Child's Homework Problem

[imhotep]

Below is a daughter's homework problem posted by her father Sir Timothy Gowers. He's a Fields Medal winner (like the Nobel Prize for Mathematicians) and currently Professeur titulaire de la chaire Combinatoire, which translates as the holder of the Combinatorics chair at at the Collège de France, formerly the Prof of Maths at Cambridge.

BTW his daughter scored 39/40 with this marked as wrong as she gave the answer as "infinity"

What do you think the answer is?

 

[-333-]

@dilann

 

[Ramiel]

25°C

 

[jamiezue]

360 degrees ? -circle

 

[topkollek]

formula for sum of interior angles of a polygon of n sides is (n-2) * 180

we can consider a circle as a polygon with infinite sides, then her answer is correct.

 

[tharakaf]

Below is a daughter's homework problem posted by her father Sir Timothy Gowers. He's a Fields Medal winner (like the Nobel Prize for Mathematicians) and currently Professeur titulaire de la chaire Combinatoire, which translates as the holder of the Combinatorics chair at at the Collège de France, formerly the Prof of Maths at Cambridge.

BTW his daughter scored 39/40 with this marked as wrong as she gave the answer as "infinity"

What do you think the answer is?

Not sure about the circle, but for the rest it should be (number of sides - 2) x 180

based on that infinity should be the correct answer for the circle since circle is technically an infinite number of sides coming together

 

[imhotep]

360 degrees ? -circle

This question is a bit ambiguous. If you go by the n sided polygon formula you would think the answer is "infinity" but it's not the right answer.
The problem is the interpretation of the word "Inside".
With a polygon inside refers to the sum of the interior angles, which is of course as many correctly said here (n-2)*180 degrees.

However, with a circle it refers to the measure of the Central Angle. With a circle it is 360 degrees which is a fundamental property of circles in geometry.

 

[MrFrog]

This question is a trap . If it was asked in a separate question, the student could have got it right.
Btw, we sometimes think a circle as a polygon with infinite sides and vertices. But can we really use that as a fact in mathematics?

 

[imhotep]

This question is a trap . If it was asked in a separate question, the student could have got it right.
Btw, we sometimes think a circle as a polygon with infinite sides and vertices. But can we really use that as a fact in mathematics?

It should not have been asked as it's not very clear to a student. BTW a circle doesn't have infinite sides either.

The apeirogon is an extension of the definition of regular polygon to a figure with an infinite number of sides. It's derived from the Greek word Aperios ἄπειρος” which means infinite or boundless. Apeirogons are the two-dimensional case of infinite polytopes.

A circle has 0 sides. Check the definition of a side/edge.

PS: You can still consider to think a circle as an extension of a polygon with infinite sides and arrive at useful results. This is exactly the approach that Archimedes, Liu Hui, and many others have used down the centuries to study circular geometry, including coming up with approximations for π and the area of the circle πr^2.

 

[Solo Rider]