## Geometry

3D to be specific!

Discuss the language of the universe.

### Geometry

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?
LjSpike

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### Re: Geometry

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. For the problem you're working on, "1" is the scale for some coordinate system. It's what "2" is twice as big as. So a prism with a depth of 2 has twice as much volume as a prism with a depth of 1, the floor plans being identical. You can test this by shearing a deck of playing cards. The volume of the deck of cards remains constant.

Stonewalls do not a prism make, nor ironic barbs a gauge.
Хлопнут без некролога. -- Серге́й Па́влович Королёв

Translation by Elbert Hubbard: Do not take life too seriously. You're not going to get out of it alive. Cito di Pense

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Age: 23 Country: The Heartland Print view this post

### Re: Geometry

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.
VazScep

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