Many artists today and throughout history have relied on mathematical formulas and principles to assist them in creating the most appealing compositions with clever leading lines, spirals and elemental relationships.

GOLDEN MEAN

GOLDEN RATIO

FIBONACCI SPIRAL

PHI GRID

RULE OF THIRDS

The spiral formed is a part of these helpful mathematical formulas for those who like to draw, paint and design and this is due to observations made throughout history, firstly, as it is also one of nature’s most common configurations.eg. Snail shells, waves, galaxies, flower petals, pine cones, snakes, storms, DNA, curly hair, and that is just a few.

Why are spirals so commonly found in nature? No one can say for certain, but scientists think that a possible answer is, because spirals are the smart way to grow!

It wasn’t actually the famous Italian Fibonacci, who discovered this fascinating natural phenomenon. It appears that the Egyptians may have used both pi and phi in the design of the Great PyramidsThe Greeks seem to have have based the design of the Parthenon on this proportion, but this is subject to some conjecture.

The sequence already had been described as early as the 2nd or 3rd century BC in the works of Acharya Pingala, an Indian mathematician who used maths in the possible patterns of Sanskrit poetry that could be formed from syllables of two lengths.

The Fibonacci sequence was the outcome of a mathematical problem about rabbit breeding that was posed in the Liber Abaci.

While growing up in North Africa, Fibonacci learned the more efficient Hindu-Arabic system of arithmetical notation (1, 2, 3, 4...) from an Arab teacher. In 1202, he published his knowledge in a famous book called the Liber Abaci, in which Fibonacci offered a mathematical solution to a  problem about rabbit breeding that was very current.

THE GOLDEN RATIO AND THE PHI GRID

The golden ratio is a ratio of approximately 1.618 to 1. Artists have used this ratio for centuries to create works of art from paintings to architecture. Phi is the only number that has the mathematical property of its square being one more than itself:  Φ + 1 = Φ²

or 1.618… + 1 = 2.618…

THE RULE OF THIRDS

It is more common today for artists to tend to use the rule of thirds for positioning focal points and leading lines, and it is only a subtle variation on the Phi grid. The end result does place the focal point (in any of these 4 intersecting zones of the blue-green lines here))in an area where all intervals vary quite nicely and if other guidelines are observed with all other leading lines, a broadly appealing composition can be easily achieved.

Fibonacci and Friends