Remake of Research Question 18 by Wendy Gutman https://padlet.com/wendy_gutman/research18 Yay math! en-us 2017-02-10 18:06:12 UTC 2025-10-09 01:35:36 UTC hello@padlet.com https://camo.githubusercontent.com/60b1c8e789efdcf2373f77f0094233428881e994/687474703a2f2f692e696d6775722e636f6d2f55317875444f6b2e706e67 Research 18 wendy_gutman https://padlet.com/wendy_gutman/research18/wish/223354535 In the early 1200’s, an Italian mathematician Leonardo of Pisa
 (nicknamed Fibonacci) discovered the famous Fibonacci sequence.
Research the Fibonacci sequence and explain the theory by writing four facts about the mathematical theory. As an option, you can also create an illustration to further explain the math theory.
On your “sticky note” write four facts about Fibonacci’s rabbit theory and your illustration if you chose to create one.]]> 2018-01-22 14:51:19 UTC https://padlet.com/wendy_gutman/research18/wish/223354535 Ethan Liu https://padlet.com/wendy_gutman/research18/wish/223536088 1. "Before the Fibonacci Sequence was known in Europe, it was used in ancient India for the metrical sciences, also known as prosody (the study of poetic meter).

2. If you divide a Fibonacci number by the number before it, (as n approaches infinity) the ratios produced settle into what is known as the Golden Ratio or the Golden Number (approximately 1.618034).

3. Two consecutive Fibonacci numbers have been found in tree branches, the number of leaves on a stem, the structure of pineapples and artichokes, etc.

4.The Fibonacci Sequence has been used in the visual arts because it is believed to produce aesthetically appealing images."

Source: http://www.studentguide.org/the-ultimate-resource-on-the-fibonacci-sequence/

]]> 2018-01-22 19:58:01 UTC https://padlet.com/wendy_gutman/research18/wish/223536088 Manya Das manyadas https://padlet.com/wendy_gutman/research18/wish/223597051 - - - - - - - - - - - - - - - - - - - - - - - 
    ~8 Excellent Facts~ About Fibonacci's Rabbit                       Theory
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1. The Fibonacci Sequence is related to the Golden Ratio.

2.The Fibonacci Sequence is found in the ancestry of a drone bee.

3. Fibonacci popularized the Hindu-Arabic numeral system in Europe.

4. It was used by Fibonacci to illustrate an idealization of rabbit population growth. It has also been applied to cow population and honey bee populations.

5. Sometimes the Fibonacci numbers are called pine cone numbers because of their application to the structure of pine cones.

6.  If you construct a set of rectangles in a spiral formation using Fibonacci numbers as unit lengths, the resulting spiral is very similar to the spirals on snail, nautilus, and other shells.

7. The Fibonacci Sequence has been used in the visual arts because it is believed to produce aesthetically appealing images. One of the most famous artists (and mathematicians!) who used the Fibonacci Sequence in his art is Leonardo da Vinci.
 
8. It has also been used in music, most notably by Mozart.
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Below is an illustration I have created of a Fibonacci Spiral
]]> 2018-01-22 23:54:07 UTC https://padlet.com/wendy_gutman/research18/wish/223597051 Lavanya S https://padlet.com/wendy_gutman/research18/wish/223604617 1. The Fibonacci Sequence has also been used in music, most notably from   Mozart



2. Sometimes Fibonacci numbers are called pine cone numbers because their structures are similar to a pinecone



3.The next number in a sequence is found by adding up the 2 numbers before it.




4.The Fibonacci sequence even effects in Mother nature!



ILLUSTRATION:
I can't draw an illustration right now, so here is a picture:
]]> 2018-01-23 00:53:17 UTC https://padlet.com/wendy_gutman/research18/wish/223604617 HAYAGRIV GIRIDHARAN https://padlet.com/wendy_gutman/research18/wish/223985934 1. The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it.
2. It starts with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth.
3. Sometimes the Fibonacci numbers are called pine cone numbers because of their application to the structure of pine cones.
4. The Fibonacci Sequence has been used in the visual arts because it is believed to produce aesthetically appealing images. One of the most famous artists (and mathematicians!) who used the Fibonacci Sequence in his art is Leonardo da Vinci.
It has also been used in music, most notably by Mozart.
I couldn't make an illustration so I got pictures.
The Fibonacci spiral.
The golden ratio.]]> 2018-01-23 19:51:11 UTC https://padlet.com/wendy_gutman/research18/wish/223985934 Ethan Liu https://padlet.com/wendy_gutman/research18/wish/224043414

1. "Before the Fibonacci Sequence was known in Europe, it was used in ancient India for the metrical sciences, also known as prosody (the study of poetic meter).

2. If you divide a Fibonacci number by the number before it, (as n approaches infinity) the ratios produced settle into what is known as the Golden Ratio or the Golden Number (approximately 1.618034).

3. Two consecutive Fibonacci numbers have been found in tree branches, the number of leaves on a stem, the structure of pineapples and artichokes, etc.

4.The Fibonacci Sequence has been used in the visual arts because it is believed to produce aesthetically appealing images."





]]> 2018-01-23 22:59:44 UTC https://padlet.com/wendy_gutman/research18/wish/224043414 KARINA L. https://padlet.com/wendy_gutman/research18/wish/224045790
1.  The Fibonacci sequence is used to search a sorted array in computer science.
-  Fibonacci sequence is used in computer science for several purposes like the Fibonacci search technique, which is a method of searching a sorted array with aid from the sequence.

2.  Fibonacci numbers can be found in several biological settings.
- Apart from drone bees, Fibonacci sequence can be found in other places in nature like branching in trees, arrangement of leaves on a stem, the fruitlets of a pineapple, the flowering of artichoke, an uncurling fern and the arrangement of a pine cone.

3.  Fibonacci sequence is related to the golden ratio.
- The ratio of consecutive Fibonacci numbers converges and approaches the golden ratio and the closed-form expression for the Fibonacci sequence involves the golden ratio.

4.  Fibonacci sequence was the solution of a rabbit population puzzle in Liber Abaci.
- In Liber Abaci, Leonardo considers a hypothetical situation where there is a pair of rabbits put in the field. They mate at the end of one month and by the end of the second month the female produces another pair. The rabbits never die, mate exactly after a month and the females always produce a pair (one male, one female). The puzzle that Fibonacci posed was: how many pairs will there be in one year? If one calculates then one will find that the number of pairs at the end of nth month would be Fn or the nth Fibonacci number. Thus the number of rabbit pairs after 12 months would be F12 or 144.




]]> 2018-01-23 23:19:28 UTC https://padlet.com/wendy_gutman/research18/wish/224045790 Eugene Li https://padlet.com/wendy_gutman/research18/wish/224058840 1. the Fibonacci Sequence can be found in Nature, as the numbers in the sequence are the numbers of the leaves in i n trees, scales in pineapples, and much more.
2. If you divide all numbers in the sequence by the previous number, like 144/89, the larger the numbers are, the closer the quotient will equal the golden ratio, which is 1.61803...and so on. Soon, one of the numbers quotient would equal the golden ratio.
3. The Fibonacci Sequence was introduced to the world as book Libar Abaci written in 1202. It introduced western European Mathematics, as well as the Fibbonaci Sequence.
4.However, Fibonacci didn't actually discover the sequence. the numbers date back to ancient India, which was used in metrical sciences. He introduced it to Europe in his 1202 book and it soon spread.]]> 2018-01-24 01:13:12 UTC https://padlet.com/wendy_gutman/research18/wish/224058840 Kyleigh O kyleigh_od https://padlet.com/wendy_gutman/research18/wish/224065064 FACT 1.
 The  Fibonacci sequence is used to search a sort array in computer science
Fact no.2.
To get the next number in a sequence you have to add the first two together. My proof is that these are the first-most letters. Here is how the sequence starts: 1,1,2,3,5,8,13,21,34.....
 Fact #3
The fibonacci sequence can be used in a spiral. In a spiral the boxes/spiral gets bigger as the numbers added together get bigger.
Fact number 4
You can use the Fibonacci sequence as a rule.  Relating to fact no.2.

00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
○○○○○○○○○○○○○○○○○○○○○○○00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

I cannot really draw on my computer so I just searched this one on the internet:

]]> 2018-01-24 02:05:35 UTC https://padlet.com/wendy_gutman/research18/wish/224065064 Alec Morris morrisalec13 https://padlet.com/wendy_gutman/research18/wish/224430911 1. The Fibonacci sequence is a series of numbers where each number is found by adding the previous two numbers before it.
2. By definition, the first two numbers in the Fibonacci sequence are either 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two.
3. If you write out a sequence of Fibonacci numbers, you can see that the last digits repeat every 60 numbers.
4. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the Fibonacci Quarterly]]> 2018-01-24 20:18:21 UTC https://padlet.com/wendy_gutman/research18/wish/224430911 morrisalec13 https://padlet.com/wendy_gutman/research18/wish/224432519 2018-01-24 20:22:08 UTC https://padlet.com/wendy_gutman/research18/wish/224432519 Ethan Hall https://padlet.com/wendy_gutman/research18/wish/224439279 1. The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it. Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth.
2. In the Fibonacci spiral
the squares fit perfectly together because of the nature of the sequence, where the next number is equal to the sum of the two before it. The spiral and resulting rectangle are known as the Golden Rectangle.
3. 
Fibonacci first noted the sequence when pondering a mathematical problem about rabbit breeding. 

 Begin with one male rabbit and female rabbit that have just been born. .  A female rabbit gives birth to one male rabbit and one female rabbit. The rabbits do not die.
4. Knowledge of numbers is said to have first originated in the Hindu-Arabic arithmetic system, which Fibonacci studied while growing up in North Africa.




]]> 2018-01-24 20:40:04 UTC https://padlet.com/wendy_gutman/research18/wish/224439279 Savannah Estes https://padlet.com/wendy_gutman/research18/wish/224449018 1. Fibonacci's sequence is used in nature such as different leaf designs.
2. Fibonacci's sequence is used in music on things such as musical scales.
3. Fibonacci's sequence works by adding the two numbers before the next number to find the next number.
4. Fibonacci's sequence starts with F1= 1 which is what he says in his book, Liber Abaci.
Here is an image of the sequence.]]> 2018-01-24 21:08:29 UTC https://padlet.com/wendy_gutman/research18/wish/224449018 Mac Wiley https://padlet.com/wendy_gutman/research18/wish/224452628 1- the fabionacci sequence was made after Leonardo Of Pisa. He lived in the years of 1170-1250. He used the arithmetic series to illustrate a problem based on a pair of breeding rabbits.
2- ]]> 2018-01-24 21:21:50 UTC https://padlet.com/wendy_gutman/research18/wish/224452628 Elizabeth Jones https://padlet.com/wendy_gutman/research18/wish/224457388 Fibonacci's Rabbit Theory!
4 facts about it!

1.Every number in the sequence(from 2)is the sum of two before it.
1,1,2,3,5,8,13...

2.It is called Fibonacci's
Rabbit Theory because it started with two fictional baby rabbits. A boy and a girl.

3. Fibonacci's sequence was first in Liber Abaci.Which was created by himself.


4.1 year=144 rabbit pairs 
3 years=over 14 million pairs =enough for every one in Georgia to have one
49 months=over 7 billion pairs enough fr every one in the world to have one.

]]> 2018-01-24 21:39:02 UTC https://padlet.com/wendy_gutman/research18/wish/224457388 Nathan Hsu https://padlet.com/wendy_gutman/research18/wish/224475657 Follow the arrow.]]> 2018-01-24 23:33:40 UTC https://padlet.com/wendy_gutman/research18/wish/224475657 Nathan Hsu https://padlet.com/wendy_gutman/research18/wish/224475996 1. The sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34.
2. The next number in the sequence is found by adding up the two numbers before it.
3. Sunflowers seeds are arranged in a Fibonacci spiral.
4. The Fibonacci numbers are nature's numbering system. ]]> 2018-01-24 23:36:21 UTC https://padlet.com/wendy_gutman/research18/wish/224475996 A picture https://padlet.com/wendy_gutman/research18/wish/224477941
]]> 2018-01-24 23:54:07 UTC https://padlet.com/wendy_gutman/research18/wish/224477941 Rylan Carter https://padlet.com/wendy_gutman/research18/wish/224853779 These are the four facts that I have found.
__________________________
1. Fibonacci numbers appear unexpectedly in mathematics, so much that there is an entire journal dedicated to their study, the Fibonacci Quarterly.
2. The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.
3. In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones.
4. Sunflower seeds are arranged in a Fibonacci spiral.

]]> 2018-01-25 20:03:24 UTC https://padlet.com/wendy_gutman/research18/wish/224853779 Luke McCook https://padlet.com/wendy_gutman/research18/wish/224864648 1: The order of Fibonacci numbers are the previous 2 numbers add up to the next number in the sequence.The order goes 0,1,1,2,3,5,8,13,21,34,55, and so on and so forth.
2:Sunflowers seeds are arranged in a Fibonacci spiral, keeping the seeds uniformly distributed no matter how large the seed head may be.
3: The shapes of spiral galaxies, such as Messier 74, and hurricanes, such as Hurricane Irene, follow the Fibonacci sequence.
4: To make a spiral you start by making squares the width of each number in the sequence.
( see diagram below.)
]]> 2018-01-25 20:31:03 UTC https://padlet.com/wendy_gutman/research18/wish/224864648 Arthur Walton https://padlet.com/wendy_gutman/research18/wish/224875304 The Fi]]> 2018-01-25 21:02:13 UTC https://padlet.com/wendy_gutman/research18/wish/224875304 Arthur W https://padlet.com/wendy_gutman/research18/wish/224875518 1. The Fibonacci Series is made from the 2 nubes before it.

2. Sunflower Seeds are also arranged in a Fibonacci Spiral.

3. It was first called Liber Acaci 

4. The sequence goes: 0,1,1,2,3,5,8,13,21,34,45,79 and so on.]]> 2018-01-25 21:03:04 UTC https://padlet.com/wendy_gutman/research18/wish/224875518 Sam Mitchell https://padlet.com/wendy_gutman/research18/wish/224879683 These are the facts I've found:
1. The Fibonacci Sequence originally was in the book Liber Abaci as an answer to a math problem. 
2. The problem asked how many rabbits could be produced by one couple of rabbits. Each new pair produces another pair of rabbits each month, and so on.
3. The numbers go 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and continue.
4. Sunflower seeds in the flower are arranged in a Fibonacci's sequence.]]> 2018-01-25 21:16:51 UTC https://padlet.com/wendy_gutman/research18/wish/224879683 Lily Watson https://padlet.com/wendy_gutman/research18/wish/224889380 1.The Fibonacci Sequence is a series of numbers where each number is the sum of each two numbers before it.
2. The Fibonacci Sequence first appeared in the book Liber Abaci by Fibonacci. It observed rabbit mating seasons. About how many pairs of rabbits each month. The mother doesn't give birth to a pair of rabbits until the second month. 
3. Fibonacci's real name is filius Bonacci. He is often called to Fibonacci or Leonardo of Pisa.
4. Multiple plants show the Fibonacci Sequence.It may be the arrangement of leaves around a stem or possibly on a pine cone. Other plants like daises and sunflowers also contain the Fibonacci Sequence. The numbers the plants might contain are 89 and 144.111]]> 2018-01-25 21:56:02 UTC https://padlet.com/wendy_gutman/research18/wish/224889380 Brynn Bondhus https://padlet.com/wendy_gutman/research18/wish/224890794 1. The sequence goes 0,1,1,2,3,5,8,13,21,34

2. Fibonacci sequence is a series of numbers where each number is found by adding the previous two numbers before it.

3. Fibonacci sequence has also been in music like Mozart

4. Sometimes the Fibonacci sequence numbers are called pinecone numbers becuase of their structure.]]> 2018-01-25 22:03:27 UTC https://padlet.com/wendy_gutman/research18/wish/224890794 Duncan Wilson https://padlet.com/wendy_gutman/research18/wish/224906381 1.  Fibonacci numbers 

 They also appear in biological settings, such as branching in trees,  (the arrangement of leaves on a stem), the fruit sprouts of a pineapple the flowering of an artichoke, an uncurling fern and the arrangement of a pinecone's bracts.

2. Fibonacci numbers are defined by the previous 2 numbers in the sequence added together.

 3.The Fibonacci sequence starts with 1 and 1.

4.Every positive whole number can be made by adding two  
Fibonacci numbers  together.

]]> 2018-01-26 00:20:35 UTC https://padlet.com/wendy_gutman/research18/wish/224906381 Noah Nelson https://padlet.com/wendy_gutman/research18/wish/224908023 1.The Fibonacci sequence of adding the last 2 numbers, like 1,1,2,3,5,8,13,21,34 and so on
2. The Fibonacci affects Mother Nature 
3. Sunflower seeds are in a Fibonacci spiral
4. Any two Fibonacci numbers added together equals any positive number ]]> 2018-01-26 00:37:31 UTC https://padlet.com/wendy_gutman/research18/wish/224908023 Nicole Smith https://padlet.com/wendy_gutman/research18/wish/224908107 1. The Fibonacci sequence is a series of numbers where a number is found by adding the two numbers before it. Always starting with 0 and 1.

2. The Fibonacci theory was named Fibonacci also known as Leonardo of Pisa or Leonardo Pisano. Fibonacci numbers were first introduced in his liberabaci in 1202. 

3. Knowledge of numbers is said to have first originated in the hinlu-Arabic arithmetic system,which Fibonacci studied while growing up in North America. 

4. Fibonacci wrote many books about geometry and also helped develop the concept of zero.]]> 2018-01-26 00:38:20 UTC https://padlet.com/wendy_gutman/research18/wish/224908107 Sources manyadas https://padlet.com/wendy_gutman/research18/wish/224909734 https://learnodo-newtonic.com/fibonacci-facts and http://www.studentguide.org/the-ultimate-resource-on-the-fibonacci-sequence/ ]]> 2018-01-26 00:53:28 UTC https://padlet.com/wendy_gutman/research18/wish/224909734 Ryan Smith https://padlet.com/wendy_gutman/research18/wish/224910263 1.the fibonacci sequence is when you add the two numbers before it.for example, 1,1,2,3,5,8,13,


2. The Fibonacci is named after the mathmatician Leonard Fibonacci.

3. It can be seen in mother nature.

4.The Fibonacci can be used in music and in musicals.]]> 2018-01-26 01:00:07 UTC https://padlet.com/wendy_gutman/research18/wish/224910263 Will C karatewillc https://padlet.com/wendy_gutman/research18/wish/224912435 1. The Fibonacci Sequence has been used in music, mainly from Mozart. 



2. Sometimes the Fibonacci numbers are called pinecone numbers because their structures look like a pinecone 



3. The Fibonacci Sequence is a series of numbers where a number is found by adding two numbers before it. Always starting with 0 and/or 1. 



4. The Fibonacci Sequence even effects in nature. 

]]> 2018-01-26 01:21:54 UTC https://padlet.com/wendy_gutman/research18/wish/224912435 Victor Cristian https://padlet.com/wendy_gutman/research18/wish/224915379 Fact 1-The Fibonacci sequence can be found in nature. For example, on pine cones the lower you go the more scales there are on the pine cone.
Fact 2- The Fibonacci sequence is seen a lot in musicals most know is Mozart.
Fact 3-The Fibonacci sequence goes like 1,1,2,3,5,8,13,21,34,55,89, etc.  
Fact 4- Last fact the Fibonacci sequence is used art to draw detailed pictures most know one is Leonardo da Vinci. ]]> 2018-01-26 01:40:07 UTC https://padlet.com/wendy_gutman/research18/wish/224915379 Jack Seel https://padlet.com/wendy_gutman/research18/wish/224920198 1. The Fibonacci sequence can be found in nature. For example, the design in leaves, the design in pine cones, and the lines on snail shells.
2. The pattern is a endless sequence.
3.  The sequence is in musical pieces. Most notably by Mozart.
4. A lot of art uses the Fibonacci sequence.]]> 2018-01-26 02:27:26 UTC https://padlet.com/wendy_gutman/research18/wish/224920198 Richard Wu https://padlet.com/wendy_gutman/research18/wish/224921340 1.The Fibonacci sequence is a sequence that goes the number and the number right before it add to get the next one
2. Fibonacci was born in 1170 in Pisa, Italy
3.Fibonacci also  popularizing the Hindu-Arabic numeral system 
4.The  Fibonacci sequence goes odd to even]]> 2018-01-26 02:37:19 UTC https://padlet.com/wendy_gutman/research18/wish/224921340