The One-Seventh Ellipse Problem: Take the decimal expansion of 1/7. We get 0.142857... repeated infinitely. These six digits are combined to make six points in the 2-D plane. For example, (1,4), (4,2), (2,8) and so on. These six points always lie on an ellipse.
My research helped me realize that this can be generalized to any conic section (ellipse, hyperbola, parallel lines, etc) given any sequence of six numbers. This program takes 3 numbers, a sum and length of digits. Using this sum and the numbers, 6 numbers are produced. The program then checks what kind of conic section any combination of these 6 numbers lie on.
I used this program to find consistencies and patterns in my research project.