1. A quick tour of our research
In our article we are going to present new facts and theorems that a group of high school students discovered.
Here we are going to present the results of our research as puzzles.
In this way it is possible for many people to appreciate our findings.
Problem 1. Can you find any patterns in the following triangle of fractions?
Problem 2. The following is the Pascal’s triangle.
It is well known that the numbers on diagonals of the Pascal's triangle add to the Fibonacci sequence
a1=1, a2=1, a3=1+1=2, a4=1+2=3, a5=1+3+1=5, a6=1+4+3=8, a7=1+5+6+1=13,....
In this way we get the sequence {1, 1, 2, 3, 5, 8, 13, ...}.
Here we colored the numbers to show how numbers on diagonals add to a sequence.
What kind of sequences you can produce by the following triangle.
