Phenomenal Phi and Fantastic Fibonacci – a new summer journey

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As a maths teacher, I have often researched the Fibonacci sequence, Phi and the Golden Ratio.   I’ve included it in my lessons every year to make things more interesting, engaging or relevant.  Despite all my previous experience and a wealth of available resources online, I still keep discovering more facts and ideas surrounding this intriguing pattern of numbers.  I have read about the patterns in plants and animals, the human body, architecture and art.  I have also looked at fascinating themes related to Sacred Geometry.  However, here are some other interesting pieces that I have stumbled across in the last few days.  The link that started my revived interest was all about the planets and the Fibonacci sequence, but I didn’t think it would again lead to much more that is fascinating and beautiful about mathematics, patterns and the world around us.  I also discovered that not all of it is true! I will assume the role of tour guide and take you on a little journey…

In the unlikely event that you are not already familiar with Phi or the Fibonacci Sequence, or perhaps you just need a reminder, then please visit these 3 introductory video links first:


1. Fibonacci, Venus, Earth and the Sun

Earth orbits the sun 8 times in the same period that Venus orbits the sun 13 times! Those numbers seem very familiar…and look at that lovely pattern in the middle when you join the lines on a weekly basis.  Visit Under the SymmeTree where you can read more about this interesting fact.

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2. The dimensions of the Earth and the Moon

The dimensions of the Earth and Moon are in Phi relationship, forming a Triangle based on 1.618.

3.  Is it possible that the shape of the Universe itself is a dodecahedron based on Phi?

New findings in 2003 based on the study of data from NASA’s Wilkinson Microwave Anisotropy Probe (WMAP) on cosmic background radiation reveal that the universe is finite and shaped like a dodecahedron, a geometric shape based on pentagons, which are based on phi.  Although it’s still a theory, the data that supports it is testing as true!  Click on this link (or on the picture) to read more about it at   There’s also a very interesting video about this theory:

4.  What does Phi sound like?

A musical interpretation of Phi.  The melodies that you hear throughout this piece are taken directly from the first 39 digits of Phi. The tempo is set at 161.8 BPM.

5.  Why is the Fibonacci Sequence important to religious people?

Christians call it “The Fingerprint of God”. In the Torah, we find the “Love Numbers” as explained in an interesting talk given by Rabbi Yitzchak Ginsburgh.

6.  Why is the Fibonacci Sequence important to investors?

7.  Why is the Golden Section important to artists and architects?

8. What do James Bond, Aston Martin and the Golden Ratio have in common?

From Gary Meisner ( Click here to visit the site and read the full article. James Bond, also known as 007, drove an Aston Martin DB5 in the movies GoldFinger and GoldenEye, and Aston Martin is now boasting its application of the Golden Ratio in the design of its latest DB9 and Rapide S automobiles. The Aston Martin Rapide S is described as:

“Breathtaking Proportions – The ‘Golden Ratio’ sits at the heart of every Aston Martin. Balanced from any angle, each exterior line of Rapide S works in concert and every proportion is precisely measured to create a lithe, pure form. Our engineering follows the same principle. A near perfect weight distribution ensures Rapide S is balanced in form and balanced in function.”

9. Golden Ratio – Top 10 myths and misconceptions

Screen Shot 2014-07-29 at 23.54.18Visit this link to read about some of the common points of confusion and debate, covering beauty, the Parthenon, the UN Secretariat Building, the Great Pyramid, Nautilus shell, use by famous artists (Da Vinci, Botticelli, Seurat, etc.) and other topics.

10. Fact versus Fiction

Professor Keith Devlin presents an all-encompassing lecture on the facts and the myths about Fibonacci and the Golden Ratio  –  Stanford University, October 2012.


If you would like to learn more, visit these links:

Classroom Makeovers to Engage Learners | Edutopia


Lucky me, today I started moving into my brand new classroom in a brand new building! The students had their last day yesterday and staff are working until Friday before going on summer break.  It’s a teacher’s dream to have a beautiful, clean, state-of-the-art classroom.  Finally I have had my dream come true.  Just looking at the picture below gives me the same feeling I have when I walk into my new classroom.  I will post in September for you to see, but before you get too envious, I can assure you that it comes with great responsibility!  Choosing just the right posters and displays, organising the shiny new trapezoidal desks into the best little arrangement of clusters, deciding exactly which shelf gets to support treasured books, selecting the perfect teacher tools to have on the sparkling, clutter-free teacher’s desk, and of course, the ultimate choice, making positive and effective decisions about how things will be when the students arrive back at school in September.  In the meantime, read through some of these interesting ideas from Edutopia about transforming your own classroom.

I hope that you will visit my blog regularly over the summer as I am planning to share and organise plenty more new ideas and resources especially for teachers in the UK, USA or any international schools around the world.  Thank-you for all your support and comments over the past academic year.  It has been such a pleasure to see how the number of visitors is increasing every month.  Please leave comments or feel free to send me your ideas if you would like me to share them on this blog.   Enjoy the summer break, hard working teachers of the world!  MrWilliamsMaths.

Click on the picture to visit the Edutopia website packed with creative ideas and suggestions.


Five-Minute Film Festival: Classroom Makeovers to Engage Learners | Edutopia.

See also “8 tips and tricks to redesign your classroom” 

Plickers – The Student Response System without handheld devices!

I love this brilliant idea for getting students to vote and still use technology without the cost and responsibility of providing a handheld device for each student.  I’m definitely going to give this a try in my lessons this week! Have a look at the printable “answer card” for each student (see below), it’s a cool QR code that the teacher scans in with the use of a phone or tablet.  One device, that’s all you need –  and of course your interactive whiteboard for displaying the results.


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Free Technology for Teachers: Plickers – The Student Response System for Classrooms That Arent 1:1.

Ken’s Dingbats | A free quiz resource (Excellent for classroom use)

I used these in one of my lessons today (we had a “fun lesson”) and the students really enjoyed the challenging nature of these puzzles.  It put their thinking skills to the test and I had to keep encouraging them not to give up too easily – in some cases I gave them clues!  We were able to try both the DITLOIDS (look it up, it has an interesting origin) as well as the DINGBATS today.

Here are some examples:

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Ken’s Dingbats | A free quiz resource.