@user21820: Hi! How you doin? Hope everything is fine?!

@DavidP Hi! Yes I'm fine. How about you?

Good to hear. Here is everything quite well too. I was preparing some stuff for school tomorrow, when I decided to take a little break, drink some coffee and drop in to say "Hi" and see how things are by you before I get back to work. :)

@DavidP Ah I see.

Thanks for checking in!

What do you think of the US election haha..

Yeah - excitedly I followed the event in newspaper and internet. And actually I'm quite happy that Biden won.

Can't imagine our president talking in TV and switched off by press with the comment he is lying all the time. :)

@DavidP Indeed I hope things go better than it did the last 4 years.

Me too - and I hope things are going peacefully in the next time. I was a little bit scared when I read how many people have guns in the US and saw pictures from crazy people in front of the houses where they were counting the votes...

So lessons are prepared. Tomorrow we will learn ordering fractions at the number line, calculating the intersection from linear functions and the pythagorean theorem.

@DavidP Guns are a very bad problem. It's unfortunate that the right to carry arms is baked into the constitution.

@DavidP Nice. With proof of Pythagoras theorem?

Incidentally, there is a non-trivial aspect to geometric proofs of Pythagoras theorem:

We already proved a^2=pc and b^2=qc with shear-mapping. So the proof for pythagorean's theorem is now not difficult. :)

@DavidP Ah. So shear preserves area by cutting the parallelogram into two?

We devided the square in two triangles (half the square) and proved that this triangle is half the rectangle. This is actually a shear, a rotation and another shear. When you have the triangle ABC and the square (over b) ACDE and the rectangle AFGH then we took the triangle ACE and sheared to triangle ABE, rotated with center A (-90°) to AFC and sheared to AFG.

@DavidP Yes see you and take care!