The Fibonacci Sequence of Pineapples

THE FIBONACCI SEQUENCE OF PINEAPPLES (Ananas Cumusus)

A Research Paper

Presented to the Faculty of the Mathematics Department

Ilocos Sur National High School

Vigan City

In Partial Fulfillment of the Requirements

 For the Subject Mathematics Research

Thrisha Ahnn Arquelada

Mika Ella Joy Gaoat

Airen Franz Inong

Christelbert Rafael

Ericka Joy Tano

2016-2017

CHAPTER I

INTRODUCTION

BACKGROUND OF THE STUDY

        The pineapple (Ananas comosus) is a tropical plant with edible multiple fruit consisting of coalesced berries, also called pineapples, and the most economically significant plant in the Bromeliaceae family.

Pineapples may be cultivated from a crown cutting of the fruit, possibly flowering in 20–24 months and fruiting in the following six months. Pineapples do not ripen significantly post-harvest.

Pineapples can be consumed fresh, cooked, juiced, or preserved. They are found in a wide array of cuisines. In addition to consumption, the pineapple leaves are used to produce the textile fiber piña in the Philippines, commonly used as the material for the men's Barong Tagalog and women's Baro't saya formal wear in the country. The fiber is also used as a component for wallpaper and other furnishings.

The pineapple is a herbaceous perennial, which grows to 1.0 to 1.5 meters (3.3 to 4.9 ft) tall, although sometimes it can be taller. In appearance, the plant has a short, stocky stem with tough, waxy leaves. When creating its fruit, it usually produces up to 200 flowers, although some large-fruited cultivars can exceed this. Once it flowers, the individual fruits of the flowers join together to create what is commonly referred to as a pineapple. After the first fruit is produced, side shoots (called 'suckers' by commercial growers) are produced in the leaf axils of the main stem. These may be removed for propagation, or left to produce additional fruits on the original plant.Commercially, suckers that appear around the base are cultivated. It has 30 or more long, narrow, fleshy, trough-shaped leaves with sharp spines along the margins that are 30 to 100 centimeters (1.0 to 3.3 ft) long, surrounding a thick stem. In the first year of growth, the axis lengthens and thickens, bearing numerous leaves in close spirals. After 12 to 20 months, the stem grows into a spike-like inflorescence up to 15 cm (6 in) long with over 100 spirally arranged, trimerous flowers, each subtended by a bract. Flower colors vary, depending on variety, from lavender, through light purple to red.

Typically pineapples are very common in Ilocos Sur during the month of June to September. Mainly, it is used for consumption.

The objective of this study is to see if the number of bud per diagonal in a pineapple manifest Fibonacci Sequence.

The researchers would like to apply their lesson in Mathematics 10, The Fibonacci Sequence.

STATEMENT OF THE PROBLEM

        This study aims to discover the Fibonacci sequence of Pineapples. Specifically, it sought to answer the following questions:

1. What is the number of buds per diagonal and per layer in a pineapple fruit?
2. Are the pattern of the pineapple’s buds manifest a Fibonacci Sequence?

SIGNIFICANCE OF THE STUDY

        Pineapple is a healthy fruit that may provide minerals and vitamins for our body. We love to it this fruit because it is delicious but we have no idea that this fruit has a pattern called the Fibonacci Sequence

        This study aims to discover the Fibonacci Sequence of  Pineapple buds.

CONCEPTUAL FRAMEWORK

            INPUT                                                PROCESS                                                OUTPUT[pic 1][pic 2][pic 3]

[pic 4][pic 5]

Figure 1: Research Paradigm

HYPOTHESIS

        There is a Fibonacci sequence exhibited by the number of buds per diagonal in a Pineapple.

SCOPE AND DELIMITATION

        This study was delimited in the Fibonacci sequence of a pineapple by studying the pattern of the buds per diagonal. This study was conducted at San Pablo, Sto. Domingo, Ilocos Sur from August to September 2016.

DEFINITIONS OF TERMS

Fibonacci Sequence - a series of numbers in which each number is the sum of the two preceding numbers. 

Buds -  a small swelling on a branch or stem, containing an undeveloped shoot, leaf, or flower.

Pattern – it is an arrangement of lines and shapes, especially a design in which the shape is repeated at regular intervals over a surface.

Pineaapple -  is the common name for low-growing, fruit-bearing, tropical plants of the species Ananas comosus in the bromeliad family 

Diagonal - the set of elements of a matrix that lie on a line joining two opposite corners.

CHAPTER II

REVIEW OF RELATED LITERATURE

[pic 6]

The pineapple (Ananas comosus) is a tropical plant with edible multiple fruit consisting of coalesced berries, also called pineapples, and the most economically significant plant in the Bromeliaceae family. Pineapples may be cultivated from a crown cutting of the fruit,[2][5] possibly flowering in 5-10 months and fruiting in the following six months.[5][6] Pineapples do not ripen significantly after harvest.