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A number is triangular if that number of dots could be arranged into a filled equilateral triangle. It is perhaps easiest to picture with billiard balls in a triangle. Each 'row' of the triangle has one more ball than the row above it, forming an equilateral triangle. The triangular numbers are 1, 3, 6, 10, 15 and so on. The complete set of triangular numbers can be represented by the formula: Tn = n(n+1)/2 Where n is any integer greater than 0.
Pyramid. Or triangular prism, depending on what exactly you mean.
a triangle, a 3 sided figure, a figure with 3 points, etc.
First, I'm assuming the by corners, you mean verticies. Second, the answer depends on what you mean by "three dimensional triangle. To some, this could be interpreted as a pyramid. However, I think it is more likely that you are referring to a triangular prism- a prism shape with a triangle as each base. In this case, there are six "corners". Each side has three, where the length-wise edges of the prism intersect the verticies of the triangle. There are three corners on each side, for a total of six. If you really meant a pyramid, then there are five corners.
Each term is a square or triangular number. In the context of the sequence of square numbers, the first term is the first square number, the second term is the second square number and so on.