Artist M.C. Escher's Circle Limit Drawings are the inspiration behind this project. When creating these drawings, Escher allegedly asked the reputed mathematician Coxeter to explain how to create circles with centers that approach gradually from the outside until they reach a limit. The aim of this math project is to answer Escher's question. Doing so will require researching hyperbolic geometry in depth. The project is recommended for students in their senior year of study who have a working knowledge of geometry, group theory and symmetry.
Newton is credited with inventing calculus in 1666 and thus has become one of the most influential mathematicians of all time. Undergraduate students may research his life and report on the process by which Newton created calculus. The report should analyze elements of Newton's society and of the existing mathematical research that inspired his work. The paper should also compare Newton's society with the contemporary world and explore any connections that exist. Student reports should describe factors that made 1666 an appropriate time for making radically new discoveries and include an overview of modern mathematicians on the brink of completing ground-breaking work today. In addition to historical analysis, this project requires that students research binomial series and Newton's technique of formal interpolation. This project is recommended for students taking any level of undergraduate math.
This project centers on describing the basic methods of ruler-and-compass construction and applying them to famous buildings of Ancient Greece. Students will also need to produce mathematical proofs showing the impossibility of trisection, circle squaring and Delian problems. To make the project more dynamic, students may create a plan for re-building ancient Greek buildings using modern constructions methods and create scale models of their modern re-designs of ancient classics. This project is recommended to seniors who have studied history, geometry and geometric construction.
Many scholars agree that Lewis Carroll's Alice in Wonderland is infused with mathematical equations. Carroll wrote parts of Alice in Wonderland with the intention of satirizing abstract math by showing what the world would be like according to its principles. Undergraduates may conduct their own unique research about allusions to math in Alice in Wonderland and create their own work of fiction based on mathematical principles.