**#3** by **VazScep** » Apr 21, 2016 5:15 pm

LjSpike wrote:Ok, I was explaining how to solve the volume of a prism to my friend via a little method I new in my head of how a 2d shape could be considered a prism with a depth of 1 (of whatever the units be).

Other people however every so often say a 2d shape has a depth of 0. Now in science this'd be correct, but mathematically speaking, would this definition of having a depth of 1 be a suitable one?

No. You definitely want to say that a 2d shape embedded in three dimensions has no depth. A triangle in three dimensions is different from the triangular prism whose depth is 1.

Given a unit length, you have a basis for comparing lengths. You construct the unit square to get a basis for area. And you construct the unit cube to get the basis for volumes. So the way you measure volume is straight-off based around having taken a square, and made its unit prism. Facts about the ratios of volumes of prisms say that you just need to compute the area of a face and then multiply by the depth.

Here we go again. First, we discover recursion.