41. Global Access To Educational Sources - Mathematics The geometry Center interact with 3-D models Geometric Dissections - A of topicsWorld of Mathematics - Encyclopedic in scope fibonacci numbers and Nature http://www.learning.caliberinc.com/math6.html

Mathematics Resources To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess. ...Paul Halmos Math Activity Sources Tessellation Fun Geometry Sources Miscellaneous Math Help ... Algebra Help (Click on any line to return to the top of the page) Math Activity Sources Kid's Web - Math - links to every kind of math subject Perplexing Problems - probles for each month Aims Puzzles - a new one each moth with great archive of past challenges Plane Math - math and aeronautics combined 20th Century Problem Solving - fun with algebra Hot list: Mathematics - links galore Brain Tricks - the puzzle of the week will keep you coming back The Fruit Game Learn the pattern and win. Math Forum: Math Tips Tricks - a little help never hurt Fibonacci Numbers and Nature - interesting Mathematics - select your problem level here Math Problems for Kids - carefully selected problems by grade level which can help you improve your problem solving skills The Grey Labyrinth - puzzles to stimulate the brain Interactive Mathematics - 36 Games and Puzzles - check the rest of the site too for even more fun The Brain and Behavior - great interactive learning Imagiware's Game Zone - interactive challenges Greg's Brain Games - try the teasers and plexers for a challenge Mathematics Lessons - You are sure to learn here and have fun too.

42. Metaphysics Selected texts and notes by Bonnie Lee Hill.Category Society Religion and Spirituality Books and Essays......Metaphysics. fibonacci numbers. Mysteries, Ancient. Freemasonry. Rosicrucians.Gurdjieff and Ouspensky. Sacred geometry. Mayan Astronomy. Tarot. Return to Index. http://www.webspace4me.net/~blhill/pages/metaphysics.html

Metaphysics Fibonacci Numbers Mysteries, Ancient Freemasonry Rosicrucians Gurdjieff and Ouspensky Sacred Geometry Mayan Astronomy Tarot Return to Index Fibonacci Numbers Fibonacci Numbers and the Golden Section Fibonacci Numbers and the Golden Section Fibonacci Numbers Course Top of Page Freemasonry e-m@son Website Hiram Abiff Kessinger Publishing Page About Freemasons ... The Tracing Board Top of Page Gurdjieff and Ouspensky Notes from "In Search of the Miraculous", Chapters 1-6 Notes from "In Search of the Miraculous", Chapters 7-12 Notes from "In Search of the Miraculous", Chapters 13-18 Fellowship of Friends ... Piotr Demianovich Ouspensky Top of Page Mayan Astronomy Aztec Astrologer Mayan Astronomy Mayan Epigraphic Database Mayan Fonts ... Rabbit in the Moon (McNelly) Top of Page Mysteries, Ancient Alchemy Web Great Pyramid Top of Page Rosicrucians Rosicrucian Fellowship Rosicrucian Texts Top of Page Sacred Geometry Glass Bead Game (Jerome Baumring Library) "God's Secret Formula" by Peter Plichta Hertz Frequencies Inner Garden Art ... Vortex Maps Top of Page Tarot Tarot @ Facade.com

43. Fibonacci: Chapter 10: Topics Remark One can also check that f N = F N f +F N1 . Remark The golden numberf and the fibonacci numbers appear in nature and geometry, art, architecture. http://www.math.ukans.edu/~mandal/math105/fibo105C10.html

Satyagopal Mandal Department of Mathematics University of Kansas Office: 624 Snow Hall Phone: 785-864-5180 e-mail: mandal@math.ukans.edu Topics in Mathematics (Math105) Chapter 10 : Fibonacci Numbers and the Golden Ratio Definition: Recall that a list of numbers a , a , a , ... , a n , ... , a n is called a sequence of numbers. So, the first term of this sequence is a , the second term of the sequence is a , and so on. Definition: The sequence is called the Fibonacci sequence and these numbers are called the Fibonacci numbers. So, The first term of the sequence is F The 2 nd term of the sequence is F The 3 rd term of the sequence is F The 4 th term of the sequence is F The 5 th term of the sequence is F The 6 th term of the sequence is F The 7 th term of the sequence is F The 8 th term of the sequence is F The 9 th term of the sequence is F The 10 th term of the sequence is F The 11 th term of the sequence is F The 12 th term of the sequence is F N) In general, F N denotes the N th -term of the sequence What is the value of F N ? To answer that you have to understand the pattern of the sequence. Note that

44. Fibonacci: Chapter 10: Topics In Mathematics Remark 3 This golden number f and the fibonacci numbers appear in natureand geometry, art, architecture. Your textbook went through http://www.math.ukans.edu/~mandal/math105/m105chap10.html

Satyagopal Mandal Department of Mathematics University of Kansas Office: 624 Snow Hall Phone: 785-864-5180 e-mail: mandal@math.ukans.edu Topics in Mathematics (Math105) Chapter 10 : Fibonacci Numbers and the Golden Ratio Definition: Recall that a list of numbers a , a , a , a n , a n is called a sequence of numbers. So, the first term of this sequence is a , the second term of the sequence is a , and so on. Definition: The sequence is called the Fibonacci sequence and these numbers are called the Fibonacci numbers. So, The first term of the sequence is F The 2 nd term of the sequence is F The 3 rd term of the sequence is F The 4 th term of the sequence is F The 5 th term of the sequence is F The 6 th term of the sequence is F The 7 th term of the sequence is F The 8 th term of the sequence is F The 9 th term of the sequence is F The 10 th term of the sequence is F The 11 th term of the sequence is F The 12 th term of the sequence is F N) In general, F N denotes the N th -term of the sequence. What is the value of F N ? To answer that you have to understand the pattern of the sequence. Note that 2 = F =1 + 1 = F + F 3 = F =1 + 2 = F + F 5 = F =2 + 3 = F + F 8 = F =3 + 5 = F + F 13 = F =5 + 8 = F + F 21 = F = 8 + 13 = F + F 34 = F =13 + 21 = F + F 55 = F = 21 + 34 = F + F 89 = F =34 + 55 = F + F 144 = F =55 + 89 = F + F So, we observe that, except for F

45. The SPHINX Group -- Astronomy, Archaeoastronomy, And Cycles Of Time LINKS Miracle (RA Schwaller de Lubicz) Egyptian Unit Fractions fibonacci numbers and Naturefibonacci numbers and the Golden Section geometry Center geometry Linking http://www.mm2000.nu/sphinxlinks2.html

ASTRONOMY, ARCHAEOASTRONOMY, and CALENDAR LINKS... Links followed by are MM Editor's Choice picks. Links updated September 1, 1999. Aboriginal Star Knowledge Aeon Ancient Astronomical Cosmology webpages Archaeoastronomy, Ethnoastronomy References (UCSD) Archaeoastronomy Images (Clive Ruggles) Astronomy History Resources Babylonian and Egyptian mathematics Bad Astronomy Beginner's Guide to Constructing the Universe Bimillenary of Christ's Birth Calendar Conversions Calendar Systems Calendar Zone Calendars and their History Center for Archeoastronomy Chaos from Above Circle and the Square and the Square Root of Two Classic Maya Calendar and Day Numbering System Egyptian Fractions Egyptian Miracle (R.A. Schwaller de Lubicz) Egyptian Unit Fractions Fibonacci Numbers and Nature Fibonacci Numbers and the Golden Section Geometry Center Geometry Linking the Great Pyramid to the Human Form Historical Astrology in Egypt Kali Yuga A Little Geometry The LIX Unit Mill of Time More Very Easy Geometry One-world Global Calendar Planetary Alignments in 2000 Pythagoras of Samos Sacred Geometry from a Kabbalistic perspective Sacred Geometry Sacred Landscape (terrific bibliography!)

46. Mathematics@work - Beauty, Purity Truth! A database of mathematics links.Category Science Math Directories...... history of hypercomplex numbers, fibonacci spirals. prime numbers, phi the goldennumber. the prime pages, sacred geometry. prime numbers factoring, solar geometry. http://www.geniusatwork.co.uk/mathematics.htm

mathematics n. the abstract science of number, quantity, and space studied in its own right. isaac newton institute for mathematical science fibonacci numbers and the golden section unsolved mathematics problems fibonacci numbers and the pascal triangle ... elements@work [ mathematics@work ] biblical prophecy@work bhoys@work playright@work mind games@work ... freebies@work

47. Publications Of The West Scientists On Fibonacci Numbers Publications of the West scientists on fibonacci numbers. Basin, SL The fibonacciSequence as it appears Coxeter, HSM, Introduction to geometry, John Wiley and http://www.goldenmuseum.com/1801Refer_engl.html

Publications of the West scientists on Fibonacci numbers BOTANIC, BIOLOGY (The growth patterns of plants; the genealogical tree of the male bee; the crossroads of mathematics and biology) Basin, S.L. "The Fibonacci Sequence as it appears in Nature", FQ 1:1 , Feb., 1963, pp. 53-56. Stephen R. B., "Botany with a Twist", Science , May, 1986, pp. 63-64. Brother Alfred Brousseau, "On the Trail of the California Pine", FQ 6:1 , Feb., 1968, pp. 69-76. Coxeter, H.S.M., Introduction to Geometry , John Wiley and Sons, New York, 1961. Douady, S., and Couder, Y., "Phyllotaxis as a Physical Self-Organized Growth Process", Physical Review Letters 68:13 , 30 mar. 1992, pp. 2098-2101. Hunter, J.A.H. and Madachy, J.S., Mathematical Diversions , Van Nostrand, Princeton, 1963, Chapter 2. Roger, V. J., "Growth Matrices in Phyllotaxis", Mathematical Biosciences , 32, 1976, pp. 165-176. Roger, V.J., The Use of Continued Fractions in Botany: UMAP Module 571 , Modules and Monographs in Undergraduate Mathematics and its Applications Project, 1986. Roger, V. J.

48. Law Of Spiral Symmetry Transformation hyperbolic rotation that is the basic transformation of the hyperbolic geometry. isa very good explanation why the fibonacci and Lucas numbers appears in http://www.goldenmuseum.com/1607SpiralSymmetry_engl.html

Law of spiral symmetry transformation As is well known from biology a relative arrangement of very different sprouts arising in the cones of shoots is characterized by the "spiral symmetry". This arrangement principle was named "phyllotaxis" . On the surface of phyllotaxis forms, especially in the closely packed botanic structures (pine cone, pineapple, cactus, head of sunflower etc.), one can see clearly visible left- and right curved series of sprouts. As to the symmetry order of phyllotaxis forms there exists a practice to indicate it through the ratios of the numbers corresponding to the number of the left- and right-hand spirals. In accordance with the law of phyllotaxis such ratios are given by the number sequence generated by the Fibonacci recurrent relationship G n G n-1 G n-2 The most widespread types of phyllotaxis are those described through the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, ... , the Lucas numbers 1, 3, 4, 7, 11, 18, ... or the number sequence 4, 5, 9, 14, 23, ... satisfying to the general recurrent formula (1). It is well known that the process of the collective fruit growing is accompanied at the certain stage by a modification of the spiral symmetry order. As this takes place the modification is strictly regular and corresponds to the general rule of constructing the recurrent number sequences generated by (1). In the case of Fibonacci's phyllotaxis the progress of symmetry order is presented through the sequence:

49. Links Page fibonacci numbers The fibonacci numbers and the Golden section;The fibonacci Association. Fractal geometry of the Mandelbrot Set. http://www.naz.edu/dept/math/Links.html

Links Topics Art and Mathematics Careers in Mathematics Computer Resources Ethnomathematics ... Student Opportunities Professional Organizations Link Organization ACM Association for Computing Machinery AMS American Mathematical Society AMTNYS Association of Mathematics Teachers of New York State AMTRA Association of Mathematics Teachers of the Rochester Area CAS Casualty Actuarial Society CSHPM Canadian Society for History and Philosophy of Mathematics IEEE The World's Computer Society MAA The Mathematical Association of America NCTM The National Council of Teachers of Mathematics NIST National Institute of Standards and Technology SIAM Society for Industrial and Applied Mathematics SOA Society of Actuaries Art and Mathematics Art and Mathematics: Hop's Gallery Bamdad's Math Comics (List of All Comics) Cartoons Escher art The World of Escher - Artwork Gallery Mathematical Art of M.C. Escher a Platonic Realms Mini-Text Mathematical Knitwear - Wolly Thoughts Sculpture: Helaman Ferguson Sculpture Tessellations - Hop's Gallery Mathematics Atlas: Mathematical Atlas: A gateway to Mathematics Borwein, Peter

50. Fibonacci Facts Facts about the fibonacci Sequence.Category Science Math Specific numbers fibonacci numbers...... Intro. to geometry. New York John Wiley, 1961. Primer for fibonacci numbers PartXIV, MorganVoyce Polynomials. FQ 12.2 (1974) 147-156. VE Hoggatt, Jr,. http://www.cs.rit.edu/~pga/Fibo/fact_sheet.html

Fibonacci Facts INFORMATION SHEET ON FIBONACCI NUMBERS The Fibonacci sequence first appeared as the solution to a problem in the Liber Abaci, a book written in 1202 by Leonardo Fibonacci of Pisa to introduce the Hindu-Arabic numerals used today to a Europe still using cumbersome Roman numerals. The original problem in the Liber Abaci asked how many pairs of rabbits can be generated from a single pair, if each month each mature pair brings forth a new pair, which, from the second month, becomes productive. The resulting Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ..., have been the subject of continuing research, especially by the Fibonacci Association, publisher of the Fibonacci Quarterly since 1963. If Fn is the nth Fibonacci number, then successive terms are formed by addition of the previous two terms, as Fn+1 = Fn + Fn-1, F1 = 1, F2 = 1. The Fibonacci numbers are found to have many relationships to the Golden Ratio F = (1 + /5)/2, a constant of nature and a value which fascinated the ancient Greeks, appearing throughout Greek art and architecture. One can verify with a hand calculator that the ratio of Fn+1 to Fn is approximated by 1.6180339..., which is the decimal equivalent of the Golden Ratio. 1. BOTANY, BIOLOGY. The growth patterns of plants; the geneological tree of the male bee; the crossroads of mathematics and biology.

51. POV-Ray: Resources: Links: 3D Resources: Math And Geometry Resources And Informa This is the Home page for the fibonacci numbers, the Golden section and the Goldenstring. Gallery of Interactive OnLine geometry. geometry Center Welcome Page. http://www.povray.org/resources/links/3D_Resources/Math_and_Geometry_Resources_a

Download Documentation Resources Community ... 3D Resources : Math and Geometry Resources and Information Links "Math and Geometry Resources and Information" sorted by popularity Sort alphabetically Eric Treasure Trove of Math Materials Dictionary of Algorithms, Data Structures, and Problems Compiled originally for the CRC Dictionary of Computer Science, Engineering and Technology. The Stony Brook Algorithm Repository Tracing Ray Differentials Sphere FAQ 3D methods The good - looking - textured - light - sourced - bouncy - fun - smart - and - stretchy - page Dave's Math Tables Computational geometry links page COMPUTER ANIMATION ALGORITHMS AND TECHNIQUES Computer Graphics On-Line Notes UC Davis Math and algorytms Computer Science Papers CiteSeer Pulications is a research paper database. It has PostScript or PDF versions of most of the papers it lists, and there are at least a few hundred research papers on ray tracing listed (try it by typing "ray tracing" in the search field). Fibonacci Numbers... This is the Home page for the Fibonacci numbers, the Golden section and the Golden string. Gallery of Interactive On-Line Geometry Geometry Center Welcome Page Geometry Formulas and Facts Geometry Junkyard This page contains links to pages with geometry related resources. The links are very well commented and there is considerable informaiton available here

52. Global-Investor Bookshop : , numbers 2. Number theoretic Properties of fibonacci numbers 3. fibonacci numbersand Continued Fractions 4. fibonacci numbers and geometry 5. Conclusion. http://books.global-investor.com/books/14911.htm

home about us contact us Search all resources Books Conferences Exam courses Freebies Glossary In-house training Training courses global-investor Books Books Search ... Shopping basket Our reference code: Published by See related Conferences Training courses Exam courses In-house training Email book details to as Text HTML Global-Investor Global-Investor sections Global-Investor Bookshop Glossary Online education Derivatives

53. Global-Investor Bookshop : Fibonacci Ratios With Pattern Recognition, By Larry P ancient geometry. fibonacci numbers are an integral part of the numbersthat make up the subject of ancient geometry. It will be http://books.global-investor.com/pages/book.htm?BookCode=5965

54. ENC: Curriculum Resources: The Fibonacci Numbers And The Golden Section (ENC-011 Other topics include the Golden Ratio, its properties and uses in geometry, andthe Lucas number series, which is closely related to the fibonacci numbers. http://www.enc.org/resources/records/full/0,1240,011674,00.shtm

Skip Navigation You Are Here ENC Home Curriculum Resources Advanced Search ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. The Fibonacci numbers and the Golden Section URL: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html ENC#: ENC-011674 Publisher: Surrey University, School of Electronic Engineering, IT and Mathematics, Department of Computing Date: Grades: 7 8 9 10 11 12 Post-secondary Abstract: This World Wide Web (WWW) site, maintained by the University of Surrey in England, is devoted to looking at the Fibonacci numbers, their properties and occurrences in nature, and related number theory topics. Puzzles with answers involving the Fibonacci numbers and a page with examples of the Fibonacci numbers in art, architecture, and music are included. The site contains illustrations, diagrams, and graphs relating the Fibonacci numbers to branching plants and to family trees for rabbits and bees. Other topics include the Golden Ratio, its properties and uses in geometry, and the Lucas number series, which is closely related to the Fibonacci numbers. There are links to other sites of interest on the Fibonacci numbers and a listing of related books and articles. (Author/JRS) Reviews and Awards: Eisenhower National Clearinghouse. (2002). Increasing Your Mathematics and Science Content Knowledge.

55. ENC: Web Links: Math Topics: Geometry geometry. 5 fibonacci numbers and the Pascal triangle Date 2002 Grade 9 12 ENC 025862 This Internet site presents ten individual pages related to Pascal's http://www.enc.org/weblinks/math/0,1544,1-Geometry,00.shtm

Skip Navigation You Are Here ENC Home Web Links Math Topics Advanced ... Frequently Asked Questions Find detailed information about thousands of materials for K-12 math and science. Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. Math Topics Lists of web sites categorized by subject areas within mathematics. Geometry The Math Forum Internet mathematics library Date: Grade: Kindergarten - 12 ENC#: This Internet site is an annotated catalog of mathematics and mathematics education web sites assembled by the Math Forum. It features hierarchical categories (mathematical topics, resource types, mathematics education topics, and educational levels) ... (For more details see Brief ENC Record or Full ENC Record Math fundamentals problem of the week Date: Grade: Kindergarten - 5 ENC#: This Internet site, developed by the Math Forum, features non-routine problems for students working in the content areas of numbers, operations, and measurement, as well as introductory geometry, data, and probability. The problems are designed to help... (For more details see Brief ENC Record or Full ENC Record Date: Grade: Kindergarten - 8 ENC#: (For more details see Brief ENC Record or Full ENC Record Ask Dr. Math

56. Links s page of www links to other sites on fibonacci numbers and Golden This page containssites relating to fibonacci Sequence and Golden Solar System geometry. http://milan.milanovic.org/math/links/links.html

Link Page PASCAL TRIANGLE Links: Pascal Triangle This Java applet graphically presents the Pascal triangle modulo an integer number p. Developed by Sergey Butkievich, Department of Mathematics, The Ohio State University ... Math Forum web pages on Pascal`s triangle Probably the best place to find out all about Pascal`s triangle ... Pascal`s Triangle and related triangles Contens: Links, Puzzles, Related Triangles, Clown Problem ( Catalan Numbers ), Tchebychev Polynomials, Bessel Polynomials, Stirling numbers ... KryssTal: Pascal`s Triangle Pascal`s Triangle and its uses in probability. The Binomial Theorem used for algebraic expansions and finding roots ... Pascal`s Triangle Image Generator Generate nice pictures with Pascal`s triangle ... Chinese Mathematics: Binomial Theorem and the Pascal Triangle So called ` Pascal ` triangle was known in China as early as 1261. In 1261 the triangle appears to a depth of six in Yang Hui and to a depth of eight in Zhu Shijiei in 1303. Yang Hui attributes the triangle to Jia Xian, who lived in ... New Theory on the Typographical Roots of the Hindu Arabic Numbers and Brahmi Scripts The Hindu Arabic numbering is named for Hindus who appear to have invented it, and the Arabs who transmitted it to the West.The Hindu Arabic 1-2-3-4 numbers are based traces with angles: The number one has one angle.The number two has twoadditives angles. The number three has three aditives angles.The number four has four additive angles. The number four get closed due to cursive hand write....

57. Fibonacci Numbers And The Pascal Triangle in Nature . in geometry . in Art and Architecture . and Continued Fractions . and fibonacci numbers . Others. Show results. Internet Krstarica Jugoslavija. http://milan.milanovic.org/math/index.php

ENGLISH SECTION Blaise Pascal Formulae for Fib(x-n) and Fib(x+2n) Leonardo Fibonacci Fibonacci number calculator ... More... DEUTSCH SECTION Fibonacci zahlen pascalsches zahlendreieck Dezimales System und arithmetisches Dreieck Teilung der lebenden Zelle und Pascalsches Zahlendreieck More... SERBIAN SECTION Decimalni sistem i aritmeticki trougao Paskalov trougao drugog reda Katanalovi brojevi i aritmeticki trougao Fibonacijevi brojevi i Paskalov trougao ... More... Welcome to WWW site Voting ! Your favourite Mathematical Constant is : Golden Section, phi Archimedes` constant, PI Natural logarithmic base, e Euler - Mascheroni constant Others Show results Calculate numbers Choose calculation... Factorial ( Fibonacci number ( Fib. number derivate ( Lucas number ( Lucas number derivate ( Pascal triangle ( Pentagonal number ( PI decimals ( Pyramidal number ( Tetrahedral number ( Triangular number ( Value: document.write(''); Author: Radoslav Jovanovic Milan Milanovic

58. InterMath | Investigations | Algebra | Patterns Section This page discuss applications, real world phenomena, puzzles, patterns,and geometry associated with the fibonacci numbers and golden section. http://www.intermath-uga.gatech.edu/topics/algebra/patterns/r06.htm

Search the Site Investigations Algebra Patterns ... Recommended Investigations Choose two whole numbers (number one and number two). Add them together and form a Fibonacci-like sequence (add number one and number two together to get number three, then add number two and number three together to get number four, etc.). End with a total of ten numbers. Repeat the process by starting with two different numbers. What is the relationship between the seventh term and the sum of the terms (for each sequence)? What is the relationship between the seventh term and the tenth term (for each sequence)? Explain. Extensions Would your result be different if you started with negative numbers or fractions? Related External Resources Fibonacci Numbers and the Golden Section This page discuss applications, real world phenomena, puzzles, patterns, and geometry associated with the Fibonacci numbers and golden section. [ web page ] http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html Fibonacci Online Assessment Take a multiple choice quiz that tests your knowledge about Fibonacci, the Fibonacci sequence, and the golden ratio. [ web page ] http://wyvern.school.hants.gov.uk/forms/fibass.htm

59. InterMath | Investigations | Algebra | Patterns | Additional Investigations TH fibonacci Fun Fascinating Activities with Intriguing numbers. Johnson, A. Now Then Fiber Meets fibonacci. Sacred geometry Philosophy and Practice. http://www.intermath-uga.gatech.edu/topics/algebra/patterns/links.htm

Search the Site Investigations Algebra Patterns External Resources Applications and Connections Fibonacci numbers and nature Fabulous Fibonacci phenomena Fibonacci tree and the golden ratio Practical uses for Pascal's triangle ... Patterns and symmetry in oriental carpets Lessons, Activities, and Units Applications The art of oriental carpets Mirror symmetry Fractals Fractals lesson by Cynthia Lanius Create your own fractal The fractory Fractals- Pascal's triangle Fibonacci's Sequence Fibonacci in nature Fibonacci online assessment Lecture notes Golden ratio ... The Fibonacci numbers, pineapples, sunflowers and the golden mean Series and Partial Sums Sum of numbers from 1 to 100 Gauss Tessellations Tessellation tutorials Totally tessellated Tantalizing tessellations Pascal's Triangle: Word problems, color configurations, and patterns The twelve days of Christmas Fractals Probability ... Visual patterns Literature Book titles related to Fibonacci numbers Chaitin, Gregory J. 1988. Randomness in arithmetic. Scientific American (July):80-85. Exploring Patterns Fibonacci Quarterly Gardner, Martin. 1989. Pascal's triangle. In Mathematical Carnival. Washington, D.C.: Mathematical Association of America.

60. Mathematics Links Golden Mean 3 Another investigation of the algebra and geometry of the The fibonaccinumbers The fibonacci numbers and Golden section in Nature An interesting http://www.msad51.org/GHS/mathlinks.html

athematics inks Curves Golden Mean Fractals Number Theory ... Geometer's Sketchpad Return to Mathematics athematical urves Famous Curves Applet Index Use Java applets to experiment with the graphs of different curves Xah: Visual Dictionary of Special Plane Curves A visual dictionary of special plane curves Famous Curves Index Witch of Agnesi A really nice discussion of this special parametric curve. Witch of Agnesi A gif animation of the curve known as the Witch of Agnesi. Return to Mathematics Links olden ean The Golden Mean, Rectangle, ... The Golden Mean #1 A nice summary of the golden ratio and its derivation. The Golden Mean #2 Some "golden geometry", Penrose tilings, and Golden Spiral. The Golden Mean #3 Another investigation of the algebra and geometry of the Golden Mean. The Golden Section Constructing the Golden Section The Golden Rectangle Constructing the Golden Rectangle and Golden Spiral The Golden Rectangle Animated Animations illustrating the Golden Rectangle and Golden Spiral The Fibonacci Numbers The Fibonacci Numbers and Golden section in Nature An interesting and well illustrated site investigating the occurrance of the golden ratio in nature.

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