The Golden 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.