The Spanish painter Salvador Dalí explicitly used the golden ratio in his masterpiece The Sacrament of the Last Supper. The Swiss architect Le Corbusier explicitly used the golden ratio in his Modulor system and many of his architectures are heavily based on the golden ratio. Among all possible "irrational numbers" Nature has opted in many cases for the "golden ratio", that's why it is know as then number of Nature or the number of God. Now, spirals are based on a "rotation ratio" that should be based on a not-rational number to avoid sooner or later overlaps. Similar logic can be applicable to seed in the fruits, petals in flowers and branches of a tree. Plants tend to grow in spirals so that new leaves don't block the sun from older leaves, or so that the maximum amount of rain or dew gets directed down to the roots. (Can you see the spirals? And the fractals?) In vertical are months, number on the dot is the ID of the pair. Count the dots in the tree at the one level and above, Anyway see the following diagram for the first 8 months. The original puzzle that Fibonacci posed was: How many pair of rabbits we will have after 1 year (12 months)?Īs you can see this is not a very natural example. Suppose that our rabbits never die and that the female always produces one new pair. So that at the end of its second month any female can produce another pair of rabbits. Suppose that every birth we have two new rabbits, one male and one female. Rabbits are able to mate at the age of one month and pregnancy is exactly one month. Suppose a newly-born pair of rabbits, one male, one female, are put in a field. The sequence in NatureĪs said above the first example of the Fibonacci sequence is related to the rabbits population growth (a natural case): If you are interested you can google them (around 2M pages). There are other maths properties, some of them really odd. Note the Logarithm scale, and note also the effect of the initial repetition of "1".)Įven if the sequence is divergent, Johannes Kepler (the known physics and astronomer of 17th century) discovered that the ratio of two successive items is convergent to a specific irrational number 1.618034. This is not a trivial number but it is known as golden ratio or "φ" and has a lot of applications (see the next paragraph). Mathematically the sequence is "not-linear" and "divergent" it is also "stronger" than a linear sequence and also "weaker" than an exponential one. Note that the Fibonacci Day is November 23rd, as it has the digits "1, 1, 2, 3" (US format for date) which is part of the sequence (Why not Jan 12th as 01/12?). The sequence was surely known before 13th century there are reference to that in some Indian literature from the 6th century. Leonardo comes into this sequence while studying how a population of rabbits can grow in time (see the next paragraph). Leonardo lived in the Italian city of Pisa ("pisano" means from Pisa in Italian) in the 13th century and he is considered one of the greatest mathematicians of all times: think that, among many other of his works, if we are using Arab digits is mostly because of him (even if he called them "Indian", and probably he was more right). The name comes from Leonardo Pisano known as the son of Bonacci where son in italian is "figlio" and Bonacci was his actual family name ("figlio di Bonacci" -> "fi' Bonacci". But this is just one of the maths behind this sequence. As you can see, many of the items are twice of the the standard one, so the second basic number can control the speed of scaling. If, by convention, we define 0 and 2 as the first digits. By convention the first 2 digits are 0 and 1. Įach number is found by adding up the two numbers in the sequence before this (for example 21=8+13). The Fibonacci sequence is the series of the following numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. Be prepared, this is not a "linear" article and you could find the real reason only at the end ( :-) ). In this short paper we will see different views, but before let me introduce the sequence and some of its interesting characteristics. But why agilists prefer to use these ugly numbers instead of others maybe easier to remember?Įven if the most known reason is "because Nature seems to following it", actually there are also more REAL and RELEVANT reasons making this sequence preferable. It is very common for Agile teams to use the Fibonacci sequence in the estimation process.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |