Lately, I’ve been looking at more information visualizations, and it’s not been said enough that simple geometry is often ignored.
Often times, I’ll see visualizations like this, where bubbles are employed to visually compare different records. It seems likely that people judge and compare difference in size by area. However, the artist/designer makes the mistake of mapping the data to the radius instead. This doesn’t work for circles because of your old 4th grade math, stating that A = pi * r^2, where the area doesn’t increase linearly as a proportion of the radius.
For the record, it’s done correctly here in the visualization above, as far as I can tell.
Here, the designer decided to use triangles. If he mapped the data to the height of the triangles, that’s fine, because for triangles, A = 0.5 * b * h, and hence area varies in linear proportion to height.
However, looking at Hungary, the red triangle doesn’t seem quite a quarter of the black triangle.
Beyond that, for these two examples, I really see no reason to use circles or triangles. People are able to judge spatial difference much more easily, as opposed to size. It would have been far more effective to use bar charts and rectangles instead of shapes like triangles and circles. In my opinion, you only use that if the spatial x and y axis are already being used to convey other information already.