Nina will graduate from Sevenoaks School in Kent, United Kingdom, in the summer of 2014 with a particular focus on the math extension syllabus. She will also graduate from the Royal College of Music Junior Department in London, where she has found a great teacher to develop her artistic and technical piano abilities these past few years. During her free time, she is a master chef in sophisticated multi-layered, multi-colored, and multi-textured French modern pastry making. Lately she has shown an increasing craze for late Saturday-evening math problem-solving with her dad.
Project: Area Under One Arch of a Cycloid
The area under one arch of a cycloid is equal to three times the area of the generating circle. The regions on either side of the circle are subdivided into rectangular strips, and the total area of each region is very close to that of a triangle with height 2r and width πr. In my project, as you increase the number of strips, the area of one region gets closer and closer to πr2, and the total area therefore approaches 3πr2 as the number of strips approaches ∞. You can drag the sliders all the way from left to right to see the full proof!