Homeschool Math Blog

Have you ever heard about the Fibonacci numbers and the Golden ratio? A tiling that uses squares whose side lengths are successive Fibonacci numbers. Ask students to continue it! Image from Wikipedia. Here's a lesson I just wrote about them: Fibonacci numbers and the golden section – lesson for middle and high school students If you like it, share it! You might ask, "Should our children or students even learn about Fibonacci numbers or the golden ratio?" True, they aren't any standard fare in math books. However, I feel that yes, students should know about them. I think it's important that our young people learn a few math topics that show how MATH appears in NATURE. You could even call it "MATH APPRECIATION". Children study "art appreciation" so they can appreciate human works of art. Shouldn't we also appreciate the "artworks" in nature, such as flower petals and seed heads? And, once you understand a little b...

Courtesy of Mararie This is an INTERESTING application of Fibonacci numbers! Fibonacci numbers are the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on. (Add two numbers in the sequence to get the next one.) Take two neighboring numbers in the sequence, such as 5 and 8. Turns out, 5 miles is approximately 8 km.  Take 34 and 55:  34 miles is about 55 km. If your number is not in the sequence, write it as a sum of numbers that are: Convert 10 miles into kilometers. 10 = 5 + 5, and 5 miles is about 8 km. So, 10 miles is about 16 km. OR Convert 25 kilometers into miles. 25 = 21 + 2 + 2. 21 km = 13 miles (about) 2 km = 1 mile (about) 2 km = 1 mile (about) 25 km = about 13 + 1 + 1 miles = about 15 miles. More details here: Adventures in Fibonacci Numbers The reason has to do with the fact that the conversion factor, (0.621371192 mi/km) is pretty close to the ratio to which sequential Fibonacci numbers converge (0.61803).

I just learned about Vi Hart's "doodling in math class" videos (hat tip goes to Fawn Nguyen ). Vi calls herself mathemusician - and definitely, she's a talented and smart gal! I'm sure you'll enjoy her videos (as long as you can follow her super fast speeaking). Here are some that I enjoyed: Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3] Here's a link to learn more about Fibonacci numbers in nature , so you can read about it at a slow pace : ) Binary Hand Dance was pretty cool too! Her series of "mathematical doodling" videos have become somewhat of a viral success. Here's one more: Doodling in Math Class: Infinity Elephants

I have combined the recent blogposts about Fibonacci numbers and golden ratio into one article on my site that you can use as a teaching guide or just to educate yourself: Fibonacci numbers and golden section - lesson plan I hope you enjoy my posts... you're welcome to leave commens about the blog - just mention in your comments it's about the blog.

In a previous post , we studied about Fibonacci numbers : 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... (add two consecutive numbers to get the next one). I noted that those numbers appear in nature in many places, and asked if your child/student know about that. My opinion is yes, he or she should know. But why? After all, that stuff is not needful in daily life. I think it's important that youngsters learn a few math topics that show how math appears in nature. It is about math appreciation - (or better yet, appreciation of the Master Mathematician of the Universe...). Kids learn Art Appreciation - so they can appreciate human works of art... Oh, how much better you can appreciate the "artworks" in nature such as flower petals or seedheads when you understand a little bit of the math behind them! Here's another amazing thing about these numbers: Let's study the RATIOS when you take a Fibonacci number divided by the previous Fibonacci number, and make a list:...

The solution to the little thinking exercise of previous week is here: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... -> Add two consecutive numbers from the sequence to get the next one following them This sequence is called Fibonacci numbers. And it isn't just any ole sequence of any ole numbers... it has some amazing properties, plus it's found in nature in many places. For example, Fibonacci numbers are found in * Petals on flowers * Seed heads * Pine cones * Leaf arrangements * Vegetables and Fruit The links go to a magnificent site about Fibonacci numbers with tons of information and pictures. Go click the links and see for yourself! It's very informative and well done, plus I don't have those photos. Then come back. I have a question for you: Should your child or student learn about this? Is this important to know? Well, you think about it - in the next post we will study just a tiny bit more about Fibonacci numbers.