MAT135T3265 SNHU Milestone 3 Mathematic Fibonacci Succession Final Project Submit the paper for Strand 2: Mathematics of your topic.I have attached the pap

MAT135T3265 SNHU Milestone 3 Mathematic Fibonacci Succession Final Project Submit the paper for Strand 2: Mathematics of your topic.I have attached the papers rubric and the papers instructions as well as the outline for the paper and the previous submission. This is the third part of this paper. the mathematics of the topic selected. Please let me know if you have any questions that I can answer! MAT 135: Final Project Guidelines and Grading Guide
Overview
The final project for this course is the creation of a comprehensive final paper that includes the following main components:
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Introduction
Strand 1: Historical Significance
Strand 2: Mathematics
Strand 3: Real-World Applications
Conclusion
The project is divided into five milestones, which will be submitted at various points throughout the course to scaffold learning and ensure quality final
submissions. These milestones will be submitted in Modules Two, Three, Four, Five, and Seven.
Outcomes
To successfully complete this project, you will be expected to apply what you have learned in this course and should include several of the following course
outcomes:
1. Communicate and problem solve in mathematics, without the constraints of formal mathematical notation
2. Demonstrate knowledge in fundamental areas of higher mathematics, including number theory, infinity, geometry, topology, fractals, and other topics
3. Experiment with viewing the world from a mathematical perspective
Main Elements
Students will select and research one of the following topics (students may also propose their own topic) and submit this for instructor approval.
MAT 135 Final Project Topic List
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Logic
Mathematical Puzzles
Irrational Numbers
Prime Numbers
Number Theory
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Fibonacci Sequence
Numbers in Nature
Euclidean Geometry
Non-Euclidean Geometry
Tessellations
Mathematical Patterns
Symmetry
Infinity
Fractals
Knot Theory
Graph Theory
Linear Algebra
Chaos Theory
Self-Selected Topic
NOTE: Instructors will approve topics for which they know sufficient research and information exists for the student to complete the final paper. Students will
research three areas of this topic and submit each “strand” for grading and feedback. The strands are as follows:
1. Strand 1: The Historical Significance: Students will research the historical development of the topic from inception through modern-day usages. Students
may select the most significant developments and contributors to the topic.
2. Strand 2: Mathematics: Students will research and explain the mathematics of the topic chosen. This may include the most significant discovery, theory,
or usage. Students will fully explain the mathematics of the topic.
3. Strand 3: Real-World Applications: Students will research and make connections between the topic and the usages in the real world. Students may make
connections to other fields where appropriate.
Final Paper: Students will write an introduction to this paper, briefly outlining the topic and explaining the three strands. Students will include all three strands as
subsections to the final paper, taking into account specific instructor feedback and suggestions for improvement. Given the nature of specific topics, students
may need to consolidate repetitive sections to make a cohesive paper. Students will write a conclusion paragraph, which will be a reflective analysis of what the
student gained from researching this topic. The final paper will include a cover sheet and reference page, using proper APA formatting. Total paper length: no less
than 10 pages (exclusive of cover page and references).
The final paper should be submitted as one document with the following components:
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Cover Sheet
Introduction
Strand 1: Historical Significance
Strand 2: Mathematics
Strand 3: Real-World Applications
Conclusion
References
Format
Milestone One: Topic Selection & Outline
In Task 2-2, you will submit your chosen topic to the instructor for approval and an outline of the three strands of the paper, including potential references. The
topic may come from the list provided above or it can be self-designed. This milestone will be graded separately using the Final Project Topic Selection and
Outline Rubric, and feedback will be provided for revisions to the final paper.
Milestone Two: Strand 1—Historical Significance
In Task 3-2, you will submit the paper for Strand 1: Historical Significance. This strand should be between 2–3 pages and fully explain the history of the topic.
Proper APA citations and references are expected. This milestone will be graded separately using the Strand Paper Rubric, and feedback will be provided for
revisions to the final paper.
Milestone Three: Strand 2—Mathematics
In Task 4-2, you will submit the paper for Strand 2: Mathematics. This strand should be between 2–3 pages and fully explain the mathematics of the topic chosen.
This may include the most significant theory, theorem, or finding. Proper APA citations and references are expected. This milestone will be graded separately
using the Strand Paper Rubric, and feedback will be provided for revisions to the final paper.
Milestone Four: Strand 3—Real-World Applications
In Task 5-2, you will submit the paper for Strand 3: Real-World Applications. This strand should be between 2–3 pages and fully explain the real-world
applications of the topic chosen. This may include common usages of the topic, applications, and/or connections to other fields. Proper APA citations and
references are expected. This milestone will be graded separately using the Strand Paper Rubric, and feedback will be provided for revisions to the final paper.
Milestone Five: Final Paper
In Task 7-2, you will submit the final paper. Include an introduction outlining the topic and what the reader can expect within each of the three strands. This
paper will then consist of the three strands of research that has been conducted over the course of the term. Finally, write a conclusion, which will be a reflective
analysis of what you learned from the research you conducted. The final paper should be cohesive and polished and take into consideration feedback provided
by the instructor throughout the term. The paper should be no less than 10 pages, excluding the cover sheet and references page. Proper APA citations are
expected. This milestone will be graded using the Final Project Rubric.
Deliverable Milestones
Milestone
Deliverables
Module Due
Grading
Paper will be graded (50 points total) with Final Project Topic Selection and
Outline Rubric —feedback will be provided
Paper will be graded (100 points total) with Strand Paper Rubric—feedback
will be provided
Paper will be graded (100 points total) with Strand Paper Rubric—feedback
will be provided
Paper will be graded (100 points total) with Strand Paper Rubric—feedback
will be provided
Graded separately; Final Project Rubric (200 points total)
1
Topic Approval & Paper Outline
Two
2
Strand 1—Historical Significance
Three
3
Strand 2—Mathematics
Four
4
Strand 3—Real-World Applications
Five
5
Final Product: Final Paper
Seven
Final Project Rubric
Requirements of submission: Written components of projects must follow these formatting guidelines when applicable: double spacing, 12-point Times New
Roman font, one-inch margins, and discipline-appropriate citations. Final paper should be no less than 10 pages, excluding coversheet and references page;
proper APA formatting is expected.
Critical Elements
Communication
Exemplary (100%)
Demonstrates comprehensive
communication of
mathematical issues and ideas
using accurate mathematical
language and proper
terminology
Demonstrates knowledge of
multiple mathematical issues
through extensive collection
and in-depth analysis of
evidence to make informed
conclusions
All of the mathematical
concepts are correctly applied
and integrated with supporting
evidence in a real-world context
Proficient (85%)
Demonstrates moderate
communication of
mathematical issues and ideas
using accurate mathematical
language and proper
terminology
Demonstrates knowledge of
some mathematical issues
through collection and in-depth
analysis of evidence to make
informed conclusions
Needs Improvement (55%)
Demonstrates minimal
communication of
mathematical issues and ideas
using accurate mathematical
language and proper
terminology
Demonstrates minimal
knowledge of mathematical
issues through collection and
analysis of evidence to make
informed conclusions
Not Evident (0%)
Does not demonstrate
communication of
mathematical issues and ideas
using accurate mathematical
language and proper
terminology
Does not demonstrate
knowledge of mathematical
issues through collection and
analysis of evidence and does
not make informed conclusions
Most of the mathematical
concepts are correctly applied
and integrated with supporting
evidence in a real-world context
Some of the mathematical
concepts are correctly applied
and integrated with supporting
evidence in a real-world context
Does not correctly apply or
integrate mathematical
concepts
20
Main Elements
Includes almost all of the main
elements and requirements and
cites multiple examples to
illustrate each element
Includes most of the main
elements and requirements and
cites many examples to
illustrate each element
Includes some of the main
elements and requirements
Does not include any of the
main elements and
requirements
25
Writing
(Mechanics/Citations)
Student meets all requirements
for submission. No errors
related to organization,
grammar and style, and
citations
Student meets most
requirements for submission.
Minor errors related to
organization, grammar and
style, and citations
Student meets some
requirements for submission.
Some errors related to
organization, grammar and
style, and citations
Student does not meet
requirements for submission.
Major errors related to
organization, grammar and
style, and citations
15
Knowledge of
Fundamental Areas
Integration and
Application
Total
Value
20
20
100%
Strand Paper Rubric
Requirements of submission: Written components of projects must follow these formatting guidelines when applicable: double spacing, 12-point Times New
Roman font, one-inch margins, and APA citations. Strand papers should be between 2–3 pages; excluding reference page; proper APA formatting is expected.
Critical Elements
Communication
Exemplary (100%)
Demonstrates comprehensive
communication of
mathematical issues and ideas
using accurate mathematical
language and proper
terminology
Proficient (85%)
Demonstrates moderate
communication of
mathematical issues and ideas
using accurate mathematical
language and proper
terminology
Needs Improvement (55%)
Demonstrates minimal
communication of
mathematical issues and ideas
using accurate mathematical
language and proper
terminology
Not Evident (0%)
Does not demonstrate
communication of
mathematical issues and ideas
using accurate mathematical
language and proper
terminology
Value
30
Knowledge of
Fundamental Areas
Demonstrates knowledge of
multiple mathematical issues
through extensive collection
and in-depth analysis of
evidence to make informed
conclusions
Demonstrates knowledge of
some mathematical issues
through collection and in-depth
analysis of evidence to make
informed conclusions
Demonstrates minimal
knowledge of mathematical
issues through collection and
analysis of evidence to make
informed conclusions
Does not demonstrate
knowledge of mathematical
issues through collection and
analysis of evidence and does
not make informed conclusions
30
Integration and
Application
All of the mathematical
concepts are correctly applied
and integrated with supporting
evidence in a real-world
context
Most of the mathematical
concepts are correctly applied
and integrated with supporting
evidence in a real-world
context
Some of the mathematical
concepts are correctly applied
and integrated with supporting
evidence in a real-world
context
Does not correctly apply or
integrate mathematical
concepts
30
Writing
(Mechanics/Citations)
Student meets all requirements
for submission. No errors
related to organization,
grammar and style, and
citations
Student meets most
requirements for submission.
Minor errors related to
organization, grammar and
style, and citations
Student meets some
requirements for submission.
Some errors related to
organization, grammar and
style, and citations
Student does not meet
requirements for submission.
Major errors related to
organization, grammar and
style, and citations
10
Total
100%
MAT135- MILESTONE 1
1
MAT135- Milestone 1
Southern New Hampshire University
Introduction
MAT135-MILESTONE 1
2
My inquisitiveness as an academician of Fibonacci Sequence and it is Golden Ratio has driven
me to choose this topic as my final project.
Stand 1: Historical Importance
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Leonardo Pisano Bigollo first discovered the history of the Fibonacci Sequence in 1202
in Pisa, Italy.
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The Leonardo DaVinci and the Golden section
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The Fibonacci Sequence, spiral and the golden mean
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The Golden section and the Golden rectangle
Stand 2: Mathematic Aspects
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Fibonacci Sequence served as a method of writing numbers in modern mathematics
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The DaVinci Golden section was crucial in renaissance art and divine proportions.
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Physical appearance in the proportion of the human body.
Stand 3: Actual Application
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The principles of Fibonacci Sequence are of much importance in the field of art and
architecture
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Its concept of appearance is applicable in photography
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The organization of its ratios and order of sequence appearance is appropriate.
Conclusion
Developing the quench to learn more about this principle will assist me in understanding the
sequence of natural occurrence that we usually witness around us. I am hopeful that this concept
MAT135-MILESTONE 1
will help develop a positive understanding and interest in all the aspects of mathematics and the
importance of such principles.
3
MAT135-MILESTONE 1
4
References
Bednarz, U., Bród, D., Szynal-Liana, A., W?och, I., & Wo?owiec-Musia?, M. (2017). ON
FIBONACCI NUMBERS IN EDGE COLOURED TREES. Opuscula Mathematica, 37(4),
479-490. doi:10.7494/OpMath.2017.37.4.479
Burger, E. B., & Starbird, M. (2013). The Heart of Mathematics (4th ed.). Danvers, MA: Wiley.
Liu, R., & Wang, A. (2016). Sums of products of two reciprocal Fibonacci numbers. Advances In
Difference Equations, 2016(1), 1-26. doi:10.1186/s13662-016-0860-0
Meisner, G. (2012, May 15). The Golden Section / Golden Ratio. Retrieved July 16, 2017, from

The Golden Section / Golden Ratio

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Meisner, G. (2014, July 7). Da Vinci and the Divine Proportion in Art Composition. Retrieved
July 16, 2017, from https://www.goldennumber.net/leonardo-da-vinci-golden-ratio-art/
Pierce, Rod. (12 May 2017). “Nature, The Golden Ratio, and Fibonacci Numbers.” Math Is Fun.
Retrieved 17 Jul 2017 from http://www.mathsisfun.com/numbers/nature-golden-ratiofibonacci.html
Reich, D. (n.d.). THE FIBONACCI SEQUENCE, SPIRALS AND THE GOLDEN MEAN.
Retrieved July 16, 2017, from https://math.temple.edu/~reich/Fib/fibo.html
MAT135-MILESTONE 1
5
Running Head: FIBONACCI SEQUENCE
Fibonacci Sequence: Milestone 2
Chris Fronapfel
Southern New Hampshire University
1
FIBONACCI SEQUENCE
2
The concepts of Fibonacci Sequence are applicable in every aspect of science, nature, and art.
Fibonacci Sequence is a concept that involves a series of numeric in which the next series f
numbers is found by summing two numbers before it. The sequence begins by either 0 or 1, and
the consequence follows 0, 1, 2…..10…….24…..50. The first digit is found by adding ‘0+1′ and
2 ‘1+1,’ and the sequence continues ((Ghose, 2018). The historical importance of this concept
can be discussed into various perspectives ranging from its time of discovery and the people
involved in its development.
Different academic articles and journals have claimed that Leonardo Bonacci discovered the
concept. Born in Pisa, Italy, in the year of 1175, Leonardo Fibonacci was recognized by his
contribution in his Fibonacci. He was a son of tax police who dealt with taxation issue within
Pisa and Bugai, an Arab Port City located in the Northern Horn of Africa. Due to the influence of
his father, who had an interest in understanding numbers, he emphasized on his son to be
schooled in mathematic courses in Bugai. It was out of this that during his time that Leonardo
showed interest in understanding the Hindu-Arabic numeric system that is the mother of the
concept of his work, Fibonacci sequence. In the Hindu-Arabic order, their texts could predate
Leonardo’s concept by centuries. As early as 1202, Leonard had published a book that was
explaining and teaching about Hindu-Arabic system in different institutions. His book was titled
‘Liber Abaci,’ and his book was considered as the onset of the concepts of calculations in
learning (Ghose, 2018). His work provided a significant solution to the ‘rabbit population
puzzle’ in his work titled ‘Liber Laci.’ Leonardo considered ‘a hypothetical situation where there
is a pair of rabbits that mate at the end of each month, and by the end of the second month, the
female produces another pair. In this situation, the rabbits never die, they mate exactly after one
FIBONACCI SEQUENCE
3
month, and the females always produce a pair where one is male, and one is female’ (Fibonacci,
2015, September 10).
The concept of Fibonacci Sequence has had a significant mathematical interest despite the late
discoveries of most of its implications and relationship. For quite several years, different
mathematic scholars have shown interest and have so far discovered the sequence throughout
nature. It was established that ‘in the spirals of pineapples, pinecones and the seeds of sunflower
heads. In the 1750s, Robert Simson noted that the ratio of each term in the sequence to the
previous term approaches, with ever greater accuracy the higher the terms, a ratio of
approximately 1:1.6180339887’ (Matson, 2010). This is what is referred to as ‘Golden Ratio.
Within the concept of the Fibonacci Sequence, the Golden Ratio has already created a perfect
spiral number that is placed a squarely measured in all dimensions. In 1877, a French
mathematician Eduardo Lucas named the ‘rabbit problem’ the Fibonacci Sequence.
Thus, throughout its discovery, the concept of Fibonacci Sequence has proved to be one of the
most significant ancient discovery that led to the development of mathematics through the help
of the work of Leonardo Fibonacci. Its importance can be felt nature, science, and art. The
concept was first introduced to the world through ‘Leonardo’s book “Liber Abaci” when
Leonardo questioned a situation with a pair of mating rabbits and how many pairs of rabbits
would be after one year’ (Fibonacci, 2015, September 10).
FIBONACCI SEQUENCE
4
References
Fibonacci. (2015, September 10). Retrieved November 17, 2018, from

Fibonacci

Ghose, T. (2018, October 24). What Is the Fibonacci Sequence? Retrieved November 17, 2018,
from https://www.livescience.com/37470-fibonacci-sequence.html
Matson, L. (2010). MEDIEVAL MATHEMATICS – FIBONACCI. Retrieved November 17, 2018,
from https://www.storyofmathematics.com/medieval_fibonacci.html

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