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Parents were divided after the reporter Mark Tighe of the Sunday Independent shared a child’s homework problem that asked how many corners does a semi-circle have. The child wrote 2, which was marked wrong with the correct answer of 0.
What do you think the answer is? I will suggest the answers of 0, 2, infinite, and 3 all have different merits.
As usual, watch the video for a solution.
How many corners does a semi-circle have?
Or keep reading.
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“All will be well if you use your mind for your decisions, and mind only your decisions.” Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon.
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Answer To How many corners does a semi-circle have?
(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).
The statistician George E.P. Box is credited with saying, “All models are wrong, but some models are useful.” Scientific models necessarily make some approximation or idealization of reality, so they are technically wrong; however, the models can be great approximations and useful practically.
Think about how we do geometry in flat surfaces, when in reality space-time is curved; or how we use the ideal gas law when in fact gases do not have perfectly elastic collisions in reality. We often talk about “cold” as if “cold” is a thing. We say don’t let the cold air in, it will be cold tomorrow, or there is a cold front coming. But there is no actual thing as cold. Temperature is a measurement of average kinetic energy, which can either be high or low. There is heat, and the feeling of cold is actually heat leaving your body. So while “cold” is wrong, the concept of cold is useful.
Similarly we can say “corners of a semicircle” is a ridiculous question, lest we first define what a corner is.
One note: a semi-circle would technically just be half of a circle, so just a half arc. This problem is asking for a closed shape, which may be more accurately describe as a half-disk.
Answers of 0 or 2
Mathematically a corner can be taken as a point where the endpoints of 2 straight edges meet. In that case there would be 0 corners to a semi-circle.
But a corner can also be where the endpoints of any two edges meet, whether the edges are curved or straight. So the semi-circle would have 2 corners where its diameter endpoints meet the curved arc. In fact, if you had a table shaped in a half moon or half round, you might be worried that someone could run into its 2 sharp corner edges. So practically 2 is a useful answer.
Answer of infinite
A semicircle’s arc can also be thought of as the limit of a polygon with n sides as the number of sides goes to infinity. While the arc ultimately is perfectly curved, in reality it can be modeled by an arc with about 20 corners, and that will be visually indistinguishable from an arc. So while the semi-circle’s arc does not actually have corners, this answer of infinite can serve a useful purpose.
I did a poll on YouTube that received well over 30,000 votes. About 75% of people felt 2 was correct. The next popular answers were 0 (9%), infinite (10%), and 3 (1%). About 5% said all of the above.
Answer of 3
Most people understood where the options came from, except 3. How can a semicircle have 3 corners?
In graphic design, an anchor point–or corner point–is the endpoint between a curved or straight edge. A semicircle is represented by 3 corners points: the 2 on the endpoints of its diameter, and 1 point in the middle of the arc. If you are creating a semi-circle in Adobe Illustrator, you will definitely be creating a shape with 3 corner points! So you could say there are 3 corners to the shape.
So ultimately most people would say the answer is 2 corners. But there are good reasons to give answers 0, infinite, or 3 corners.
References
Mark Tighe Sunday Independent reporter
https://twitter.com/MarkLTighe/status/1726637186957926802
Poll
https://www.youtube.com/post/UgkxL3J_k11IT6Z9dOAS3k1LoYsDcuW0ZYAe
All models are wrong, but some are useful, George Box
https://jamesclear.com/all-models-are-wrong
https://en.wikipedia.org/wiki/All_models_are_wrong
Vertex
https://en.wikipedia.org/wiki/Vertex_(geometry)
Adobe
https://helpx.adobe.com/illustrator/using/artwork-essentials/paths-and-shapes.html
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