Explaining math is difficult, however when ‘squaring the circle’ got here up at school, I couldn’t resist to elucidate the connection between circles and squares.

I began straightforward by introducing Pythagoras’ theorem

Then I launched pi because the is the ratio of a circle’s circumference to its diameter, and continued with explaining extra geometry, esp. $sin^2+cos^2 = 1$;

Having established the connection, I might see the category was already very confused by this ‘ineffective’ info, so I continued rapidly with

“Pi is an ideal sq.!”

Now I utterly misplaced my class, who thought they knew higher.
One mentioned: “Pi shouldn’t be an ideal sq., e.g. Four is.”
After this it was clear that even the brightest of my college students didn’t get it. After all, 4 clearly shouldn’t be a sq..

So I switched to some quantity principle

“An integer quantity is 9142057518”
“Yes”, mentioned the category.
“An actual quantity is 2571.72”
“Yes” mentioned the category.
“A model quantity is 2.3.5569.6739151”
The class appeared confused however agreed.
“An odd quantity is 4.193.2”
One began smiling. I assumed she lastly understood it, however then she mentioned jokingly:
“That is an odd quantity!”
“Of course not! That is a fair quantity”, I mentioned.

As final one I discussed:
“An imaginary quantity is 3300647498274i/300”

No matter how exhausting I attempted to elucidate it; they didn’t perceive it.

Can you clarify the category why 3300647498274i/300 is imaginary? (and take away any remaining confusion)