Kakeya Needle Problem

Given a needle (or stick), what is the smallest area shape that we need to rotate the needle 360 degrees?

We will look at this problem from the perspective of several different shapes, we will start with a circle and slowly shave off parts of the shape to see that we can get smaller and smaller shapes and still see that we may still rotate our stick by 360 degrees and end with a general construction.

Videos:

• Simplified version of problem:
  • https://www.youtube.com/watch?v=IM-n9c-ARHU
• Slightly harder explanation:
  • https://www.youtube.com/watch?v=j-dce6QmVAQ
• Perron needle intuition:
  • https://www.youtube.com/watch?v=pWk57HpPJmQ

Additional Resources:

• A paper by Sean Gasiorek and Tina Woolf describing the problem and some solutions:
  • https://static1.squarespace.com/static/5f6c23246ba9a664dd96c4b1/t/5f6d64d7db1e987c6d988122/1601004765874/Senior_Thesis.pdf