A golden rectangle with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a. This illustrates the relationship

The Fibonacci sequence (also known as the Golden Ratio) has interested mathematicians, artists, designers, and scientists for centuries.

The Fibonacci sequence starts like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on forever. Each number is the sum of the two numbers that precede it. It’s a simple pattern, but it appears to be a kind of built-in numbering system to the cosmos.

Golden ratio – In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.

15 Uncanny Examples of the Golden Ratio in Nature

phi = 1.61803…

The Golden Rectangle – The Greeks used the 1.618 proportion to construct The Golden Rectangle. It was a rectangle with sides measuring one and 1.618 (or with side measuring to consecutive Fibonacci Numbers). This was considered the most mathematically beautiful structure, and frequently used in architecture. The Parthenon incorporates a number of Golden Rectangles into its structure and decoration.

Pascal’s Triangle – a geometric arrangement of the binomial coefficients in a triangle. It is named after Blaise Pascal in much of the western world

Engineering ideas

  • ratio, proportion, pattern, sequence, value, sum, rectangle

Do It
Challenges for you to work on…

  • find some other examples of the Fibonacci sequence or Golden Ratio.

Learn more…

  • Golden Ratio – The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon, pentagram, decagon and dodecahedron.