







Fibonacci and induction 
20100712 

From James: I'm trying to prove by induction that F(n) <= 2^(n1)
where f(1)=f(2)=1 and f(k)=f(k1)+f(k2) for k >=3 is the Fibonacci sequence Answered by Stephen La Rocque and Tyler Wood. 





Body measurements 
20100406 

From Amirul: Recently I'm proposing my research question to my teacher for my extended essay. I'm an IB student.
My research question is regarding the estimation of human in buying trousers through reference of neck. What does the relation between the diameter of the neck and the diameter of the waist?
I want to see how far does the estimation theory is true for different type of people with different BMI(body mass index)..
But teacher said that it is golden ratio...so nothing interesting... =(
really??? But i search on net.... state that my idea seems do not have any relation with the golden ratio so far..... i just want ask you... am I able to perform in my extended essay if i continue with this research question?? Answered by Robert Dawson. 





Art and Integers 
20080917 

From pamela: how do artists use integers? Answered by Janice Cotcher. 





The sum of the squares of the fibonacci numbers 
20080427 

From Thomas: Hey I have a question for a research topic that our teacher set us, It is regarding the sum of the squares of the fibonacci numbers.
The question says describe the pattern that exists and write a general formula that describes the relationship illustrated above.
I can see the pattern that is occurring but i cannot put this into a general formula.
Any help would be appreciated.
Thanks Tom Answered by Victoria West. 





1, 1, 2, 3, 5, 8, 13, ___ ___ ___ 
20080313 

From Karen: What is the rule for the following pattern, and what would come next?
1, 1, 2, 3, 5, 8, 13, ___ ___ ___ Answered by Penny Nom. 





Fibonacci numbers 
20080130 

From Beth: You've answered a question for a Linda Bach on Oct. 25, 1999 that has to do with a pet rabbit and stairs. (Working Backwards) We were wandering if there is a formula we can use to plug the numbers in? My 7th grader got that exact same problem. I've spent several hrs trying to come up with a formula. I've tried the combinations formula, the Pascal's triangle and the Permutations formula. It seems like it is something real close to those, but can't quite get anything to work. What kind of formula would work for finding the outcome of this problem? Thanks so much for your help. Beth Answered by Penny Nom. 





What number best completes the series? 
20071112 

From Grace: What number best completes the series?
2 3 7 13 27 ____ Answered by Stephen La Rocque, Penny Nom and Harley Weston. 





0,1,2,3,6,11,20,37,68... 
20071016 

From Pat: Describe the rule for this pattern:
0,1,2,3,6,11,20,37,68...
Thanks Answered by Penny Nom. 





The Fibonacci sequence 
20061121 

From Ross: Let f0 = 0; f1 = 1,... be the Fibonacci sequence where for all n greater than or equal to 2 fn = fn1 + fn2. Let Q = (1+square root of 5)/2. Show that for all positive n greater than or equal to 0, fn less than or equal to Q^(n1). Answered by Penny Nom. 





The stair problem 
20051206 

From Arnold:
My daughter had me help her with some of her college math problems that require finding the pattern. The problem was the stair problem where you can climb either 1 step or 2 steps at a time. How many combinations are there to get to the 10th step. I found the data set that solves the answer to the question, but is there an equation that expresses the answer in terms of n?
1 2 3 4 5 6 7 8 9 10 stair number
1 2 3 5 8 13 21 34 55 89 number of possible combinations
Answered by Harley Weston. 





A Fibonacci triangle 
20040425 

From Marcelle: Is it possible to construct a triangle with sides that are three consecutive Fibonacci numbers? Answered by Walter Whiteley. 





Fibonacci exam 
20030128 

From Mike:
My son will be participating in the national math contest. He is a grade 4 student but will be writing the Fibonacci exam for grade 5. He has been given last years exam for practice. Parents have been ask to assist for this part. I was therfore hoping for a little "inside" help on several questions with answers & short explanations. This with a would be greatly appreciated.(from last years exam)  With 3 weights, Mathusalem can weigh any object that has a weight which is smaller or equal to 13 kg, but that weighs a whole number of kilograms. He wants to weigh an object of 7 kilograms. To do so, he must place two of the weights on the left side of the scale, and the third one on the right side. Which one will he have to place on the right side
a)4 b)3 c)6 d)2 e)5  Mathilda uses a rectangular prisms to build stairs. The cross section of each prism is a square which has a side of 1 dm. Mathilda has already put in place 4 steps of a staircase that must have a height of 10 dm. When finished, the staircase will have a volume of 550 dm3. What will the width of the staicase in dm be?
a)10 b)55 c)11 d)1 e)100  The year 1991 was the last palindrome year of the second millennium. The year 2002 is the first palindrome year of the third millennium. Including 2002, how many palindrome years will there be, altogether, in the third millennium ?
a)8 b)2 c)10 d)182 e) 9 Greatly appreciated, Mike
Answered by Penny Nom. 





Squares of Fibonacci numbers 
20010424 

From Vandan: What discoveries can be made about the sum of squares of Fibonacci's Sequence? Answered by Penny Nom. 





Fibonacci 
20010228 

From Shona: We have been doing pattern finding with him, talking to a friend he mentioned the "Fibbinacci Series" ?, while I have tried to find a bit about it, how works etc.. what it is about, I have not really found out much, what I have I feel is way beyond him, but am still curious to know the basics of it myself. Would you be able to tell me in laymans language. Would be very much appreciated. Answered by Claude Tardif. 





Fibonacci 
20001207 

From A student: Can you give me any info about Fibonacci?? Answered by Penny Nom. 





Fibonacci Numbers 
19991215 

From Gary Nelb: I'm doing a project on fibonacci numbers and I'm using different starting values and finding out if different starting values to see whether or not the ratios still get closer to phi. I was wondering, what numbers should I use. Should I use two of the same # like 2 and 2, or numbers like 1 and 2, or even something totally different. Answered by Denis Hanson. 





Pay Phone Problem 
19980226 

From Shameq: Hi, I've been given a problem that I'm having some trouble with. I'd really appreciate any help. Here's the question (it's called the Pay Phone Problem) A pay phone will take only 10p, 20p, 50p, and £1 coins"(It's British). A woman has plenty of 10p and 20p coins. She has no other coins. She can put the coins into the pay phone in any order. INVESTIGATE the number of different ways, she could put the 10p and 20p coins into the pay phone. Answered by Penny Nom. 





Stairs 
19960212 

From Marianne and Carrie: How many ways can you run up a flight of stairs? Answered by Denis Hanson. 





Magic Square 
19951020 

From Marianne and Carrie: How can an 8 by 8 square have the same area as a 5 by 13 rectangle? Answered by Denis Hanson. 

