First or two articles about Fibonacci, written for students.
The first part of an investigation into how to represent numbers
using geometric transformations that ultimately leads us to
discover numbers not on the number line.
Introduces the idea of a twizzle to represent number and asks how
one can use this representation to add and subtract geometrically.
There was a
lot of interest and a big response to this problem. However finding
an answer should prompt the questions: "Why does this happen?" ,
"Can I explain and prove it?", "Can the result be proved for ALL
values of n?" This question remains a Tough Nut and the challenge
is to prove that the method using both scale pans always
Thank you to Phil of Garforth Community
College for this diagram.
Can you prove
the following result which was spotted by Chanwc from Hong Kong and
Utku Alhan from Robert College of Istanbul who realised that the
number of weights is given by:
It remains to
prove that the folllowing method, described by Joris from Claremont
High School, will always work for all n.