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What do we use the golden ratio also known as phi for?
The main use for the golden ratio is its aesthetic appeal - in art and architecture. Rectangles with the golden ratio as their aspect appeal to the human mind (for some reason). So various aspects of the Parthenon in Athens, for example, have dimensions whose ratio is phi. Phi is closely related to the Fibonacci sequence: the ratio of successive terms of the sequence approaches phi and so, just like the Fibonacci sequence, phi appears in many natural situations. However, there is no particular application based on phi.
Why is the golden ratio used?
There are two main areas where the ratio is used and they are for different reasons.One reason is that the human mind finds the Golden ratio aesthetically pleasing. It is, therefore, used in art and architecture.The second reason is directly related to its mathematical properties (the ratio of the whole to the larger part is the same as the ratio of the larger to the smaller parts). This is used in designing paper sizes like the A and B series. Divide an A3 sheet in half and you will get two A4 sheets which have the same aspect ratio as the A3. Repeat and you get two A5s with the same property and so on.
Where are irrational numbers used?
Pi is used in work with circles or ellipses. For example, how far a car will move in one rotation of its tyre. That may seem a silly question but that is how the odometer works. Irrational square roots will occur in many measurements. The diagonal of a square or the principal diagonal of a cube will always be irrational. That will also be the case for most rectangles and cuboids. The number e has many uses in advanced mathematics. In art and architecture, the Golden Ratio is an irrational number. The Fibonacci sequence, which crops up in nature in many situations, is closely related to the Golden Ratio. These are some examples.
What Roman art is used today still?
Roman art that is still used today includes the design of buildings and columns that are used in architecture and city planning to this day. Techniques like contrast and bass relief are also still used today.
Why are Fibonacci numbers so special?
Fibonacci numbers are important in art and music. The ratio between successive Fibonacci numbers approximates an important constant called "the golden mean" or sometimes phi, which is approximately 1.61803.
