Here is a number trick that is not too well known and so you can use it to impress your friends. In fact this doesn't require a computer and
can even be done with paper and pencil. It involves a series known as the Fibonacci number sequence, named after the Italian mathematician Leonardo Fibonacci (11701250).


A Fibonacci number sequence is formed by starting with any two numbers, adding those to get a third number, adding the second and third to produce a fourth number and so on.
This is much easier to see with a short example:
2
3
5
8
13
21
34
55
89
144


As can be seen, the sequence is formed by adding the previous two numbers.
2 plus 3 = 5, 3 plus 5 = 8, 5 plus 8 = 13, 8 plus 13 = 21 and so on.
Using the calculator below, if you input 2 and 3 into the first two boxes, when you click "Calculate", you will see all 10 boxes filled in with the same numbers in the list above.
Now, for the "trick" with the Fibonacci number sequence.
Ask your friend for two numbers.
You could then enter the numbers in this computer page but it is much more impressive if this trick is done on paper.
Adding the two numbers, create a Fibonacci sequence that is exactly ten steps long.
When you reach the tenth number, tell your friend you can total all ten numbers in your head!
And what's the secret?
Whenever you have a Fibonacci sequence of 10 numbers, the total will always be the seventh number times 11.
For practice, input two and three in the first two boxes and then click "CALCULATE".
Yes, you could get the total by clicking "Calc Total" or by using the trick.
If you entered two and three for the first two numbers, the seventh number will be 34 and multiplying this by 11 gives a result of 374.
It isn't that difficult to multiply by 11 in your head.
For example, to multiply 34 by 11, think of summing 34 and 34 but shift one number one decimal place.
34
34
374
Obviously, when you ask a friend for two numbers make sure you mention they should be kept relatively small.
Doing this trick on paper is much more impressive than on a computer so why not use this computer page just for practice?
Remember, before you show this to anybody, the best advice is to practice.
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And, if you are curious, here are the first 100 Fibonacci numbers:
1  1 
2  1 
3  2 
4  3 
5  5 
6  8 
7  13 
8  21 
9  34 
10  55 
11  89 
12  144 
13  233 
14  377 
15  610 
16  987 
17  1,597 
18  2,584 
19  4,181 
20  6,765 
21  10,946 
22  17,711 
23  28,657 
24  46,368 
25  75,025 
26  121,393 
27  196,418 
28  317,811 
29  514,229 
30  832,040 
31  1,346,269 
32  2,178,309 
33  3,524,578 
34  5,702,887 
35  9,227,465 
36  14,930,352 
37  24,157,817 
38  39,088,169 
39  63,245,986 
40  102,334,155 
41  165,580,141 
42  267,914,296 
43  433,494,437 
44  701,408,733 
45  1,134,903,170 
46  1,836,311,903 
47  2,971,215,073 
48  4,807,526,976 
49  7,778,742,049 
50  12,586,269,025 
51  20,365,011,074 
52  32,951,280,099 
53  53,316,291,173 
54  86,267,571,272 
55  139,583,862,445 
56  225,851,433,717 
57  365,435,296,162 
58  591,286,729,879 
59  956,722,026,041 
60  1,548,008,755,920 
61  2,504,730,781,961 
62  4,052,739,537,881 
63  6,557,470,319,842 
64  10,610,209,857,723 
65  17,167,680,177,565 
66  27,777,890,035,288 
67  44,945,570,212,853 
68  72,723,460,248,141 
69  117,669,030,460,994 
70  190,392,490,709,135 
71  308,061,521,170,129 
72  498,454,011,879,264 
73  806,515,533,049,393 
74  1,304,969,544,928,657 
75  2,111,485,077,978,050 
76  3,416,454,622,906,707 
77  5,527,939,700,884,757 
78  8,944,394,323,791,464 
79  14,472,334,024,676,221 
80  23,416,728,348,467,685 
81  37,889,062,373,143,906 
82  61,305,790,721,611,591 
83  99,194,853,094,755,497 
84  160,500,643,816,367,088 
85  259,695,496,911,122,585 
86  420,196,140,727,489,673 
87  679,891,637,638,612,258 
88  1,100,087,778,366,101,931 
89  1,779,979,416,004,714,189 
90  2,880,067,194,370,816,120 
91  4,660,046,610,375,530,309 
92  7,540,113,804,746,346,429 
93  12,200,160,415,121,876,738 
94  19,740,274,219,868,223,167 
95  31,940,434,634,990,099,905 
96  51,680,708,854,858,323,072 
97  83,621,143,489,848,422,977 
98  135,301,852,344,706,746,049 
99  218,922,995,834,555,169,026 
100  354,224,848,179,261,915,075 
An interesting aspect of the Fibonacci Number Sequence is that if you divide one Fibonacci number by the previous Fibonacci number, this produces a quotient called the phi ratio φ which is also known as the golden ratio.
For example, Fibonacci #20 divided by Fibonacci #19 =
6,765 ÷ 4,181 = 1.618033963166...
Fibonacci #50 divided by Fibonacci #49 =
12,586,269,025 ÷ 7,778,742,049 = 1.6180339887499...
As we go further down the Fibonacci sequence, this number approaches a limit of {1 + Square Root (5) } ÷ 2
= 1.6180339887498948482...
Another way to express the phi ratio is:
φ = 0.5 + 5^{.5} • 0.5 = 1.6180339887498948482...
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The Fibonacci Sequence appears in many places.
Here is a website that explains the arrangement of seeds in a sunflower being based on the Fibonacci Sequence.
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Leonardo Fibonacci (1170  1250) is thought to be the western world's most skillful mathematician of the Middle Ages.
In his 1202 book Libre Abaci he strongly advocated for the use of Arabic Numerals as opposed to Roman Numerals.
He stated that Arabic Numerals were much easier to read and calculations could be done more quickly and accurately with them.
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