Exploring Infinity
This week in Geometry, students explored the concept of infinity. The unit we are in is about polygons, so we extended our understandings of polygons to ask if a circle should be considered a polygon. To help students construct an argument for this question, they were first asked to observe certain trends. The first observation was to note that as we add more and more sides to a regular polygon, these polygons start to look like a circle. Then from there, students were asked questions such as whether they think a circle has no straight sides, or an infinite number of them. To build on this dialogue, we also did a close read on how scientists have struggled with the concept of infinity as it applies to our universe. Is the universe infinite or finite? Is it growing or static in size? These are the questions we read about and tried to answer for ourselves in conjunction with our conversation on polygons and circles. During these discussions, students had brilliant insights, such as questioning what happens at the border between the finite and the infinite. Where is infinity minus one? Even if a pattern closely approaches a certain outcome, does it ever actually reach that outcome? How do we represent this concept of infinity when applying something that is infinite to an equation? Students were encouraged to have meaningful dialogue to help them form an opinion on these questions, and were told to explore the possible answers without fear of being wrong. Students took well to this challenge, despite never being given any direct answers to their questions, and in contrast, only receiving more questions to think about! To start getting more concreate answers, students were told to stay tuned for our next unit…circles!