Oh FFS. This simple question has apparently caused all sorts of mayhem among the innumerate:
The answer is of course “FALSE” — and to think otherwise is to be ignorant of two of the simplest definitions in mathematics, i.e.
- “A right angle is defined as two straight lines meeting at a 90-degree angle”, and
- “There are no straight lines in the circumference of a circle.”
And in the above picture, there’s only one straight line.
That anyone can even be fooled by the question means that math education has been completely screwed up. I agree that it’s quite a tough question for a seven-year-old child (as posed in the article), but nobody with more than a seventh-grade education should be stumped by it, let alone a professor of mathematics.
By the way, ignore the red herring that a straight line consists of two right angles: that’s only a partial definition of straight line. (“The shortest linear distance between two points” contains only implied angles, not actual ones.)
And by the way: the correct spelling is “two right angles”, no hyphen necessary.
I need another gin.
Update: Oh FFS-squared.
For the above diagram to contain two right angles, one would have to add a third radius, thus:
Now the question “There are two right angles” has the answer “True” (A0C, B0C). If you were to answer “False”, giving “because there are four right angles” as your reasoning, you would (rightly) be given an “Incorrect” because there are only four right angles in the imaginary world (i.e. Thales’ Theorem et al.). However, we are not in an imaginary world because we are not talking concepts, we are talking about an actual diagram. And to cap it all, we are talking about a question posed to a seven-year-old child, for whom Thales has no existence.
As I explained to a Reader in an email on this very topic, it always pays to remember that mathematics has little basis in reality, e.g. where a line can have direction but no thickness and a point has a position but no size. And I’m not even going to touch on division by zero… [eyecross]