02-04-2025, 08:45 PM
Here's a question that was asked on a child's maths homework: how many corners does a semicircle have? They gave the answer 2... but, the teacher marked this wrong, and said the correct answer was, in fact, 0. So, which is correct?
Well, in the above video, mathematician Presh Talwalkar makes the case for both of these - but he also argues that infinity is a valid answer, and even 3 might be

- The case for 2: A 'corner' is where two lines meet. But do the lines have to be straight? If not, then the two points where the curved edge meets the straight edge both count as 'corners'.
- The case for 0: On the other hand, we could just as easily define a 'corner' as a point where two straight lines meet. A semicircle doesn't have any of those!
- The case for infinity: Think about a 3-sided equilateral triangle; a 4-sided square; a 5-sided regular pentagon; a 6-sided regular hexagon; and so on. As the number of sides increases, the shapes appear more and more circular (a 50-sided one already looks very much like a circle
). In fact, if you kept this up forever, you'd end up with a circle! So, you can argue that a circle has infinitely many corners (and thus, a semicircle also has infinitely many corners, since it's half a circle
!)
- The case for 3: This one comes from the world of graphics design. A 'path' consists of one or more straight or curved line segments, that you draw on a canvas. The shape of the path is controlled by 'anchor points' - and the anchor points at the ends of a path are called 'control handles' or 'corner points'. But to draw a semicircle, you need three of these: two where the curve meets a straight line, and one in the middle of the curve.
Personally, I think the case for 2 is the most compelling - but, what about you?
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