Jim Loy
Jl's Math Page: The Golden Rectangle and the Golden Ratio
This is a personal site from Jim Loy that describes the golden rectangle and the golden ratio. Includes several diagrams and pictures as well as formulas. A good background in math is helpful.
Other
Mathman: The Fibonacci Numbers, Pineapples, Sunflowers, and the Golden Mean
Here is an exercise to do using a pineapple to explore Fibonacci numbers. Then find the ratios of larger to smaller of each consecutive pair of Fibonacci numbers and graph them to find out the sequence.
Wolfram Research
Wolfram Math World: Golden Rectangle
This site contains the definition for the term "Golden Rectangle," complete with detailed pictures, charts, and explanations.
Other
Mathematics: Fibonacci Numbers and the Golden Section
This resource contains everything you ever needed to know about Fibonacci numbers. You'll find mathematical and historical facts, examples, problems, interactive demonstrations, and more.
Texas Instruments
Texas Instruments: Numb3 Rs: It All Started With a Pair of Rabbits
Based off of the hit television show NUMB3RS, this lesson introduces students to the set of Fibonacci numbers and shows how this set is present in many aspects of nature. Through the lesson, students explore the first 13 elements in the...
National Council of Teachers of Mathematics
The Math Forum: Leonardo Da Vinci Activity
At Math Forum, middle schoolers explore the Vitruvian Man diagram and test Leonardo's theory of the ratio of height to arm span.
Other
Golden Artist Colors: Color Mixing Guide
Golden Artist Colors presents a guide to mixing acrylic paint. An explanation of color theory and mixing color with paint is included on this site. There are also color charts and exercises that can be done with paint that explore how...
Curated OER
Science Kids: Science Images: Golden Ratio Spiral
This image shows the golden ratio spiral with colors used to show the different sections.
Science Buddies
Science Buddies: The Golden Rules of Photography
What is it that famous photographers do to make their images so pleasing to the eye? Find out if simple rules of geometry and symmetry can make you a better photographer.
Math Open Reference
Math Open Reference: The Golden Rectangle
Gain an understanding of the golden rectangle with this helpful reference tool. Provides a detailed definition, examples, and an interactive activity that enhances further explanation. Includes links to related topics.
Dartmouth College
Dartmouth College: Mqed: Geometry in Art and Architecture
Learners learn about art and mathematics. Topics include the golden ratio, platonic solids, and number symbolism. The learning resource includes a description, requirements, syllabus, and bibliography.
Other
P.u.e.m.a.c.: Que Es La Razon Aurea?
Find out how to calculate the Golden Ratio in this exercise.
Math Words
Math words.com: Golden Mean
A basic definition for what the Golden Mean (Golden Ratio) is and how to find its reciprocal.
Ministry of Education and Universities of the Region of Murcia (Spain)
Ministerio De Educacion Y Ciencia: El Numero Aureo
Discover the golden ration in everyday life and in the art with this interactive activity.
Mathigon
Mathigon: Algebra: Fibonacci Numbers
This lesson focuses on Fibonacci numbers, a pattern based on the sum of the two previous numbers. It offers examples and practice exercises using some form of Fibonacci numbers.
Cuemath
Cuemath: Irrational Numbers
Learn how to identify irrational numbers. This lesson reviews the irrational number list, the difference between irrational and rational numbers, and whether or not irrational numbers are real numbers. Examples are provided along with a...
Annenberg Foundation
Annenberg Learner: Part C: Fibonacci Numbers
Look at an interesting application of ratios that demonstrates the amazing patterns that emerge when we examine mathematics. The Fibonacci numbers are found in art, music, and nature.
TeachEngineering
Teach Engineering: The Fibonacci Sequence & Robots
Using the LEGO NXT robotics kit, students construct and program robots to illustrate and explore the Fibonacci sequence. Within teams, students are assigned roles: group leader, chassis builder, arm builder, chief programmer, and...
Discovery Education
Discovery Education: Numbers in Nature
This Fibonacci sequence lesson plan is aimed at grades 9-12, but would be appropriate for some junior high classes. It includes historical background and examples of Fibonacci numbers in nature, as well as suggested readings and ties to...
Rice University
Rice University: Cynthia Lanius: Geometry Online
This is a site for geometry lovers. Chock-full of puzzles, games, interesting geometry facts, and online activities.
Mathigon
Mathigon: Alice in Fractal Land
When Alice falls down the rabbit hole, she discovers a wonderful world of mathematics: Pascal's triangle, sequences of rabbit generations, and beautiful, never-ending fractals.