Click on 'related links' below. The link will take you to some pictures of rectangles some are squares some are not.
All positive integers which are not perfect squares.
Every non-rectangular parallelogram has. (It's not correct to say that a parallelogram has, because rectangles and squares are parallelograms too.)
Quadrilaterals are things with four sides, like squares, rectangles, diamonds, trapezoids, rhombuses. Anything that doesn't have four sides (an infinite list) is a non-example of a quadrilateral.
No. 1.5^2 = 2.25 is rational.
Not if the rectangles are non-overlapping.
A chess board has 64 squares - but if you look closely, you can make another square out of every 2x2 (49), 3x3 (49) 4x4 (25) 5x5 (16) 6x6 (9) 7x7 (4) and finally one 8x8 square - so 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204 squares. If we assume "rectangles" are all other rectangles that are not also squares (it could be argued that a rectangle is a square - in which case you add 204 to the number I compute here), then you can see a whole bunch more. It helps to know that 1 + 2 + 3 + ... + n = n x (n+1) / 2 (speeds up the math) 1 square tall: 2 x 1: 7 per row times 8 rows = 56 3 x 1: 6 per row ... = 48 for a total of (7+6+5+4+3+2+1) x 8 (rows) = 8 x 8 x 7 / 2 = 224 2 squares tall: (7 + 6 + ...) x 7 x 2 = 8 x 7 x 7 / 2 You can see that if we keep going we get 8 x (8 + 7 + 6 + ... + 1) x 7 / 2 = 8 x ( 8 x (8 + 1 ) / 2 ) x 7 / 2 = 2 x 8 x 9 x 7 total number of rectangles = 1008 So the answer is 204 squares and 1008 (non-square) rectangles, or 204 squares and 1212 "rectangles" (including squares).
All sorts of figures. The only regular polygons that can tessellate by themselves are triangles, squares and hexagons. Irregular polygons such as rectangles, rhombuses, parallelograms and trapeziums will as well. Regular octagons combined with squares will. Other regular polygons can be combined with appropriate star-shapes to tesselate. There are also Penrose tilings which, although they cover the plane, are non-periodic in the sense that the pattern does not repeat itself if you move along. Finally there are many irregular shapes that will tessellate.
The number line includes all rational numbers but also has irrational ones. It is the REAL number line. The square root of non-perfect squares are on it and pi is also on it and they are not rational.
A polygon is usually defined as a plane figure bounded by straight line segments. Any figure which does not correspond to this definition would be a non-polygon. For example, triangles, rectangles, squares, and even star shapes are called polygons. A circle, semicircle or oval is not a polygon. The have curved boundaries.