In the following image, there are two rows of shapes.
For each row, which shape do you perceive to be the largest and which shape do you perceive to be the smallest? If you would like, feel free to explain your answers.
Bonus question: All three shapes in the top row have something in common. All three shapes in the bottom row have something different in common. What are these common properties, and does one influence your perception of size more than the other?
Thank you for your answers! I suppose I should have given some background on why I'm asking the question. I'm designing three user interface elements that represent similar information. I found that one good visual way of differentiating between them was to make them different shapes.
However, I wanted these elements to be the same "size". When varying shapes are involved, different people perceive their sizes different ways.
My first attempt was to make all the shapes equal in area. (Those are the shapes you see in the top row. Good work identifying that property!) I thought that because each shape provides the same amount of luminosity information to the brain, they would all be perceived to be of equal size. However, it's pretty obvious that they appear very different in size to almost everyone.
My second attempt was to make all the shapes equal in perimeter. (Those are the shapes in the bottom row.) To me, they appear closer to the same "size" than before. I'm still not completely satisfied, though.
While same height and width would seem to be an obvious choice for "same size", having circles and squares (or orthogonal and curved lines, to simplify) in the same context causes an interesting optical phenomenon. The curved surfaces will appear to be smaller and "shrink" away from the orthogonal ones.
One example of this in practice is in fonts. Curved contours must protrude above and below the baseline in order to achieve the same optical size as straight contours.
A very similar effect (but based on different pattern recognitions in the brain) is true for sharp angles in opposition to orthogonal lines. For example, the peak of the triangle will diminish if it does not extend above the top of an adjacent square.
If I rotated the square 45 degrees to obscure its horizontal and vertical lines, these effects would not be so great.
I'll try and provide a few more examples in a little bit to get your feedback.
Edit: Here is an example of three shapes with the exact same height and width:
To most people, the square will be obviously larger than the other shapes. In fact, compared to the triangle, it now has twice the area and is about 33% larger in perimeter.