[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-48701-en":3,"doc-seo-48701-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},48701,687197207639,"Asher","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","The Fascinating Fibonaccis","An educational overview of how number patterns are formed and interpreted, starting with simple sequences based on adding or subtracting a fixed value. It then demonstrates a more complex growing-difference pattern, converting a number pattern into a triangle “shape pattern” built from dot counts. The guide introduces the Fibonacci (Hemachandra) sequence and explains that each term equals the sum of the previous two, connecting Fibonacci numbers to flower petal counts observed in nature.","The Fascinating Fibonaccis Shonali Chinniah  \nHari Kumar Nair  \nNumbers. We use them everyday. To count, measure, call friends on the phone and even to find out what something costs.  \nBut did you know you can also use numbers to create patterns-geometrical shapes, rangoli designs, and more? Did you know number patterns can be seen within patterns in nature?  \nBut first, what is a ’Number Pattern’?  \nA Number Pattern is a sequence of numbers where each number is connected to the previous one in ONE specific way.  \nTake this very simple number pattern: 0, 1, 2, 3, 4 . .. How is each number in this sequence connected to the one before it? Well, every number in this sequence is the previous number with 1 ADDED to it.  \nHere’s another number pattern: 14 ,12 ,10  \n,8, 6. .. Each number in this sequence is the previous number with 2 SUBTRACTED from it.  \nNow for a slightly more tricky pattern: 0, 1, 3, 6, 10 ,15 ...  \nHow does this sequence work? Let’s see .  \n0 + 1 = 1  \n1 + 2 = 3  \n3 + 3 = 6  \n6 + 4 = 10  \n10 + 5 = 15  \nDo you see the pattern here? What will the next number in this sequence be?  \nYes, 21 , because 15 + 6 = 21 .  \nNow, let’s take the ’number pattern’ we just discussed: 1, 3, 6, 10 ,15 ... , and see if we can create a ’SHAPE pattern’ from it.  \nWe can! We now have a ’shape pattern’ of triangles that get bigger and bigger as we increase the number of dots according to our number pattern!  \nA number pattern has become a shape pattern!  \nIf you found that interesting,  \nit’s time you were introduced to a beautiful number sequence called the Fibonacci (or Hemachandra) Sequence of numbers. The Fibonacci Sequence of numbers goes like this:  \n0, 1, 1, 2, 3, 5, 8, 13 ,21 ,34 ...  \nCan you find the pattern that connects these numbers? Yes! Every number in the Fibonacci Sequence is the sum of the two numbers  \nbefore it! Like this.  \n0+ 1 = 1  \n1+ 1 = 2  \n2+ 1 = 3  \n3+ 2 = 5  \n5+ 3 = 8  \n8+ 5 = 13  \n13 +8 = 21  \n21 +13 = 34  \nGot it? Good. Now for the REALLY interesting part-linking this number pattern to patterns in nature .  \nThe number of petals flowers have are often linked to Fibonacci numbers!  \nCan you think of flowers with 1, 3 and 5 petals? (These are all Fibonacci numbers.) Here are some examples to help you along.  \n1 petal-1. Anthurium; 2. Calla lilies  \n3 petals-2. Bougainvillea; 3. Clovers  \n5 petals-4. Temple tree; 5. Hibiscus; 6. Jasmine","cbCaienuobaPJoly","https://ap.wps.com/l/cbCaienuobaPJoly","pdf",1050177,2,1,30,"English","en",105,"# Number Patterns\n## From Sequences to Shapes\n# Fibonacci (Hemachandra) Sequence\n## Pattern Rule\n## Fibonacci in Nature: Flower Petals","[{\"question\":\"What is a number pattern, according to the text?\",\"answer\":\"A number pattern is a sequence where each number is connected to the previous one in one specific way.\"},{\"question\":\"How does the text define the Fibonacci sequence?\",\"answer\":\"Each number in the Fibonacci sequence equals the sum of the two numbers before it.\"},{\"question\":\"How are Fibonacci numbers connected to patterns in nature?\",\"answer\":\"The text links Fibonacci numbers to the number of flower petals, noting examples such as flowers with 1, 3, or 5 petals.\"}]",1783570494,76,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"the-fascinating-fibonaccis","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/the-fascinating-fibonaccis/48701/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-18","2026-07-09",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is a number pattern, according to the text?","Question",{"text":75,"@type":76},"A number pattern is a sequence where each number is connected to the previous one in one specific way.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the text define the Fibonacci sequence?",{"text":80,"@type":76},"Each number in the Fibonacci sequence equals the sum of the two numbers before it.",{"name":82,"@type":73,"acceptedAnswer":83},"How are Fibonacci numbers connected to patterns in nature?",{"text":84,"@type":76},"The text links Fibonacci numbers to the number of flower petals, noting examples such as flowers with 1, 3, or 5 petals.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,122,127,130,134],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":22,"slug":121},"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]