Presentation – Charlie Jonas

The weekly presentation today was given by myself and covered the topic of differential geometry, specifically using integration to find the length of an arc.

I started with an brief overview of integration and differentiation and the use of infinitesimals in calculus which is highly relevant since the derivation of the arc length formula involves taking infinite tangents. Using a graph of the function y^2=x^3, I showed how the formula is derived simply from rearranging Pythagoras’ theorem. We then used this to complete an example question from the OCR MEI FP3 maths syllabus, an additional part of our A-level maths course that we do not normally study in school. I ended the presentation by touching on the similarly related field of line integration which is especially relevant for calculation involving scalar fields in physics. I hope my presentation was enjoyable and accessible by all!