Drexel dragonThe Math ForumDonate to the Math Forum

The Math Forum Internet Mathematics Library

Browse and Search the Library
Home : Math Topics : Arithmetic/Early : Number Sense/About Numbers : Golden Ratio/Fibonacci

Library Home || Search || Full Table of Contents || Suggest a Link || Library Help

  Selected Sites   (see also All Sites in this category)

  1. Fibonacci Numbers and the Golden Section - Ron Knott
    Information about the Fibonacci series, including a brief biography of Fibonacci, the numerical properties of the series, and the ways it is manifested in nature. Fibonacci numbers are closely related to the golden ratio (also known as the golden mean, golden number, golden section) and golden string. Includes: geometric applications of the golden ratio; Fibonacci puzzles; the Fibonacci rabbit binary sequence; the golden section in art, architecture, and music; using Fibonacci bases to represent integers; Fibonacci Forgeries (or "Fibonacci Fibs"); Lucas Numbers; a list of Fibonacci and Phi Formulae; references; and ways to use Fibonacci numbers to calculate the golden ratio. more>>

  2. The Fibonacci Series - Matt Anderson, Jeffrey Frazier, and Kris Popendorf; ThinkQuest 1999
    The Fibonacci Series is deceptively simple, but its ramifications and applications are many. Learn more about the Fibonacci Series itself: an introduction, the rabbit problem, Binet's formula, the successor formula (given only one term in the Fibonacci series, determine the term that directly follows it), binomial form, Fibonacci spiral. See how the Fibonacci Series relates to the golden ratio: the golden rectangle, the golden ratio, the golden spiral. Explore applications of the Fibonacci series: Fibonacci ratios, Binet revisited, one over eighty-nine (examining the decimal expansion of 1/89), apartment buildings (an explanation of why the number of combinations for each set of a certain group of apartment buildings is a Fibonacci number), nature, Leonardo da Vinci. Learn about the lives of Fibonacci and other important mathematicians: Leonardo Fibonacci, Édouard Lucas, Jacques Binet, Jordanus Nemorarius. A quiz is available for each of the four main sections of the site; an index organizes all of the site's Shockwave Flash demonstrations; and the authors also provide further reading, a bibliography, and documentation on the site's development. Much of the site's content is available in streaming Real Audio narration. more>>

  3. Golden Ratio, Fibonacci Sequence - Math Forum, Ask Dr. Math FAQ
    About the Golden Ratio (or Golden Section or Golden Mean), the Golden Rectangle, and the Fibonacci Sequence. more>>


Mason error

component stack:   /library/branch.html
code stack:   /var/lib/mason/obj/library/branch.html:208

debug info:   Debug file is '/var/lib/mason/debug/anon/10'.


raw error:

error while executing /library/branch.html:
Server message number=1105 severity=17 state=1 line=1 text=Can't allocate space for object 'keystorage' in database 'catalog' because 'default' segment is full/has no free extents. If you ran out of space in syslogs, dump the transaction log. Otherwise, use ALTER DATABASE or sp_extendsegment to increase size of the segment.
Statement=INSERT INTO keystorage ( keys ) VALUES ( '62434;67288;67396;10978;60289;6614;12146;11316;70313;10914;63627;3969;12151;75714;9225;4873;10366;3968;13496;72760;3964;19796;3154;3849;3965;8568;3970;12213;6693;7157;8473;3770;16349;5560;12323;8559;3971;3967;...
Server message number=7101 severity=17 state=1 line=1 text=Unable to allocate new text value, dbid 6.
Statement=INSERT INTO keystorage ( keys ) VALUES ( '62434;67288;67396;10978;60289;6614;12146;11316;70313;10914;63627;3969;12151;75714;9225;4873;10366;3968;13496;72760;3964;19796;3154;3849;3965;8568;3970;12213;6693;7157;8473;3770;16349;5560;12323;8559;3971;3967;...
HTML::Mason::Interp::__ANON__('Server message number=1105 severity=17 state=1 line=1 text=Can\'...') called at /usr/lib/perl5/site_perl/5.6.0/Forum/Key.pm line 284
Forum::Key::store('Forum::Key=HASH(0x8e7855c)') called at /var/lib/mason/obj/library/branch.html line 208
HTML::Mason::Commands::__ANON__('passed_args', 'HASH(0x8e5f420)', 'tree', 'topics', 'branch', 'golden_ratio') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Component.pm line 131
HTML::Mason::Component::run('HTML::Mason::Component::FileBased=HASH(0x8f158d0)', 'passed_args', 'HASH(0x8e5f420)', 'tree', 'topics', 'branch', 'golden_ratio') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
HTML::Mason::Request::comp('HTML::Mason::Request::ApacheHandler=HASH(0x8e1a8fc)', '/library/branch.html', 'passed_args', 'HASH(0x8e5f420)', 'tree', 'topics', 'branch', 'golden_ratio') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Commands.pm line 70
HTML::Mason::Commands::mc_comp('/library/branch.html', 'passed_args', 'HASH(0x8e5f420)', 'tree', 'topics', 'branch', 'golden_ratio') called at /var/lib/mason/obj/library/dhandler line 90
HTML::Mason::Commands::__ANON__('start_at', 1, 'num_to_see', 50, 'keyid', 39099156) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Component.pm line 131
HTML::Mason::Component::run('HTML::Mason::Component::FileBased=HASH(0x8ecd038)', 'HTML::Mason::Component::FileBased=HASH(0x8ecd038)', 'HTML::Mason::Component::FileBased=HASH(0x8ecd038)', 'start_at', 1, 'num_to_see', 50, 'keyid', ...) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
HTML::Mason::Request::comp('HTML::Mason::Request::ApacheHandler=HASH(0x8e1a8fc)', 'HASH(0x8e5fbcc)', 'HTML::Mason::Component::FileBased=HASH(0x8ecd038)', 'start_at', 1, 'num_to_see', 50, 'keyid', ...) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 159
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 159
HTML::Mason::Request::exec('HTML::Mason::Request::ApacheHandler=HASH(0x8e1a8fc)', '/library/topics/golden_ratio', 'start_at', 1, 'num_to_see', 50, 'keyid', 39099156) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/ApacheHandler.pm line 914
HTML::Mason::ApacheHandler::handle_request_1('HTML::Mason::ApacheHandler=HASH(0x8de2afc)', 'Apache=SCALAR(0x8e082dc)', 'HTML::Mason::Request::ApacheHandler=HASH(0x8e1a8fc)', 'HASH(0x87f1b20)') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/ApacheHandler.pm line 560
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/ApacheHandler.pm line 560
HTML::Mason::ApacheHandler::handle_request('HTML::Mason::ApacheHandler=HASH(0x8de2afc)', 'Apache=SCALAR(0x8e082dc)') called at /etc/httpd/conf/handler.pl line 97
HTML::Mason::handler('Apache=SCALAR(0x8e082dc)') called at /dev/null line 0
require 0 called at /dev/null line 0