle.

 

Two minds absorbing, spilling.

 

A system, and it's collapse...upward.

 

I do not understand the formula, I never passed Algebra in high school..

 

But, I see this! I see it with my own two eyes it's like music...

Genius music.

[TheBigDog]

I found two errors in the primary graph and have made the corrections. Given the complexity at this level, I think a triple-check is in order before I continue with the tiling. While writing software to generate the graphs would speed things up, there is a lot yet to learn through doing the work long-hand (if nothing else, how to properly write the software!).

 

As I make haste slowly, I note with interest that the admonition to 'make haste slowly' comes from my dear old friend Ben Franklin. I have little doubt, given his interest in magic squares, that he would find this work very interesting. :hihi:

It is officially in the queue. I have another project that is consuming my time right now. Plus school. But when the nights get long and cold and my only source of warmth is the heat coming off of the laptop computer, that is when we will jump into writing the Katabatakator. I think that we are just one cycle of obsession away.

 

Bill

[anglepose]

those are pretty cool tiles man perhaps you should try doing hidden images within the tiled squares by changing what number you start on so as to make a slight off sequence on the image line wonder how that would look especialy in kaliedescope style and after my long long break ive just cuaght up again :)

[anglepose]

I havent read the thread!!!!!!!!

i mean llike pictures as in ducks and trees and houses

ill show you what i mean its not realy mathmatical just a bit of fun

:teeth:

 

 

 

ive read nearly every post

[Buffy]

Hey that's an idea Turtle: instead of just colors, you could have little icons of bucks and dunnies! They'd be *so* cute! :teeth: We'd have to come up with 16 of them though.

 

Back on colors though: Have you ever tried a 256 color mapping? I hate "the 16 colors you have to say on the PC." Yes, I know that would require you to change your algorithm to use base-64, but I proposed supporting alternative bases way back in this thread....

 

QTπ,

Buffy

[anglepose]

yep i had that idead too shades of colors and the likes

and for the pics i gues you could even have.....

 

TURTLES

[anglepose]

funk out lol some artistics added hehe :teeth:

 

[ATTACH]863[/ATTACH]

 

and that is only where the fun begins

[anglepose]

Not quite with the drift, but has tormod come up with any musicall incorperations for katabatak

 

oh and altohugh reading every post im afraid i went into blind reading mode picking up the odd fact after page 3 post 24 as i could not quite understand it. could you please do a draft up for a 13 year old that will get me doing some of that mathematical arabic style art and being able to understand the math behind it instead of aimlesly drawing my interpretation. Just enough to get me to under stand how you basicly transfer it to triangle, like the obvius i can go back then and reread the posts with a better under standing.

 

No worries if it takes to much time and you dont want to ill just go along with the flow till i can understand it.

[InfiniteNow]

Been busy tonight. Don't stay in the dungeon too long. Fresh air is good for the neurons. More obsessed than Calvin Klein, but with the spirit of Fermat you are. :cup:

 

 

Inspired,

[Buffy]

Shift your shades to red and green, and blue and gold, and you've got a successful holiday wrapping paper line there Mr. Turtle!

 

He knows when you've been tesselating,

Buffy

[anglepose]

so what i did earlier this week comes out as such:

[ATTACH]875[/ATTACH]

[anglepose]

aah so the base of your table must must equal the sides. I copyed it from the previus table of mine onto your blank chart becuase thats the only isometric paper on the computer i can easily find But now i realise that it was acceptable on my previus table as they were repetions of the origanal sqaure but when put in to triangular context they are not repetitions but an extrapalation of the origanal triangle.

:cup:

i will now fix it up and complete my origanal intention of repetition.

[anglepose]

this more mathmatical .... i have done a base ten chart and repeated to form a hexagon

 

[anglepose]

Could you please explain where I am going wrong.

I am determined to acheive an understanding and create a table.

Currently i am converting the preius "funky" table i did in a spreadsheet into a triangular katabatak chart is the origanal spreadsheet chart rite in the first place and im sticking to the most basic chart to just build an understanding then i can move on to more of the complicated tables .Could you also please help to clarify how your complicated charts work in the case of the base 3-10 tables i cannot see the link you are creating to form those k digits.

[anglepose]

You Are A Legend :confused:

[anglepose]

How would you change the base it is probably blatently obvios but i cannot understand base 9 8 7 6 5 4 3 2 and 11 12.... i get base 10 but as for the rest i relate to some sections but it does not make sense to me and it was an area i think you jumped as page 6 jumps straight to base 12 but i perfectly under stand base 10 now and what is involved in the triangle. and then when i can figure out how to create a base 13 chart i will be able to go to my home ground of music with katabatak.