Yesterday we dove into the world of the infinite and the paradoxical, with questions such as; "What is infinity?" and "Is something infinite also unlimited?"
Since our students are very creative they did not have any trouble accepting the concept of infinity. In fact, I enjoyed some of their definitions:
It's something that never ends
It's like numbers that never end
It's like the galaxy
We looked at pictures, both modern and ancient, that symbolize infinity and immortality -- the ouroboros and the mandala and the recycle sign.
We created homemade infinity with mirrors and drew fractals -- a self-repeating pattern that can go on forever.
We briefly discussed two very odd paradoxes; one by the Greek philosopher, Zeno, and the other by the German mathematician, David Hilbert. We demonstrated Zeno's Paradox in class, but I would like the students to view two videos by The Open University -- one titled "Achilles and the Tortoise" and the other "Hilbert's Infinite (Grand) Hotel." If you can view with your student and discuss together, that would be ideal. I would like to get their comments next week. If they think the paradoxes can be disproved, I would like to know their reasoning. After viewing the videos, have them write a few sentences in their binders stating whether or not they agree or disagree with Zeno and Hilbert, and why.
The last video is for pure artistic fun. A beautiful video by Vi Hart, please encourage your student to doodle along with her. My boys viewed this video over the summer, and it prompted lots of wonderful drawings. Please bring to class next week, so we can share those, as well.
We did not quite finish a game we were playing on Monday that involves randomness and predictions, so we will take the first several minutes of class next week to have another crack at our predictions!
Lastly, there is almost an hour long program from NOVA on fractals, which looks very interesting. I leave that one to your own discretion. Enjoy!