Triangles like Pascal's triangle?

[foggel]

Are there other triangles like Pascal's triangle? His triangle amazes me, and have inspired me to make my own, and I'm just convinced about that numbers are more than just numbers. But are there other triangles or "models" except those who are listed under "See also" in wikipedia?

 

http://en.wikipedia.org/wiki/Pascal%27s_triangle#See_also

 

I enjoy comparing my own triangles with other triangles and see how it all just fits together. Yeah, I'm a total nerd... But ofcourse, I'm not going to hide that I want to see if my triangles already have been "presented", or whatever the correct wording would be.

[the tree]

I'm fairly sure that Wikipedia lists all the well studied or interesting triangle-like sequences. There are of course other objects based around triangles like the Sierpinski triange (which can be aproximated by Pascal's, as you'd have read).

 

If you're interested in that sort of number play then maybe you'd be just as interested in Latin squares and Magic squares.

 

It might be the case that in your experimenting you've come across something that just hasn't been commonly formatted as a triangle before - novel representations can sometimes be very useful so keep with that.

[crownedconquern]

My triangles are better.

triangles up,triangles down,triangles all,all around....

 

 

Yes,mine is the best in the world.

 

um here are some magick squares....

 

4,9,2

3,5,7

8,1,6

 

4,14,15,1

9,7,6,12

5,11,10,8

16,2,3,13

 

11,24,7,20,3

4,12,25,8,16

7,5,13,21,9

10,18,1,14,22

23,6,19,2,15

 

6,32,3,34,35,1

7,11,27,28,8,30

19,14,16,15,23,24

18,20,22,21,17,13

25,29,10,9,26,12

36,5,33,4,2,31

 

22,47,16,41,10,35,4

5,23,48,17,42,11,29

30,6,24,49,18,36,12

13,31,7,25,43,19,37

38,14,32,1,26,44,20

21,39,8,33,2,27,45

46,15,40,9,34,3,28

 

8,58,59,5,4,62,63,1

49,15,14,52,53,11,10,56

41,23,22,44,48,19,18,45

32,34,35,29,25,38,39,28

40,26,27,37,36,39,31,33

17,47,46,20,21,43,42,24

9,55,54,12,13,51,50,16

64,2,3,61,60,6,7,57

 

37,78,29,70,21,62,13,54,5

6,38,79,30,71,22,63,14,46

47,7,39,80,31,72,23,55,15

16,48,8,40,81,32,64,24,56

57,17,49,9,41,73,33,65,25

26,58,18,50,1,42,74,34,66

67,27,59,10,51,2,43,75,35

36,68,19,60,11,52,3,44,76

77,28,69,20,61,12,53,4,45

 

Here is some more magick numbers:

 

7,1,2,3,3,4,5,6,6,7,8,9,9,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3

5,5,2,0,7,5,2,0,7,5,2,0,7,0,1,2,2,3,4,5,5,6,7,8,8,9,0,0,1,2,3,4,4,5,6,7,7,8,9,0,0,1,2,3,3,4,5,6

3,6,9,3,6,9,3,6,9,3,6,9,3,6,9,3,6,9,3,6,9,3,6,9,3,6,9,3,6,9,3,6,9,3,6,9,3,6,9,3,6,9,3,6,9,3,6,9

[khaled]

magic numbers,

 

sometimes, i think that magic numbers can with some ways lead to lucky streams,

[ewmon]

A while back, I discovered recursive patterns in density values using a hexagonal grid, but I didn't think people paid much attention to such things. How do I go about learning if I've found something new? (I had also discovered that the least squared method can be computed {much more naturally} without squaring or minimizing anything, and I chased that around for a few years before finding a university professor who told me I hadn't found anything new.)

[khaled]

i think it's better to think of a mathematical system that can have mass effects on the real world,

[Sisyphus]

magic numbers,

 

sometimes, i think that magic numbers can with some ways lead to lucky streams,

 

i think it's better to think of a mathematical system that can have mass effects on the real world,

 

What are you talking about?

[khaled]

Sisyphus,

 

sorry, and i won't write my new thoughts in Replies again ...

 

or maybe im not good enough to be a scientist,

[ajb]

I have used a "triangle " or "pyramid ", but I called it a "tower" to represent a sequence of differential equations. It can give a nice way of spotting symmetries, finding what vanishes under certain conditions, gives a possible method of solving...

 

However, I don't think there was anything deep involved in this. It was a nice way of writing a sum of terms and separating them order by order in something.

Edited April 24, 2010 by ajb

[the tree]

Sometimes arranging data in just the right way visually can be exceptionally helpful, our brains are often better handled to see patterns in shapes and colours than patterns in series of numbers or symbols. It's up to you if you think "deep" when something can reveal information that was otherwise hidden or difficult to see - sometimes it can be pretty exciting.

[ajb]

... and colours...

 

A friend of mine was working with tensors with indices that had "three flavours". The index carried all this "extra information". So what he did was simply colour the indices "Red", "Green", "Blue" in order not to clutter the notation. This also made it easier to spot what was going on. He implemented this in Mathematica!

 

Years ago I started to look at the cohomology of tiling and graphs. (Don't ask as I have forgotten what I was doing!) I managed to spot some "scaling relations" via careful colouring.

 

One drawback could be the lack of colour printers and colour blindness!