Some context would help. If you could tell us where you read a statement about a "distinct square" or "distinct squares", and what it said, that might help.

If it is the plural, "distinct squares", it might mean just mean squares that are distinct, meaning different, from each other.

"There are only 31 numbers that cannot be expressed as the sum of distinct squares: 2, 3, 6, 7, 8, 11, 12, 15, 18, 19, 22, 23, 24, 27, 28, 31, 32, 33, 43, 44, 47, 48, 60, 67, 72, 76, 92, 96, 108, 112, 128 (Sloane's A001422; Guy 1994; Savin 2000). "

For example I can write 6 = 2^{2} + 1^{2} + 1^{2} = 4+ 1+1, and that's a sum of squares, but the squares in that sum are not all different from each other, i.e. not distinct.

"21 is the smallest number of distinct squares needed to tile a square."

And this page, http://www.squaring.net/sq/ss/ss.html seems to say the same thing. Plus it has a drawing of what that square tiled with 21 smaller squares looks like.

I'm guessing that the teacher is asking for you to show a square that is easily recognizable (or distinct). So in geometry, you could show a distinct square in a graph where corresponding horizontal and vertical measurements allow you to clearly see that all four sides are in fact equal. (Obviously, if they are not, you probably have a rectangle).

active| newest | oldestIf it is the plural, "distinct squares", it might mean just mean squares that are distinct, meaning

different, from each other.I found all kinds of weird stuff searching on this phrase. This page:

http://mathworld.wolfram.com/SquareNumber.html

uses the phrase in this sentence: For example I can write 6 = 2

^{2}+ 1^{2}+ 1^{2}= 4+ 1+1, and that's a sum of squares, but the squares in that sum are not all different from each other, i.e. not distinct.Getting back to something that looks like geometry, I read here,

http://www2.stetson.edu/~efriedma/numbers.html

the statement:

And this page,

http://www.squaring.net/sq/ss/ss.html

seems to say the same thing. Plus it has a drawing of what that square tiled with 21 smaller squares looks like.

I feel the google translator has fail at this point.

I'm guessing that the teacher is asking for you to show a square that is easily recognizable (or distinct). So in geometry, you could show a distinct square in a graph where corresponding horizontal and vertical measurements allow you to clearly see that all four sides are in fact equal. (Obviously, if they are not, you probably have a rectangle).