Menu
The Fibonacci Sequence is the series of numbers:
- Answer by Akshat Sinha: Firstly I will show you it is not possible by direct sum, then I'll demonstrate the different ways to do so. ANSWER:- Not Possible by direct sum in base 10, because If you take the numbers to be modulo 2, five odd numbers would sum up to 1, but 30 is 0 modulo 2.
- 1 Corinthians 3:5-9 Together We Can Do Alot is a sermon about cooperation in the International Baptist Convention.
- 3:5-9 The ministers about whom the Corinthians contended, were only instruments used by God. We should not put ministers into the place of God. He that planteth and he that watereth are one, employed by one Master, trusted with the same revelation, busied in one work, and engaged in one design.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ..
The next number is found by adding up the two numbers before it:
Note: Better Together over Ethernet is enabled by default on supported VVX business media phones with UC Software 5.6.0 or later and Polycom BToE Connector 3.9.0 is compatible with UC Software 5.8.0 or later. System Constraints and Limitations. The following list includes information on system constraints and limitations. How can you put the word “and” 5 times in a row in the same sentence? I need to tell a story. The landlord of a pub called The Pig And Whistle asked a signwriter to make a new sign. When he saw it he thought that the words were too close together so he said to the signwriter “I want more space between Pig and And and And and Whistle”.
- the 2 is found by adding the two numbers before it (1+1),
- the 3 is found by adding the two numbers before it (1+2),
- the 5 is (2+3),
- and so on!
Example: the next number in the sequence above is 21+34 = 55
It is that simple!
Here is a longer list:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ..
Can you figure out the next few numbers?
Makes A Spiral
Nxpowerlite 8 0 8 inches. When we make squares with those widths, we get a nice spiral:
Do you see how the squares fit neatly together?
For example 5 and 8 make 13, 8 and 13 make 21, and so on.
For example 5 and 8 make 13, 8 and 13 make 21, and so on.
Microsoft excel 2016 vl 16 10 download free.
This spiral is found in nature!
See: Nature, The Golden Ratio,and Fibonacci
This spiral is found in nature!
See: Nature, The Golden Ratio,and Fibonacci
The Rule
The Fibonacci Sequence can be written as a 'Rule' (see Sequences and Series).
First, the terms are numbered from 0 onwards like this:
n = | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | .. |
xn = | 0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 | 89 | 144 | 233 | 377 | .. |
So term number 6 is called x6 (which equals 8).
Example: the 8th term is the 7th term plus the 6th term: x8 = x7 + x6 |
So we can write the rule:
The Rule is xn = xn−1 + xn−2
where:
- xn is term number 'n'
- xn−1 is the previous term (n−1)
- xn−2 is the term before that (n−2)
Example: term 9 is calculated like this:
= x8 + x7
= 34
Golden Ratio
And here is a surprise. When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio 'φ' which is approximately 1.618034..
In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation. Let us try a few:
B | |
---|---|
2 | 1.5 |
3 | 1.666666666.. |
5 | 1.6 |
8 | 1.625 |
.. | .. |
144 | 1.618055556.. |
233 | 1.618025751.. |
.. | .. |
We don't have to start with 2 and 3, here I randomly chose 192 and 16 (and got the sequence 192, 16, 208, 224, 432, 656, 1088, 1744, 2832, 4576, 7408, 11984, 19392, 31376, ..):
A | B / A |
---|---|
16 | 0.08333333.. |
208 | 13 |
224 | 1.07692308.. |
432 | 1.92857143.. |
.. | .. |
11984 | 1.61771058.. |
19392 | 1.61815754.. |
.. | .. |
It takes longer to get good values, but it shows that not just the Fibonacci Sequence can do this!
Using The Golden Ratio to Calculate Fibonacci Numbers
And even more surprising is that we can calculate any Fibonacci Number using the Golden Ratio:
xn = φn − (1−φ)n√5
The answer comes out as a whole number, exactly equal to the addition of the previous two terms.
Example: x6
x6 = (1.618034..)6 − (1−1.618034..)6√5
When I used a calculator on this (only entering the Golden Ratio to 6 decimal places) I got the answer 8.00000033 , a more accurate calculation would be closer to 8.
Try n=12 and see what you get.
You can also calculate a Fibonacci Number by multiplying the previous Fibonacci Number by the Golden Ratio and then rounding (works for numbers above 1):
Example: 8 × φ = 8 × 1.618034.. = 12.94427.. = 13 (rounded)
Some Interesting Things
![Together Together](https://i.ytimg.com/vi/CmcSLGR_vP4/maxresdefault.jpg)
Here is the Fibonacci sequence again:
n = | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | .. |
xn = | 0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 | 89 | 144 | 233 | 377 | 610 | .. |
There is an interesting pattern:
- Look at the number x3 = 2. Every 3rd number is a multiple of 2 (2, 8, 34, 144, 610, ..)
- Look at the number x4 = 3. Every 4th number is a multiple of 3 (3, 21, 144, ..)
- Look at the number x5 = 5. Every 5th number is a multiple of 5 (5, 55, 610, ..)
And so on (every nth number is a multiple of xn).
1/89 = 0.011235955056179775..
Notice the first few digits (0,1,1,2,3,5) are the Fibonacci sequence?
In a way they all are, except multiple digit numbers (13, 21, etc) overlap, like this:
0.0 |
0.01 |
0.001 |
0.0002 |
0.00003 |
0.000005 |
0.0000008 |
0.00000013 |
0.000000021 |
.. etc .. |
0.011235955056179775.. = 1/89 |
Terms Below Zero
The sequence works below zero also, like this:
n = | .. | −6 | −5 | −4 | −3 | −2 | −1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | .. |
xn = | .. | −8 | 5 | −3 | 2 | −1 | 1 | 0 | 1 | 1 | 2 | 3 | 5 | 8 | .. |
(Prove to yourself that each number is found by adding up the two numbers before it!)
In fact the sequence below zero has the same numbers as the sequence above zero, except they follow a +-+- .. pattern. It can be written like this:
x−n = (−1)n+1xn
Which says that term '−n' is equal to (−1)n+1 times term 'n', and the value (−1)n+1 neatly makes the correct +1, −1, +1, −1, .. pattern.
History
Fibonacci was not the first to know about the sequence, it was known in India hundreds of years before!
About Fibonacci The Man
His real name was Leonardo Pisano Bogollo, and he lived between 1170 and 1250 in Italy.
'Fibonacci' was his nickname, which roughly means 'Son of Bonacci'.
As well as being famous for the Fibonacci Sequence, he helped spread Hindu-Arabic Numerals (like our present numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) through Europe in place of Roman Numerals (I, II, III, IV, V, etc). That has saved us all a lot of trouble! Thank you Leonardo.
Together 3 5 90 Degree
Fibonacci Day
Fibonacci Day is November 23rd, as it has the digits '1, 1, 2, 3' which is part of the sequence. So next Nov 23 let everyone know!
MULTI-PLATFORM
You can watch LINE TV on mobile phones, tablets, and PCs.
Just enter tv.line.me on your desktop or laptop browser!
Just enter tv.line.me on your desktop or laptop browser!
FIND VIDEOS IN THE CATEGORIES YOU LIKE
Together 3 5 90
Find all the latest and most popular videos organized
into categories including Drama, Music, Entertainment, Beauty,
Animation, Sports and more. You can also sort videos by play count,
recently uploaded date, and Like counts in each category.
into categories including Drama, Music, Entertainment, Beauty,
Animation, Sports and more. You can also sort videos by play count,
recently uploaded date, and Like counts in each category.
BE A FAN OF YOUR FAVORITE PROGRAMS
If you want to subscribe to your favorite channel, just tap the
'Fan' button and you'll be notified any time something new is
added to that channel. Go to 'My List' and check the 'Updated' menu tab for updates. Also, check out the 'Fan' list to see
which of your LINE friends like the same programs you do!
'Fan' button and you'll be notified any time something new is
added to that channel. Go to 'My List' and check the 'Updated' menu tab for updates. Also, check out the 'Fan' list to see
which of your LINE friends like the same programs you do!
WATCH YOUR PERSONAL PLAYLIST OVER AND OVER
If you want to save a video to watch later, just tap the
“Watch Later” icon on the video player. LINE TV remembers
the exact point in the video that you pressed the button,
so you can always continue watching right where you left off.
(This feature is available on the mobile app only.)
“Watch Later” icon on the video player. LINE TV remembers
the exact point in the video that you pressed the button,
so you can always continue watching right where you left off.
(This feature is available on the mobile app only.)
SMART CONTROL VIDEO PLAYER
Control the volume and brightness of videos with your fingertips. Contexts 3 4 4.
Also, LINE TV's smart video player automatically adjusts
your settings to the best video quality for you.
Meet the smartest video player around on LINE TV!
Also, LINE TV's smart video player automatically adjusts
your settings to the best video quality for you.
Meet the smartest video player around on LINE TV!