Pascal+Fractions+Triangle+Idea

One of the richest arrangement of numbers that I have ever looked at:



Sample questions: 1. How many fractions are listed? How many of them are in lowest terms? 2. Is every fraction listed somewhere? In what row is 15/31? 3. Explain why there are no more fractions than natural numbers using this triangle. 4. What are all the patterns that you notice? 5. Connect 1/2 with a line to all of the fractions equivalent to it. Do the same for 2. How are the two lines related? 6. Where are 0 and infinity on the triangle?