Leonardo Fibonacci was an Italian mathematician. His so-called Fibonacci number system relates to any number in an infinite series in which each number after 1 is the sum of the two preceding numbers. For example 1,1, 2, 3, 5, 8. This 12th century mathematician was an easy to understand system to more easily work with pi or phi.
fibonnaci fibonnaci fibonnaci
It is 354,224,848,179,261,915,075.
Fibonnaci (c.1170 - c.1250) was also known as Leonardo of Pisa because he was born in and lived most of his life in Pisa, Italy.
That'd be the Fibonnaci sequence (this time without the wikipedia URL :P)
Well, rather a lot I expect. One specific thing in particular happened between those dates: Fibonnaci, the Italian mathematician (born 1170, died 1250).;
The fibonacci sequence if is where each number is the sum of the previous 2 numbers. Here are the first few numbers.0 1 1 2 3 5 8 13 21
There is no missing number. The Fibonacci sequence continues: 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, ...
It's a reference to Leonardo Fibonacci, a famous medieval mathematician, after whom the "Fibonnaci sequence" is named (in which each number is the sum of the previous two).0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.
The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence, ie the higher the pair of Fibonacci numbers, the nearer their ratio is to 1.618034. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987... 3/2 = 1.5, 21/13 = 1.615, 610/377 = 1.618037, 987/610 = 1.618033
It may be surprising but there is a lot of geometry and math used in famous works of art and commercial or graphic design. Perspective drawing uses geometry extensively, parallel, intersecting and converging lines. These are also evident in art works and form the designers grid used for unity and variety. Ratios are also an important part of art and design. The most important one to know is the golden mean, first discovered by the Greeks, it is the ratio that is most pleasing to the human eye because it mimics patterns in nature. The familiar symbol for this is a rectangle containing squares and a spiral that forms when intersections of the interior lines are connected. Fractals and Fibonnaci numbers are also used, especially in computer aided design.
God does exist whether you believe in Him or not. Examples are; the overwhelming proof against climate change and global warming, the Bible, mathematical equations that take you forever to work out and which go on forever eg. Fibonnaci, and the universe. Believing in God changes your entire life, even if everything is going smoothly at the time. Think about it: what happens when you die? What happens to your soul? Does it just lie there in your coffin, or turn into a spirit? The Bible clearly states that those who believe in Him will live with him for eternity in heaven, and those who refuse to accept Him as the creator and saviour shall go to hell. It's not necesarrily the present that will be impact and only the present, it's the rest of Time, and you're life.
If L1=1 and L2=2, we would just get the Fibonacci sequence. Recall that the Fibonacci sequence is recursive and given by: f(0)=1, f(1)=1, and f(n)=f(n-1)+f(n-2) for integer n>1. Thus, we have f(2)=f(0)+f(1)=1+1=2. If L1=1 and L2=2 then we would have L1=f(1) and L2=f(2). Since the Lucas numbers are generated recursively just like the Fibonacci numbers, i.e. Ln=Ln-1+Ln-2 for n>2, we would have L3=L1+L2=f(1)+f(2)=f(3), L4=f(4), etc. You can use complete induction to show this for all n: As we have already said, if L1=1 and L2=2, then we have L1=f(1) and L2=f(2). We now proceed to induction. Suppose for some m greater than or equal to 2 we have Ln=f(n) for n less than or equal to m. Then for m+1 we have, by definition, Lm+1=Lm+Lm-1. By the induction hypothesis, Lm+Lm-1=f(m)+f(m-1), but this is just f(m+1) by the definition of Fibonnaci numbers, i.e. Lm+1=f(m+1). So it follows that Ln=f(n) for all n if we let L1=1 and L2=2.