Explaining math is hard, but when 'squaring the circle' came up in class, I could not resist to explain the connection between circles and squares.
I started easy by introducing Pythagoras' theorem
Then I introduced pi as the is the ratio of a circle's circumference to its diameter, and continued with explaining more geometry, esp. $sin^2+cos^2 = 1$;
Having established the connection, I could see the class was already very confused by this 'useless' information, so I continued quickly with
Now I completely lost my class, who thought they knew better.
One said: "Pi is not a perfect square, e.g. Four is."
After this it was clear that even the brightest of my students did not get it. After all, four clearly is not a square.
So I switched to some number theory
"An integer number is 9142057518"
"Yes", said the class.
"A real number is 2571.72"
"Yes" said the class.
"A version number is 2.3.5569.6739151"
The class looked confused but agreed.
"An odd number is 4.193.2"
One started smiling. I thought she finally understood it, but then she said jokingly: "That is an odd number!"
"Of course not! That is an even number", I said.
As last one I mentioned:
"An imaginary number is 3300647498274i/300"
No matter how hard I tried to explain it; they did not understand it.
Can you explain the class why 3300647498274i/300 is imaginary? (and remove any remaining confusion)
A minor hint for if you still want to solve this, but avoid the big spoiler when reading the answer:
Apply Pythagoras on the bottom picture - why is it correct?
Look at the statement about integers, this exact integer is chosen for a reason.