Design for Tracking Progress
When the ISSN came and saw my school, they had a document to show our growth in several different categories that I thought looked cool. It consisted of a circle with various rings to show your level in a category, and split into wedges for each category. The person presenting it, however, pointed it out that is was fairly flawed, because the outside ring looked so much bigger than the inside ones, so even when you reached 3/4 it looked fairly empty.
Of course, the problem was purely mathematical. Whoever had designed the chart had split the radius of each wedge into 4 parts equally, so that the first ring started 1/4 of the way down the radius, the second ring was 1/2 of the way, etc. Clearly that will make the areas very different. So I quickly made up a version where the areas were proportional, which isn’t too hard in graphing software, since the formula for a circle uses r^2 anyway.
Afterwards, I decided to make one for my own class. I also decided that, because each mark (Novice, Apprentice, Proficient, and Master) was not weighed the same (for example, Novice is a 50, worth a whole lot more than any other category from the start), I would have the areas of the circles have similar weights. Here’s what I made: