Leonardo of Pisa (1170 - 1250), also known as Fibonacci, was one of the most important mathematicians of the age Media in Europe. He made important contributions to arithmetic, algebra and geometry. As more is known today for his famous series, surely you've seen in more than one occasion:
1, 1, 2, 3, 5, 8, 13 , 21, ...
As you may have noticed, this sequence starts with two ones, any term of the sequence is obtained by adding the previous two and the sequence is infinite. And why is famous for this succession?. Because the Nature is wise and has proven it as multiple patterns of plants, animals, ... follow this sequence ... For example, in the procreation of a pair of rabbits for months ...
But not only this, for example, if you divide each number in the sequence between its immediate neighbor on the right gives the sequence of fractions called Fibonacci ratios (1 / 1, 1 / 2, 2 / 3, 3 / 5, 5 / 8, 8 / 13, ...). As they move these ratios tend to infinity the result at:
This number is the most famous in the mathematical world, is known Number Gold (talk at length about this in another post I'm prepared) and it has to do with the famous Golden Ratio symbol of natural beauty, and used from the Greeks to the present day in many buildings, works of art , pictures or simply our DNI. Proportion that is assumed in many natural examples, but as I said, goes a long way and I prefer to leave this topic for another post, just leave a sign of the close relationship of this sequence, with the golden ratio and nature .. .
I leave you with a couple of mathematical games related to succession Fibonacci:
1 º. A geometric fallacy
Draw a rectangle with sides of 8 and 21. Cut it out for the marks shown in the figure. With parts that are built a square whose side measures 13.
- Calculate the area of \u200b\u200bthe rectangle.
- Calculate the area of \u200b\u200bthe square.
Are they the same these areas?. What is happening, is it correct the result you got?. Does it have something to do that 8, 13 and 21 are consecutive numbers of the Fibonacci sequence?.
2 º. Fibonacci Trick
Think two numbers and builds, starting with those numbers, a sequence like the Fibonacci, meaning that each term is the sum of the two.
The sum of the first ten terms of your estate will be eleven times the seventh term. This happens in the Fibonacci sequence and any other that is built the same way. Surprising, right?.
But not only this, for example, if you divide each number in the sequence between its immediate neighbor on the right gives the sequence of fractions called Fibonacci ratios (1 / 1, 1 / 2, 2 / 3, 3 / 5, 5 / 8, 8 / 13, ...). As they move these ratios tend to infinity the result at: 
This number is the most famous in the mathematical world, is known Number Gold (talk at length about this in another post I'm prepared) and it has to do with the famous Golden Ratio symbol of natural beauty, and used from the Greeks to the present day in many buildings, works of art , pictures or simply our DNI. Proportion that is assumed in many natural examples, but as I said, goes a long way and I prefer to leave this topic for another post, just leave a sign of the close relationship of this sequence, with the golden ratio and nature .. . 
I leave you with a couple of mathematical games related to succession Fibonacci:
1 º. A geometric fallacy
Draw a rectangle with sides of 8 and 21. Cut it out for the marks shown in the figure. With parts that are built a square whose side measures 13.
- Calculate the area of \u200b\u200bthe rectangle.
- Calculate the area of \u200b\u200bthe square.
Are they the same these areas?. What is happening, is it correct the result you got?. Does it have something to do that 8, 13 and 21 are consecutive numbers of the Fibonacci sequence?.
2 º. Fibonacci Trick
Think two numbers and builds, starting with those numbers, a sequence like the Fibonacci, meaning that each term is the sum of the two. The sum of the first ten terms of your estate will be eleven times the seventh term. This happens in the Fibonacci sequence and any other that is built the same way. Surprising, right?.
- Build more like Fibonacci sequences and found that the trick is always true.
- tries to show why it happens.
For students in 3 º ESO
We started looking at the concept of succession then moved to the progressions both arithmetic and geometric, here are the notes and exercises that I preached, so that you can download comfortably at home. We continue to work in class ... Hang and interesting anecdotes and little things progressions in future posts ... ok?
- tries to show why it happens.
For students in 3 º ESO
We started looking at the concept of succession then moved to the progressions both arithmetic and geometric, here are the notes and exercises that I preached, so that you can download comfortably at home. We continue to work in class ... Hang and interesting anecdotes and little things progressions in future posts ... ok?
