Yanlin Yang Tackles the Undrawable Curve 

  • Prof. Annalisa Crannell and student researcher Yanlin Yang examine a spiral staircase leading to the second floor of Shadek-Fackenthal Library. Prof. Annalisa Crannell and student researcher Yanlin Yang examine a spiral staircase leading to the second floor of Shadek-Fackenthal Library.

"Independent research is an excellent chance for students to explore more in their interesting fields and work together with their professors. I learned new knowledge together with Prof. Crannell and we met almost every day for discussion,” says Yanlin Yang  '18.

 

“Sometimes research is about creating or defining new things and you can name them with your own name, which is very exciting!”

 

Yanlin, a Summer Hackman Scholar, teamed up with Associate Math Prof.  Annalisa Cranell to delve into, “Undrawable Curve in the Real World,” setting out to prove that a spiral is not a drawable curve.  The research expanded the ancient Greeks’ ruler and compass construction and added some knowledge of projective geometry.  “Since we can draw the images of points, lines and circles, it's easy for people to ask what other kind of curves in the real world we can draw on our picture plane using only classical ruler and compass contructions. The spiral is the next step,” describes the math major.

Yanlin offers some tips from her own recent research experience for those interested in being a student researcher:

  •  Keep in touch with the professors with whom you want to work together.

  •   Prepare early.

  • Professors need time to schedule and sometimes they require you to take some courses before the research so that you have some background knowledge for your particular project.

Faculty also benefit from the research relationship. “I love getting the chance to work with students who come to the project knowing almost nothing about the math we're tackling, but leave the project being the expert.  This summer, our math and computer science research students gave talks to each other, and their talks showed how much they had come to own their research,” notes Prof. Crannell.  

“For me personally," continues Prof. Crannell,  "it's good to get to see my own research questions through the eyes of someone unfamiliar with my field.  It often takes the work in directions I hadn't thought of going, and because of that leads to really serendipitous results."With Yanlin, our work in geometry and algebra eventually discovered we had to rely on a theorem in Transcendental Number Theory I hadn't heard of before, but now love (the Lindemann–Weierstrass theorem).” 

Adds Yanlin, “Prof. Crannell taught me how to do research; for example, where to find useful resources, how to do presentations to other people who are familiar with my project, and how to use LaTeX (math software).   I think this will help a lot for my graduate studies after F&M."