I have decided to devote some time to Mathematical reading, the kind of play and explorations which mathematicians do, and as a result, end up making some beautiful discoveries.
I started out by the reading and playing with Fibonacci series, and very soon in my pursuit, I read and discovered something beautiful I couldn't resist sharing.
I won't go into too much details about the Fibonacci series (which is amazing by the way from a historical, mathematical beauty and applications point of view) for now, and share crisply something that just blew my mind. I know this article isn't doing justice to the series in any way, but the that's not the point of this article.
Fibonacci series is the series with the 1st and 2nd term as 1, and the all the further terms obtained by adding the previous 2 terms. So, the series turns out be :
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ......
As per the series, the 11th Fibonacci number is 89. Following are some of the observations and discoveries made by mathematicians, students and which make this occurrence really amazing.
- 11 and 89 are both prime numbers. (Ok....Not that great)
- 8/9 = 0.89... (Somewhat interesting)
- If we see 11 as (8+3), 89 is the (8+3)rd Fibonacci number, and it is also (8*3)rd prime number. (Tell me something which is more beautiful)
- 8+9 = 17, which is the sum of all 4 prime numbers smaller than 11. Interestingly enough , 8*9 = 72, which is the sum of 4 prime numbers greater than 11 (13,17,19,23) . (This seems to be getting somewhere)
- 8*9 + (8 + 9) = 89
These are nice. But what really blew my mind is the following observation.
Squaring the digits of a number and adding them
Start with 89. Square the digits and add them. This gives us a new number. Let's keep doing that and see what happens.
89 --> 8^2 + 9^2 = 64 + 81 = 145 --> 1^2 + 4^2 + 5^2 = 42 --> .....
If we keep doing this, what we get is the following :
89 --> 145 -> 42 --> 20 --> 4 --> 16 --> 37 --> 58 --> 89
Wow. We come back to 89.
What if we start at a different number, and repeat the process. Would we arrive at the initial number always. Lets check that out with say...43.
43 --> 25 --> 29 --> 85 --> 89
And it's 89 again.
What's really cool is that, you could start with any number, with any number of digits, and you would always end at 89 or 1. Isn't this just amazing? Try that out for a few numbers, and you could share your sequence in the comments.
Now, a really curious mind would never be satisfied here. The real question now would be.......Why does this happen? Could you dare to explore that?
It may be hard to define mathematical beauty, but that is true of beauty of any kind. -- G.H Hardy
PS: 89 is the 11th Fibonacci number, and there are 1189 gospels in the Bible. Seems like a part of the God's plan.
PSS:I have skipped some of the more technical discoveries, for the sake of simplicity, so this is not an exhaustive list is any way. I might share them in a separate post.
FAQs
Is 89 the 11th term of the Fibonacci sequence? ›
Fibonacci series is the series with the 1st and 2nd term as 1, and the all the further terms obtained by adding the previous 2 terms. So, the series turns out be : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ...... As per the series, the 11th Fibonacci number is 89.
Why does 1 89 represent the Fibonacci sequence? ›The Punch Line
The decimal expansion of 1/89 is just the Fibonacci series, added together in an appropriate fashion. Specifically, think of the Fibonacci series as being a sequence of decimal fractions, arranged so the right most digit of the nth Fibonacci number is in the n+1th decimal place.
So eleventh number is 89.
What is the missing Fibonacci number 89? ›Fibonacci number sequence
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584... In this list, a person can find the next number by adding the last two numbers together.
The notation that we will use to represent the Fibonacci sequence is as follows: f1=1,f2=1,f3=2,f4=3,f5=5,f6=8,f7=13,f8=21,f9=34,f10=55,f11=89,f12=144,…
What is the golden ratio of 144 and 89? ›1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … So, dividing each number by the previous number gives: 1 / 1 = 1, 2 / 1 = 2, 3 / 2 = 1.5, and so on up to 144 / 89 = 1.6179…. The resulting sequence is: 1, 2, 1.5, 1.666…, 1.6, 1.625, 1.615…, 1.619…, 1.6176…, 1.6181…, 1.6179…
What is so magical about Fibonacci numbers? ›Fibonacci numbers appear in so many contexts in our lives and surroundings, for example, the number of the petals in a flower, the seed heads of a flower, paintings and a lot more. In fact, the beauty of a human face is based on Golden Ratio whose nth power forms the nth Fibonacci number.
What are the most important Fibonacci numbers? ›The most commonly used ratios include 23.6%, 38.2%, 50%, 61.8%, and 78.6%. These levels should not be relied on exclusively, so it is dangerous to assume that the price will reverse after hitting a specific Fibonacci level.
Why do Fibonacci numbers matter? ›Why are Fibonacci numbers so important? They are nature's favourite numbers. You find them all over the natural world. Count the number of petals on a flower and often it's a Fibonacci number.
Why is 11 23 Fibonacci day? ›November 23 is celebrated as Fibonacci day because when the date is written in the mm/dd format (11/23), the digits in the date form a Fibonacci sequence: 1,1,2,3. A Fibonacci sequence is a series of numbers where a number is the sum of the two numbers before it.
What is the 11th number? ›
11 (eleven) is the natural number following 10 and preceding 12. It is the first repdigit. In English, it is the smallest positive integer whose name has three syllables.
Are the Fibonacci number 1 1 2 3 5 8? ›What is the Fibonacci sequence? The Fibonacci sequence is a famous group of numbers beginning with 0 and 1 in which each number is the sum of the two before it. It begins 0, 1, 1, 2, 3, 5, 8, 13, 21 and continues infinitely.
What comes after 89 in Fibonacci? ›Fibonacci Numbers (Sequence):
1,1,2,3,5,8,13,21,34,55,89,144,233,377,... Fn=Fn−2+Fn−1 where n≥2 . Each term of the sequence , after the first two, is the sum of the two previous terms.
A perfect example of this is the nautilus shell, whose chambers adhere to the Fibonacci sequence's logarithmic spiral almost perfectly. This famous pattern shows up everywhere in nature including flowers, pinecones, hurricanes, and even huge spiral galaxies in space.
What are the 10th and 11th Fibonacci numbers 55 and 89 What are the 8th and 13th Fibonacci numbers? ›The list of first 20 terms in the Fibonacci Sequence is: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181. … and so on. … and so on.
What are the first 11 terms of the Fibonacci sequence? ›Fibonacci Sequence List. The list of first 20 terms in the Fibonacci Sequence is: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181. … and so on.
What is the 93th term of Fibonacci sequence? ›The value of fibo(93) is 12200160415121876738 , which clearly is greater than the maximum value that fits in a long . This is the way integers work in a computer program, after all they're limited and can not be infinite.
What is the 11th term in the Fibonacci sequence 1 1 2 3 5 8? ›The 11th term will be 89. The eleventh term of the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, …... It is a fibonacci sequence in which previous terms is added to get next term.
What is the 12th term Fibonacci? ›The first 12 terms of the Fibonacci sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The 12th term (144) gives the number of rabbits after one year, which answers Fibonacci's original question to his readers.