Geometry

3D to be specific!

Discuss the language of the universe.

Moderators: Calilasseia, ADParker

Geometry

#1  Postby LjSpike » Apr 21, 2016 3:42 pm

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
THREAD STARTER
 
Posts: 89
Age: 20
Male

United Kingdom (uk)
Print view this post

Ads by Google


Re: Geometry

#2  Postby Cito di Pense » Apr 21, 2016 4:30 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. 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.
User avatar
Cito di Pense
 
Name: Fay Smask
Posts: 29351
Age: 23
Male

Country: The Heartland
Mongolia (mn)
Print view this post

Re: Geometry

#3  Postby 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.
VazScep
 
Posts: 4590

United Kingdom (uk)
Print view this post


Return to Mathematics

Who is online

Users viewing this topic: No registered users and 1 guest