# Summer SAVY, Session 4 Day 4, Mathematicians in History (3rd – 4th)

Hello SAVY Families,

We had another amazing day at SAVY! The mathematicians once again exceeded the expectations and rose to the challenge of our incredibly complex math course. I am grateful for the opportunity to share about our work today!

Today, we learned about two more historical mathematicians, one that most SAVY mathematicians had heard of, and one that most SAVY mathematicians had not heard of. The first mathematician we learned about was Isaac Newton. A connection that the SAVY mathematicians quickly made is that Newton is similar to Galileo: remembered as a scientist, but also contributed to the field of mathematics. The SAVY mathematicians were impressed to learn that Newton is credited with “discovering” calculus. Once again — did he “discover” calculus, or did he “invent” calculus? Newton’s work is easily connected to that of Pascal, as he also used the powers of 2 and Pascal’s triangle. To work with powers of 2, we took a piece of paper and ripped it, noting that we had 2 pieces. We kept this process up as long as we could before having to stop and notice patterns. Students used patterns to figure out that if you rip a paper 50 times, you would have 2 to the 50th power pieces of paper. Way too many for us to count in this classroom! To extend the activity, I asked the SAVY mathematicians to predict how many times you could fold a piece of paper. Many mathematicians were surprised to know that the widely accepted answer is 7. We, of course, tried this for ourselves. The most shocking fact of the day was that if you were to complete this process of cutting or folding a paper 50 times, the height of the stack would be 17,769,885 miles! To finish our work on Newton, we looked back at Pascal’s triangle and the binomial theorem. We defined a binomial as an algebraic expression with two non-zero terms. We noticed patterns in the expansion of binomials, and we used these patterns to continue expanding binomials. While this concept was challenging for many SAVY mathematicians to grasp, I was impressed with their perseverance.

The next mathematician that we studied was Hypatia, our first woman mathematician! To start our study on Hypatia, we learned about the time period when Hypatia was living, Ancient Rome, and the time period between Hypatia and the Renaissance, known as the Middle Ages. We learned that there are a lot of myths surrounding both Ancient Greece and the Middle Ages, and once again discussed the significance of these myths and how we generally understand history. Hypatia is known for her work with both ellipses and parabolas. Using string, cork board, and graph paper, students were able to make accurate ellipses, a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant. Using paper, we also specially folded the paper to represent a parabola, the shape that the path of a projectile under the influence of gravity ideally follows.

Questions for tonight:

- Who was Isaac Newton? What contributions did he make to mathematics?

- Who was Hypatia? What contributions did she make to mathematics?

- How can we connect the work of these mathematicians to our generalizations of relationships?

- How did you use patterns, order, and relationships in your study of historical mathematicians today?

I hope the SAVY mathematicians are looking forward to one more exciting day of patterns, order, and relationships in Mathematicians in History! I am looking forward to seeing all of their new knowledge culminate tomorrow.

Sincerely,

Ms. Gruchot