Fibonacci Sequence

What is the "rule" of the Fibonacci sequence?

(Insert formula)

What is the value for the Golden Ratio?

1.618034...

What is the relationship between Fibonacci Sequence and The Golden Ratio?

Any consecutive pairs of Fibonacci numbers has a ratio that is approximately akin to the Golden ratio.

Why is the Fibonacci sequence so important in the study of Mathematics?

Because it is ubiquitous in nature and can be found in the fields of geometry, algebra, number theory, etc...

Why do we study Mathematics?

For Calculation, Application, and Inspiration

in addition to referring to Indo-Arabic numbers, which subsequently took the place Roman numerals, also included a large collection of problems addressed to merchants, concerning product prices, calculation of business profit, currency conversion into the various coins in use in the Mediterranean states, as well as other problems of Chinese origin.

Liber Abacci

which studies the arrangement of leaves, branches, flowers or seeds in plants, with the main aim of highlighting the existence of regular patterns.

Phyllotaxis

Fibonacci Sequences are found in the shell of a nautilus, the spirals of sunflowers, flower petals, takes the shape of a wave, and etc... TRUE or FALSE?

TRUE

The bigger the value of the Fibonacci pair, the closer their ratio is to 1.618034...TRUE or FALSE?

TRUE

Fibonacci numbers that are lower than 0 have a +-+- pattern to their numbers. TRUE or FALSE?

TRUE. (Insert the rule)

For Fibonacci numbers that are bigger than 1, can we get the next term in the sequence by multiplying the previous term with the golden ratio?

YES

Can we use the golden ratio in order to compute for fibonacci numbers?

Yes (insert formula)

Can non-consecutive numbers lead to a ratio that is approximately akin to the golden ratio?

Yes. If we take numbers 192 and 16 then proceed to make a Fibonacci sequence out of it, we can make a golden ratio with bigger consecutive pairs.

Patterns

are formed when colors, shapes, numbers, or sound are repeated over and over again.

two segment lengths have the same proportion as the proportion of their sum to the larger of the two lengths and the limit of the ratio of consecutive Fibonacci numbers.

golden section or golden proportion

Mathematics

the science of patterns that we study in order to think logically, critically, and creatively

published a number of important studies on this sequence, which he claimed to have found in Liber Abaci and which, in the honour of the author, he called "Fibonacci sequence".

Édouard Lucas