1. The geometry of a curved string, which can be extended beyond simple fabric weaving to knots, braids and links, can be used to connect ancient traditions to the modern world. Nowadays, we can also use technology, such as virtual reality, to incorporate indigenous ideas and bridge the past with our modern society. This is also one way in which elements of indigenous cultures could be introduced into a mathematics classroom.
2. Another idea that I found interesting is the complexity theory, which is novel to me. It can applied to climate change and geographic information analysis. The idea that geometry has a lot more dynamics than I am accustomed to can be extended to my teachings by connecting certain concepts in math with the real world.
Thank you for your comments Jackson! I like your ideas of extending geometry teachings though connecting to the real world.
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