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Fibonacci Triangle Matrices
12-20-2018, 02:29 PM
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Fibonacci Triangle Matrices
Original blog post: https://edspi31415.blogspot.com/2018/12/...nacci.html

This program is the request of John Cvetan. I thank you for your suggestion.

To generate the Fibonacci triangle,

1. Let r the row and c be the column with

f_0,0 = 1
f_1,0 = 1
f_1,1 = 1
f_2,1 = 1

2. Each row will be determined by adding the last two terms going diagonally. You can use one of two formulas:

f_r,c = f_r-1,c + f_r-2,c

f_r,c = f_r-1,c-1 + f_r-1,c-2

The Program FIBMAT

FIBMAT generates a Fibonacci triangle in matrix form. It's the result is a triangle that is "tilted". n will need to be 3 or greater.

Code:
EXPORT FIBMAT(n)
BEGIN
// Fibonacci "triangle" in
// matrix form
// 2018-12-17 EWS
LOCAL M1,k;
M1:=MAKEMAT(0,n+1,n+1);
M1(1,1):=1;
M1(2,1):=1;
M1(2,2):=1;
FOR k FROM 3 TO n+1 DO
M1(k):=row(M1,k-1)+row(M1,k-2);
M1(k,k):=M1(k-1,k-1)+M1(k-2,k-2);
END;
RETURN M1;
END;

The Program FIBTRI

This is a visual program for Fibonacci Triangle.

FIBTRI(n) generates a visual Fibonacci Triangle - although I don't recommend going beyond 12 rows due to the constraints of the screen. I used the small font for the rows.

HP Prime Program FIBTRI
Code:

EXPORT FIBTRI(n)
BEGIN
// Fibonacci triangle
// 2018-12-17 EWS
LOCAL M1,k;
M1:=MAKEMAT(0,n+1,n+1);
M1(1,1):=1;
M1(2,1):=1;
M1(2,2):=1;
FOR k FROM 3 TO n+1 DO
M1(k):=row(M1,k-1)+row(M1,k-2);
M1(k,k):=M1(k-1,k-1)+M1(k-2,k-2);
END;

RECT();
LOCAL s;
FOR k FROM 1 TO n+1 DO
s:=STRING(SUB(row(M1,k),1,k));

IF k≤6 THEN
TEXTOUT_P(s,
140-5.5*(k-1),(k-1)*15,2);
END;

IF k>6 AND k≤11 THEN
TEXTOUT_P(s,
140-8*(k-1),(k-1)*15,2);
END;

IF k>11 THEN
TEXTOUT_P(s,
140-11.5*(k-1),(k-1)*15,2);
END;

END;
WAIT(0);
END;
Source:

Hosoya, Haruo. "Fibonacci Triangle" Ochanomizu University, Tokyo, Japan. 1976. https://www.fq.math.ca/Scanned/14-2/hosoya.pdf
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Messages In This Thread
Fibonacci Triangle Matrices - Eddie W. Shore - 12-20-2018 02:29 PM
RE: Fibonacci Triangle Matrices - DA74254 - 12-22-2018, 07:07 AM
RE: Fibonacci Triangle Matrices - pier4r - 12-23-2018, 09:59 PM



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