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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.
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...
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Fibonacci Sequence
This site from the Math Forum explains the explicit formula for fibonacci numbers.
Other
University of Surrey: The Fibonacci Number Sequence
This resource provides extensive information on the Fibonacci number sequence. It has numerous formulas and examples.
Math Is Fun
Math Is Fun: Golden Ratio
A clear explanation, with drawings and examples, of the golden ratio. The examples demonstrate the beauty of mathematics, such as how two Fibonacci numbers can approximate the golden ratio, and why the golden ratio can be called the...
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...
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: Discovering Phi: The Golden Ratio
Students discover the mathematical constant phi, the golden ratio, through hands-on activities. They measure dimensions of "natural objects"--a star, a nautilus shell and human hand bones--and calculate ratios of the measured values,...
Texas Instruments
Texas Instruments: Class of Gold
Students investigate Fibonacci numbers and the ratios of successive Fibonacci numbers.
Ministry of Education and Universities of the Region of Murcia (Spain)
Ministerio De Educacion Y Ciencia: Sucesion De Fibonacci
In Spanish. This unit is about Fibonacci numbers, some of its most interesting properties and their occurrence both in nature and art.
University of Cambridge
University of Cambridge: Nrich: 1 Step 2 Step, Fibonacci
See if you can find the patterns on the staircase. Mr. Fibonacci would be so proud to know you found the solution. You can check your solution right at this nifty one-page website.
Other
Fascinating Triangular Numbers
Patterns of numbers don't come along every day, and so when they do, they need to be bragged about! The basic definition of triangular numbers begins this site which also lists many of the properties of these numbers, highlights the...
Texas Instruments
Texas Instruments: At a Snail's Pace for the Ti 73 Explorer
It is hard to imagine a way to mathematically describe a spiral. Spirals are commonly seen in nature. There are a number of different types of spirals. Some interesting examples include the spiral arrangements of scales in pine cones,...
Texas Instruments
Texas Instruments: Sequences
Students learn how to graph the first n terms of a sequence, how to set the window and how to evaluate the nth term of a sequence. They also explore the Fibonacci sequence and Web plots.
University of Cambridge
University of Cambridge: Nrich: Gnomon 1
This interactive activity gives you an opportunity to explore a specific number pattern named the "Fibonacci sequence." See what other patterns you can discover while you manipulate the blocks. There is a "Printable Page" link if you...
Math Is Fun
Math Is Fun: Pascal's Triangle
A detailed explanation of Pascal's trianlge, with lots of examples and patterns described.
Texas Instruments
Texas Instruments: Numb3 Rs: Pythagorean Triples
Based off of the hit television show NUMB3RS, this lesson has students explore the notion of Pythagorean triples, the "traditional" method for finding Pythagorean triples, and a method to find triples which utilizes the Fibonacci...
Wolfram Research
Wolfram Math World: Golden Ratio
Math World explains the Golden Ratio, gives the formula for finding the irrational number, and expresses this value as an infinite series. Also defines and represents the Ratio geometrically, its relationship to the Fibonacci numbers,...
Varsity Tutors
Varsity Tutors: Hotmath: Graphing Calculator Practice Problems Pythagorean Theorem
Practice using your graphing calculator for real number problems, including the Pythagorean Theorem. If you get stumped or if you would like to check your work, then select the View Solution button, which is located directly under each...
Math Is Fun
Math Is Fun: Common Number Patterns
Developed by a mathematics teacher from the UK, this page identifies and illustrates several common number patterns.
Wolfram Research
Wolfram Math World: Inverse Tangent
This site is all about inverse tangents. The site includes a definition, color graphs, formulas, and many links to related terms.
Rice University
Rice University: Cynthia Lanius: Golden Rectangles All Around
This site is a lab sheet that students can use to explore the golden ratio. It also has other informative links on it.
Wolfram Research
Wolfram Math World: Pascal's Triangle
This site from MathWorld provides great information on Pascal's Triangle. Links are provided throughout for additional information, along with several helpful charts and formulas. This is a good site to check out on the subject.
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