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Browse High School Fibonacci Sequence/Golden Ratio
Stars indicate particularly interesting answers or
good places to begin browsing.
 Appearances of the Golden Number [06/03/1998]

Why does the irrational number phi = (1 + sqrt(5))/2 appear in so many
biological and nonbiological applications?
 Calculating the Fibonacci Sequence [11/28/1996]

Is there a formula to calculate the nth Fibonacci number?
 Congruum Problem [04/04/2002]

I have found a reference to Fibonacci and his congruum problem. But
something has me stumped...
 Fibonacci sequence in nature, Golden Mean, Golden Ratio [12/6/1994]

I need examples of where the Fibonacci sequence is found in nature and how it relates to the Golden Mean.
 Fibonacci Series [11/7/1994]

I was helping an Algebra student with a "bonus" problem recently. It
asked something about drawing a spiral using the Fibonacci series. What
is this series? Does it draw a spiral?
 Golden Ratio [01/03/1998]

Do you have any topics that I can use in my term paper about the golden
ratio?
 The Relation of the Golden Ratio and the Fibonacci Series [1/28/1996]

I am trying to figure out how the Golden Ratio and the Fibonacci series
are related.
 Why Is Math Important? [01/02/2002]

Some of it we don't need to know in the real world, so why do they teach
us things we won't need to know?
 The 1000th Fibonacci Number [09/25/1998]

How can you find the 1000th Fibonacci number, both approximate and exact?
 500th Fibonacci Number [04/16/1997]

How do you find the 500th term of the Fibonacci sequence?
 Binet's Formula and Induction [11/28/2001]

What is induction? Can you prove Binet's formula by induction?
 Consecutive Fibonacci Numbers Relatively Prime [11/17/2001]

Prove two consecutive Fibonacci numbers are relatively prime.
 Constructing the Golden Ratio Using a Compass [12/30/2003]

I am writing a paper on the Golden Ratio and want to include a section
on how to construct the ratio on a line using a compass. Could you
please explain the construction?
 Expressing the Golden Ratio as a Decimal [03/04/1998]

Using Newton's method to express the value l+sqrt(5)/2 as a decimal.
 Fibonacci [01/31/1997]

Where can I learn more about Leonard of Pisa?
 Fibonacci Addition Trick [10/10/2002]

Given 10 numbers in a Fibonacci sequence, why does multiplying the
seventh number by 11 give the sum of all 10 numbers?
 Fibonacci Algorithm and Egyptian Fractions [04/25/1999]

How long an Egyptian fraction can you write?
 A Fibonacci and Lucas Number Relation [08/24/1998]

Prove that F(2n) = F(n) * L(n) where F(x) is the xth Fibonacci number and
L(y) is the yth Lucas number.
 Fibonacci Formula Inductive Proof [11/05/1997]

I must prove by induction that F(n) = (PHI^n  (1  PHI)^n) / sqrt5...
 FibonacciGCD Proof [11/20/2002]

Can you help me prove that fib(gcd(m, n)) = gcd(fib(m), fib(n)) ?
 Fibonacci Identity [12/10/2001]

I am trying to create an inductive proof for the particular identity of
Fibonacci numbers that: F(n1) * F(n+1) = (1)^n + (Fn)^2.
 A Fibonacci Jigsaw Puzzle [04/29/1999]

Why is the area of our rectangle, formed from a square, 65 when the
square's area was 64?
 Fibonacci Numbers [9/25/1995]

What is the rule of Fibonacci numbers in math and life?
 Fibonacci Numbers in Pascal's Triangle [04/03/2003]

How do you find the Fibonacci numbers in Pascal's Triangle?
 Fibonacci Proof [01/29/2001]

This proof is giving me major problems: F(2n) = (F(n))^2 + (F(n1))^2.
...
 A Fibonacci Proof by Induction [06/05/1998]

Let u_1, u_2, ... be the Fibonacci sequence. Prove by induction...
 Fibonacci Ratio, Golden Ratio, and 8:5 [06/01/1997]

What is the connection between the ratio 8:5, the Fibonacci sequence, and
the Golden Ratio?
 Fibonacci Recurred, Composed, Summed [02/18/2011]

Given g(n) = 2n + 1, how do you show that sum{f(4n + 3)} = sum{f(g(g(n)))}? Doctor
Vogler shows how to begin by using an explicit Fibonacci formula and sum of a
geometric series.
 Fibonacci Riddle [11/21/2001]

We can cut an 8x8 square with an area of 64 into four pieces and
reassemble to get a 5x13 rectangle with an area of 65. Where does the
extra 1x1 square come from?
 Fibonacci sequence [1/28/1996]

What is the explicit formula for the Fibonacci numbers?
 Fibonacci Sequence [01/29/2001]

Is there a formula for the nth Fibonacci number?
 Fibonacci Sequence [06/18/2001]

I need help understanding what the Fibonacci sequence really is.
 Fibonacci Sequence and Grapefruit [12/6/1995]

How can the Fibonacci recursive sequence be related to or used to
explain the appearance of the sections of a grapefruit sliced in half?
 Fibonacci Sequence  An Example [05/12/1999]

Glass plates and reflections.
 Fibonacci sequence, Golden Ratio, Golden Rectangle, Industry [11/16/1994]

Do you know of any industries that purposefully employ the Fibonacci
Sequence in their product design?
 Fibonacci Sequence in Nature [12/08/1997]

I need examples of how the Fibonacci sequence is used in nature.
 Fibonacci Sequence Property [11/29/2001]

I have to prove that in the Fibonacci sequence, F(k) is a divisor of
F(nk), where n is a natural number (so, F(nk) = A*F(k) where A is a
natural number).
 Fibonacci Sequences [01/08/1998]

Please help me with a proof.
 Fibonacci Trick [06/01/1999]

The Fibonacci trick states that F(n+1) * F(n1)  [F(n)]^2 = (1)^n. Why
does this work?
 Formula for the Fibonacci Sequence [4/8/1996]

What is the implicit formula for the Fibonacci sequence?
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