Talk:Pascal's pyramid

From Wikipedia, the free encyclopedia

Why is this called a pyramid? The base is a triangle, so isn't it a tetrahedron?

A tetrahedron is a pyramid. Factitious 00:47, Jun 25, 2005 (UTC)

Summing the numbers in each column of a layer of Pascal's pyramid gives the nth power of 111 in base infinity (i.e. without carrying over during multiplication), where n is the layer - 1.

Is it really accurate to call this "base infinity"? It's more accurately base 10 (but without said carry-over). Actually, more generally, it's the nth power of 111 in any base. For example, in base 9, 111^2 = 12321:
1 + 2*9 + 3*9^2 + 2*9^3 + 1*9^4 = 8281 = (1 + 9 + 81)^2. --Matthew0028 13:53, 14 February 2006 (UTC)

Yes, base 9 works for 111^2, however as you get into higher powers of 111, you are forced, according to the rules of multiplication, to carry over. Higher number bases allow for higher nmbers to not be carried over. Base "infinity" makes the rule applicable to all powers of 111. I take the blame for making up the term "base infinity", however in this situation I feel that it is quite a good description of what is actually happening.

[edit] Dead Link?

http://people.ucsc.edu/~erowland/pascal.html : Not Found The requested URL /~erowland/pascal.html was not found on this server. --NeoUrfahraner 10:00, 15 November 2006 (UTC)

the numbers in Pascal's pyramid can be found by summing the three numbers in the preceding layer. The same as you can find the numbers of pascal's triangle by summing the two numbers in the preceding row.