What does it mean to be Golden??


Welcome to the wonderful world where everything is Golden!!

presented to you by Pete

Welcome! I am currently enrolled in a college course at the University of Illinois called The History of the Calculus and I thought for one of my course projects it would be very helpful for my fellow scholars to have a webpage that would help explain what it means to be "Golden" (that is in the mathematical sense). The topic of Golden is one of the more exciting topics in mathematics and one people should be familiar with. The goal of this annotated webpage is to list some very helpful websites that will give an overview of Golden with examples and some sites that contain some superb activities and lesson plans involving the concept of Golden for teachers.

A quick description of the Golden Ratio:

The Golden Ratio is often represented by Phi. Its approximate value it 1.61803... but more accurately is represented by (sqrt.of 5 + 1) / 2. As you notice Phi is an irrational number and has some very interesting properties and is often seen in the real world. To find out more about Phi please look at some of the intriguing webpages below.

Links on the Golden Ratio:

Fibonacci Numbers and the Golden Section- by Dr. Ron Knott. This is a very detailed webpage with a lot of information on the Golden section and Fibonacci Sequence but on numerous pages. Be ready to maneuver yourself through this page to find what you are looking for, but don't worry it is probably there. There is an overview on what Golden is; there are examples of the Golden section in nature, art, architecture, and music; Golden section occurring in Geometry and Trigonometry; constructions; you name it.

The Golden Ratio and The Fibonacci Numbers- by Kelley L. Ross, Ph.D. This webpage contains information on the Golden ratio with a lot of mathematical calculations and connections to Fibonacci numbers.

The Golden Ratio- by Steve Blacker, Jeanette Polanski, and Marc Schwach. This is a student project that contains information on the Fibonacci Sequence and Golden ratio. It includes a calculator investigation and some worksheets.

The Golden Mean- by Brian Joseph Snyder. This is a website with very detailed explanations of how to make the constructions of the Golden ratio, rectangle, spiral, etc. It also has many examples of the Golden ratio in nature and a proof of the Golden Mean.

Golden Ratio- by jyce3@yahoo.com. This page contains a slight overview of the Golden ratio but has many excellent examples of where the Golden ratio can be seen in biology, art, ancient, and mathematics. It also contains some other good links and books.

"Unified Field" Physics- by Alex Kaivarainen. This webpage is essentially a student paper that includes basic information about why Golden Mean Wave ratios create mathematical model of gravitation. It is an interesting paper dealing with the Golden mean in other areas of sciences, in particular Physics.

First 10,000 Digits of the Golden Ratio- by stephan@cc.wwu.edu. This webpage is just a list of the first 10,000 digits of the Golden Ratio and a formula on how he found all the digits.

Some interesting lesson plans incorporating the Golden Ratio:

Golden Ratio- by Cynthia Lanius. This webpage gives a quick overview of the Golden ratio and then it has a lab sheet which is used by the students to measure different objects and rank which object is closest to the Golden ratio. There is also another page in which you attempt to build a Golden rectangle.

Is Your Body in "Golden" Shape- by Patricia Winkler. This is an excellent site in which students are asked to measure different students and different body measurements to see who is "Golden." Within the lesson there is a list of procedures and as a whole is very well written out with objectives and all.

A Golden Ratio Activity and Resource par excellence!- by Mark Wahl. This is another lesson plan but which focus on measuring the dimensions of one's face. This lesson uses a particular Golden Greek face, do you know whose it is?

Investigating the Golden Ratio Project- by Mr. Frank. This webpage is a worksheet that focuses on measuring ancient architecture and also a seashell with a list of questions for the students to answer.

Thanks for visiting and feel free to email me with questions: