What are triangular numbers? Do you mean there are rectangular or octahedral numbers too?

Question

What are triangular numbers? Do you mean there are rectangular or octahedral numbers too?

Please explain and any examples are kindly accepted.

Answer 1

There are pentagonal, octahedral, etc numbers. See http://mathworld.wolfram.com/FigurateNumber.html for more info. Basically you just count up the points in the shape, and that is the value of the number. Then put one mor epoint around the edge (perimeter) and that is the next number in the sequence.

Answer 2

Triangular numbers are well covered by the previous posters.

there are also squares and cubes. (1, 4, 9, 16, 25...) and (1, 8, 27, 64, 125...).

In the complex field there are "rectangular numbers" of the form a + ib (where i is the square root of -1) as opposed to "polar numbers" of the form r ( Cos(t) + i Sin(t) ).
It's a descritive term of how a complex number is written, not a qualifier of the number itself (any number can be written in rectangular form). Same goes for 2-D Euclidean space (rectangular coordinates vs polar coordinates)

And, of course, there are "round figures" (when fractions are rounded).

But no octahedral numbers. I did find an octahedral group: the symmetric group of order 4! (4! = 1*2*3*4)

Oops. Frogot "Pascal's triangle" (see wiki)

Answer 3

1 = 1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15
1 + 2 + 3 + 4 + 5 + 6 = 21
etc...

http://www.mathematische-basteleien.de/triangularnumber.htm

Answer 4

You mean OCTOGONAL numbers. An octohedron is a solid figure. Anyway, a triangular numbet has the form n(n+1)/2. A rectangular number has the form ab.

Answer 5

If you take some coins and put them:

1 in the top row
2 in the second row
3 in the third row
etc

It forms a triangle, hence the term "triangular number."

In essence they are numbers that are the sum of numbers 1 thru n.

Σi for i=1 to n

The sum of the numbers 1 thru n is: n(n+1)/2.

Answer 6

http://en.wikipedia.org/wiki/Triangular_number