Home > Maths > The Golden Section

The Golden Section

By: Suzanne Elvidge BSc (hons), MSc - Updated: 27 Oct 2012 |
Ratio Mathematical Constant Section

The golden ratio (also known as the golden section or golden mean, or as the Greek letter 'phi') describes a rectangular shape that people find an attractive shape, particularly in art or architecture. No-one is quite sure why this is a particularly pleasing shape, but it appears to be something to do with maths.

Calculating The Golden Ratio

The golden ratio is actually a mathematical constant, a number used in maths that does not change (for another example of a mathematical constant, see 'Calculating Pi').

The golden ratio is 1.6180339887 (roughly 1.62). For something to be in the golden ratio, the length of the longer side divided by the length of the shorter side must be equal to this number.

Measure rectangular shapes (pictures, doors, windows, books) and divide the long side by the short side – are any of these in the golden ratio? Try measuring the walls of a room (this may need help) – is this the golden ratio?

Look some photographs or some pictures printed from the Internet – are these in the golden ratio? Would changing them to the golden ratio make them look better?

Examples Of The Golden Ratio

The Parthenon in Athens, Greece, a temple built in the 5th century BC, uses the golden ratio for the front of the temple, and for the spaces between all the columns.

The Western face of the Cathedral Notre Dame in Paris, built in the 12th to 14th Century, was designed according to the Golden Ratio.

An architect called Le Corbusier (Charles-Edouard Jeanneret-Gris), born in Switzerland and who lived in France, used the golden ratio and the proportions of the human body for his “Modulor” system. Here are a number of examples of his buildings in France, including the Villa Stein in Garches, near Paris and the Unité d'Habitation in Marseilles.

Fibonacci Numbers

Fibonacci numbers are a sequence of numbers, starting with 0 and 1, where each number is the total of the last two numbers added together:0, 1, 1, 2, 3, 5, 8 (and so on).

Every third number is even, and the ratio (dividing the larger number by the smaller one) between two Fibonacci numbers in sequence is phi, or the golden ratio.

Fibonacci numbers appear in nature and can be used to describe the ways that trees branch. Spirals based on Fibonacci numbers can be seen in the shapes of pine cones and pineapples, and the arrangement of leaves on branches and seeds in flower heads, including sunflowers and daisies.

This natural arrangement is likely to be because it is the most efficient way to lay out the seeds, or the way to get the most light possible to the leaves.

Find a picture of a sunflower head (or grow a sunflower from seed – the seed head is great for feeding the birds in the winter after the maths is finished!) and look for the spirals in the layout of the seeds.

Find a pine cone or pineapple (or a picture of one) and look for the spirals in the layout of the scales.

You might also like...
Share Your Story, Join the Discussion or Seek Advice..
I'm trying to do a science research project on the golden ratio, but I can't find an indepent variable, dependent variable, or control group.
CL - 12-Aug-12 @ 11:39 PM
would you please send me some info about golden ratio and fibonnaci seriese. tnx, BM.
BM - 27-Apr-11 @ 11:57 AM
Share Your Story, Join the Discussion or Seek Advice...
(never shown)
(never shown)
(never shown)
(never shown)
Enter word:
Latest Comments
  • The Science Guy
    Re: Why Oil and Water Don't Mix
    I’m a 10th grade student and I’m hoping S.O would write a paragraph on how to properly react Al or other metals with HCl or other…
    27 December 2019
  • Sarah
    Re: Making an Emulsion
    i hate airplane food they overheat EVERYTHING
    12 December 2019
  • Delly
    Re: Why Oil and Water Don't Mix
    I’m doing a project and it’s due in two days thanks for the info. I can finally rest after a long day of researching I’m in six…
    10 December 2019
  • Allycat
    Re: Why Oil and Water Don't Mix
    I am doing a fourth grade science project on this.My question is how or do a graph for this.?
    6 December 2019
  • Potent Pickle
    Re: Making an Emulsion
    My chin is very itchy... is it the lava laamp's greatness…
    21 November 2019
  • Timmy Timmy Timmy
    Re: Making an Emulsion
    bruh... what the heck is up with airline food
    21 November 2019
  • Mosey Cook
    Re: Make Yoghurt and Grow Yeast
    This article on natural yeast and good bacteria has been the best read I’ve read on the Internet
    1 November 2019
  • Tee
    Re: Vibrations: Seeing and Feeling Sound
    I have just witnessed a fork vibrating so fast on its own on the kitchen top. It made a sound while vibrating as if the…
    24 August 2019
  • simran panaich
    Re: Soap and Detergent Chemistry
    thnx!! It helped me a lot !!! THank YOu so much
    6 June 2019
  • Mar2
    Re: Why Oil and Water Don't Mix
    I am doing this as a demo for homogeneous mixture examples. It really helps, it is interesting, and thank you so much for it!!!
    5 June 2019