Thread: Transformations: Shape and Size

I've been thinking about this for some time and would like your views on the same. 2 questions..

1.

When we are comparing the size of two objects, does the shape have to be the same?
Suppose you have a circular plot and a rectangular plot of the same area, do they have the same size then?
Or can we even talk about the size of two objects of different shape? Suppose we have two objects of the same size, in that case, is it taken for granted that the 2 have the same shape as well?

2.

When we talk about size, what are we talking about?
For example if someone points to an object and asks what the size of it is. Is it the area, the volume or either of the 2 depending on the object?

Please put forth your views..

What I want specifically is, in transformations when we talk about preservation of size, is it the same as preservation of shape and size or is there a difference between the two? I understand that technically, it won't be possible to transform any shape into a different one using either of the transformations- reflection. translation or rotation and so talking about it might be futile but let's take a general look at size and shape.

Cheers!

Originally Posted by freakinda

1. When we are comparing the size of two objects, does the shape have to be the same?

Why would they have to be the same? And if they were the same, then what would there be to "compare"?

Originally Posted by freakinda

Suppose you have a circular plot and a rectangular plot of the same area, do they have the same size then?

If "size" means "area", then yes, they have the same area and thus the same size.

Originally Posted by freakinda

Or can we even talk about the size of two objects of different shape?

Why would we not be able to refer to the sizes of differently-shaped objects? That would be like saying that, since the kitchen is square-ish and the pantry is rectangular, we are not allowed to discuss square footage and how much tile we'll need to buy to upgrade the flooring in each.

Originally Posted by freakinda

Suppose we have two objects of the same size, in that case, is it taken for granted that the 2 have the same shape as well?

Why would the shape have to follow from the size? "Size" and "shape" are two different things; there is no reason that equality of the one would require equality of the other. Just because the pantry turns out to have the same square footage as the kitchen, doesn't mean the pantry transmogrifies and turns into a square-ish area, too.

Originally Posted by freakinda

2.When we talk about size, what are we talking about?

What is meant will probably depend upon the context. In mathematics, the term should be defined before use.

Originally Posted by freakinda

For example if someone points to an object and asks what the size of it is. Is it the area, the volume or either of the 2 depending on the object?

You'd have to ask the person; only he knows what he meant.