Pascal Triange - Fibonacci Sequence

  • Thread starter Thread starter l-1j-cho
  • Start date Start date
  • Tags Tags
    Pascal Sequence
Click For Summary
A direct proof of the relationship between Pascal's Triangle and the Fibonacci Sequence is sought, specifically avoiding methods like induction. The discussion highlights that when rows of Pascal's Triangle are left-justified, diagonal bands sum to successive Fibonacci numbers. While some resources provide insights, they may not directly answer the query. A suggested link offers a more comprehensive explanation of the connection. The exploration of this relationship remains an intriguing mathematical topic.
l-1j-cho
Messages
104
Reaction score
0
Does anyone have a DIRECT proof of the relationship between Pascal Triangle and Fibonacci Sequence? I mean not like induction or other method of proof but a direct method. I try to google it but couldn't find one
 
Mathematics news on Phys.org
Last edited by a moderator:

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad 1-dim Penrose tiling = "musical sequence"? Why?
  • · Replies 5 ·
Replies
5
Views
2K
What makes the Fibonacci sequence and its related concepts golden?
  • · Replies 11 ·
Replies
11
Views
5K
High School Is there a relationship between the harmonic mean and the standard deviation?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Is There a Hidden Pattern in This Sequence of Numbers?
  • · Replies 7 ·
Replies
7
Views
2K
Finding the n'th term of fibonacci like sequence
  • · Replies 3 ·
Replies
3
Views
3K
What is the equation for predicting the middle number in Pascal's triangle?
  • · Replies 6 ·
Replies
6
Views
2K
High School Golden Ratio in Collatz-like sequences
  • · Replies 1 ·
Replies
1
Views
2K
Finding GCD with Fibonacci: Base Case
  • · Replies 1 ·
Replies
1
Views
2K
High School Heard of Another Kind of "Rational" (Fraction) Addition?
  • · Replies 8 ·
Replies
8
Views
2K
Deriving the Formula for the nth Term of the Fibonacci Sequence Using Matrices
  • · Replies 8 ·
Replies
8
Views
4K