...MATHEMATICS BEHIND FLOWER PETALS Have you ever observed a flower from the mathematical point of view? Have you ever given a thought on why flowers are aesthetically appealing? In nearly all the flowers, the number of petals is one of the numbers that occur in the strange sequence 1, 2,3,5,8, 13, 21, 34, 55, 89, 144. They form the beginning of the so-called Fibonacci series, in which each number is the sum of the two that precedes. In order to verify this, we collected 30 different samples of flowers from Somaiya Vidyavihar Campus and counted the number of petals present in each flower. These data were then added to excel from which we observed that 60% of the 30 samples of flowers considered had petal counts in the above Fibonacci sequence. No of flowers | Fibonacci | Non Fibonacci | 30 | 18 | 12 | Proportion | .6 | .4 | Z value | 1.09 | | P value | .1366>.05 | Null acceptance | As we can see the above table, the p value is greater than .05, (level of significance) the alternate hypothesis that the number of petals in flowers follows Fibonacci series is not conclusively proved. However even the proportion of 0.65 would have proved the Fibonacci hypothesis. We feel that sample size of 30 is insufficient. GOLDEN RATIO What is it exactly? Think of any two numbers. Make a third by adding the first and second, a fourth by adding the second and third, and so on. When you have written down about 20 numbers, calculate the ratio of the last to the second from last...
Words: 593 - Pages: 3
...PROBLEM Are red flowers really red? Two students were having an argument about pigments in red flower. One said that red petals can only contain the red color, whereas the other students thought that the red color could actually be a mixture of color. Plan an experiment to investigate if the pigment in red flowers consists of one or more colors. In your investigation think about how you can extract the pigment and check whether it consists of one or more color. PLAN FOR INVESTIGATION A. Purpose of the Investigation The purpose of this investigation is to know whether the pigment in red flowers consist one or more colors. The goal of this experiment is to analyze the pigments found in flowers using paper chromatography. B. Materials/ Apparatus The materials used in this experiment include filter paper, scissors, pencil, ruler, clean jar or drinking glass, large- mouth glass jar, water (at least 60 mL, distilled water is preferable, but tap water is also suitable), 70% isopropyl alcohol, measuring cup, piece of scratch paper, coin, timer or clock, and of course red flower petals. You will need at least 2 flower petals from at least 3 different plants. Tip: Larger petals work better than smaller petals. C. Steps/ Procedure Cut the chromatography filter paper into strips that are about 2 cm wide and as long as the large-mouth glass is tall (the strips should all be the same size). You will want to make at least three strips for each flower you want to investigate...
Words: 2026 - Pages: 9
...previous numbers of pairs in the sequence. The Fibonacci numbers or, sequences as you may call it was named after an Italian mathematician Fibonacci and was first introduced to Western European society in his 1202 book Liber Abaci. In mathematics, the Fibonacci sequence are the pattern of sequences (as you can see in these two sequences) that always start with numbers 1 and 1, or 0 and 1. 1,1,2,3,5,8,13,21,34,55,89,144 or 0,1,1,2,3,5,8,13,21,34,55,89,144 Although many people are not aware of it, Fibonacci numbers appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. And here are some of the famous examples. 1. Flower petal The number of petals in a flower consistently follows the Fibonacci sequence. The lily, which has three petals, buttercups, which have five, the chicory's 21, the daisy's 34, and so on. 2. Pinecones Pinecones are another great example. The seed pods on a pinecone are arranged in a spiral pattern and each cone consists of a pair of spirals, each one spiraling upwards in opposing directions. 3. Tree Branches The Fibonacci sequence can also be seen in the way tree branches form or split. A main trunk of a tree grows until it produces a branch, which creates two...
Words: 367 - Pages: 2
...“great spiritual heroes, the bodhisattvas, and the great disciples with heavenly flowers.”(Pg.58) “When the flowers fell on the bodies of the bodhisattvas, they fell off on the floor, but when they fell on the bodies of the great disciples, they stuck to them and did not fall.”(Pg.58) After debate between Sariputra and the goddess and whether or not the flowers were appropriate for religious purposes, the goddess tells Sariputra that “such flowers have neither constructual thought nor discrimination. But the elder Sariputra has both constructual thought and discrimination”(Pg.59) Sariputra suffers from distractions which is conventional truth. Instead, he should focus on no-distractions and live with the idea of highest truth. The same ideas of the two-fold truth run together between the idea of form and distractions and emptiness and no distractions. “Thus, these flowers stick to the bodies of those who have not eliminated their instincts for the passions’ and do not stick to the bodies of those who have eliminated their instincts.” (Pg.59) The bodhisattvas have eliminated the idea of distractions from their life and focus on non-distractions. This is an alternative to the idea of form and emptiness. Without distractions in life, one would be emotionally and physically empty which is the main emphasis of Buddhism. Sariputra was given the test of dealing with distractions in the form of flower petals. By not having constructual thoughts and discriminations, one has no distractions...
Words: 950 - Pages: 4
...are borne alternately on the stem. In most species they are 5 to 15 centimetres (2.0 to 5.9 in) long, pinnate, with (3–) 5–9 (–13) leaflets and basal stipules; the leaflets usually have a serrated margin, and often a few small prickles on the underside of the stem. Most roses are deciduous but a few (particularly from South east Asia) are evergreen or nearly so. The hybrid garden rose "Amber Flush" The flowers of most species have five petals, with the exception of Rosa sericea, which usually has only four. Each petal is divided into two distinct lobes and is usually white or pink, though in a few species yellow or red. Beneath the petals are five sepals (or in the case of some Rosa sericea, four). These may be long enough to be visible when viewed from above and appear as green points alternating with the rounded petals. There are multiple superior ovaries that develop into achenes.[4] Roses are insect-pollinated in nature. The aggregate fruit of the rose is a berry-like structure called a rose hip. Many of the domestic cultivars do not produce hips, as the flowers are so tightly petalled that they do not provide access for pollination. The hips of most species are red, but a few (e.g. Rosa pimpinellifolia) have dark purple to black hips. Each hip comprises an outer fleshy layer, the hypanthium, which contains 5–160 "seeds" (technically dry single-seeded fruits called achenes) embedded in a matrix of fine, but stiff, hairs. Rose hips of some species, especially the dog...
Words: 481 - Pages: 2
...significant correlation between the management of an area and percentage cover of buttercups. Alternate Hypothesis (H1): There is a significant correlation between the management of an area and percentage cover of buttercups. Background information The Buttercups are considered to be simple because the floral parts of the plant: petals, sepals, stamens and pistils-are all of an indefinite number and separate from one another. Also, the stamens and pistils are spirally inserted in a cone-like vessel, although it is often very small to see. Buttercups can have either regular or irregular flowers with anywhere from 3 to 15 sepals, often coloured like petals, and 0 to 23 actual petals.[2] There are often, but not always, numerous stamens and numerous simple pistils (also known as apocarpous). The floral parts are all independently attached below a superior ovary. Figure 1 The most accurate pattern to look for is the multiple simple pistils at the centre of the flower. In more advanced plant families there is typically only one pistil, the result of a reduction in numbers along with the fusion of several pistils to make a single compound pistil. A flower with multiple pistils is very likely a Buttercup, but could potentially be confused with species from the Rose subfamily of the Rose Family. A secondary pattern that is often easier to see, but not as consistent, is the hooked tips on the pistils. If you are not sure if you are looking at several separate pistils or some that are...
Words: 1853 - Pages: 8
...of flowering plants, how they function, and how they respond to the environment. 1. FLOWERS, SEEDS, and FRUITS -Some flowers are large and showy. Some are small. Even though flowers look different, they have the SAME FUNCTIONS. Flowers are the structures of sexual reproduction in angiosperms. RECEPTACLE-enlarged end of the stem under the flower. SEPALS-Circle of green leaf-like parts found around the bottom of the flower. They cover and protect the developing bud. PETALS-is found inside the sepals. These are usually the bright colored parts you see in flowers. Petals surround the reproductive parts of the flower. STAMENS-slender structures with knobs on top are near the middle of the flower. The slender parts are the FILAMENTS and the knobs are the ANTHERS. The tall, vase like part in the middle of the flower are called the PISTIL. Notice the sticky stigma is supported by the STYLE. At the base of the pistil is the OVARY. Inside the ovary are one or more ovules. An egg is produced inside each ovule. PERFECT FLOWERS-have both stamens and a pistil. IMPERFECT FLOWERS-have either stamens or a pistil, but not both. HOW SEEDS AND FRUITS DEVELOP For seeds to form in Angiosperms, a pollen grain should be transferred from an Anther to a Stigma. Stigma helps trap the pollen. Recall chapter 11. When a seed begins to form, a flower changes in many ways. The flower’s petals and stamens wither and fall off. SEED COAT-it protects the embryo from drying out. As...
Words: 1293 - Pages: 6
...THE ASSESMENT OF THE ACCEPTABILITY OF ROSE ICE CREAM CHAPTER 1 INTRODUCTION Considering the vast food source of the country, the people are properly informed about the various available aromatic flowers particularly the native and popular flower like Rose, Sampaguita, etc… The Filipino are indeed very lucky because the Philippines is blessed with different kind of flowers that gives us medicine, food, perfume and other that provide our needs and that has been concerned people in our country. Rose ice cream is creamy, soft and velvety like fragrant bouquet of rose. Luscious summer with fresh rose petals. Ice cream (derived from earlier iced cream or cream ice) is a frozen food usually made from dairy products, such as milk and cream and often combined with fruits or other ingredients and flavors. Most varieties contain sugar, although some are made with other sweeteners. In some cases, artificial flavorings and colorings are used in addition to, or instead of, the natural ingredients. The mixture of chosen ingredients is stirred slowly while cooling, in order to incorporate air and to prevent large ice crystals from forming. The result is smoothly textured semi-solid foam that is malleable and can be scooped. (www. Wikipedia.com). No single person can lay claim to inventing ice cream. There is no exact origin or date of inception, but myths abound on how it came about. Its existence in olden times...
Words: 2457 - Pages: 10
...FOOD from the SUN HOW PLANTS LIVE AND GROW LIFESCIENCE © 2008 Rourke Publishing LLC All rights reserved. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical including photocopying, recording, or by any information storage and retrieval system without permission in writing from the publisher. www.rourkepublishing.com PHOTO CREDITS: p. 17: Sally Bensusen/Science Photo Library; p. 26: Jonathan S. Blair/ Getty Images; p. 33: Vera Bogaerts/istockphoto.com; p. 27, 34: Nigel Cattlin/FLPA; p. 4: Elena Elisseeva/istockphoto.com; pp. title page, 19, 36: Chris Fairclough/CFWImages.com; p. 13 both: Chris Fairclough/Discovery Picture Library; p. 30: Foto Natura Stock/FLPA; p. 39: Joe Gough/istockphoto.com; p. 10: Paul Gsell/istockphoto.com; p. 8, 15, 41: istockphoto.com; p. 16: Silvia Jansen/istockphoto.com; p. 21: Chee-Onn Leong/ istockphoto.com; p. 9: Brenda McEwan/istockphoto.com; p. 29: Dave Michaels/Corbis; p. 38: Neil Nathan/istockphoto.com; p. 12: David Nunuk/Science Photo Library; pp. 42, 43: Ed Parker/EASI-Images/CFWImages.com; p. 31: Susanna Pershern/istockphoto.com; p. 23, both, 24: Photodisc; p. 7: Corey Rich/Aurora/Getty Images; p. 37: Rey Rojo/ CFWImages.com; pp. 34, 35 bottom: Malcolm Romain/istockphoto.com; p. 35 top: Yali Shi/ istockphoto.com; p. 18: Stephen Strathdee/istockphoto.com; p. 25: Herbert Zetti/Zefa/Corbis. Cover picture shows the early green shoots of a plant. [istockphoto.com] Produced...
Words: 11210 - Pages: 45
...variety of materials. You can approach Rangoli as an advanced art project for an experienced artist, or modify it for a fun activity with kids. This tradition is made using materials such as colored rice, dry flour, colored sand, beads, or flower petals. Urja Vaidya only used acrylic paint in her design. Rangoli designs can be simple geometric shapes, deity impressions, or flower petal shapes; depends on the given celebration. Traditionally, Rangoli is made on a square grid in North India and on a hexagonal grid in South India while Onam Rangolis are typically circular. Due to rapid and widespread migration and mixing of people these styles are now freely adopted and mixed. The purpose of rangoli is decoration, and it is thought to bring good luck. Design depictions may also vary as they reflect traditions, folklore and practices that are unique to each area. It is traditionally done by women. Generally, this practice is showcased during occasions such as festivals, auspicious observances, marriage celebrations and other similar milestones and gatherings. Rangoli is made in two ways. Dry and wet. The rangoli made by adding points to the first white paint on the ground in a particular size are made certain point then shaking the points is a beautiful figure takes shape. After creating the desired shape, there are full color. Although the basic color of rangoli is white, it is dyed different colors creating an attractive, multi-colored...
Words: 316 - Pages: 2
...a whole different level. They envision something, and act upon it, creating something that not everyone could successfully pull off. Every single work of art was unique in it’s own way, but one of the piece managed to truly catch my eye. The title of the work was inflorescence by Bhakti Baxter, which was created back in 2006. The name actually fits this work of art very well, which I found to be rather humorous. Sometimes a name of an art piece can have no relation to what it actually displays, as opposed to those which just state what they want you to see. Inflorescence, by definition, means the complete flower head of a plant, or the arrangement of the flowers on a plant. That is exactly what this looked like, just the top and main part of the flower. Start by picturing this beautiful pink lotus flower, but then start to picture it has a hard and solid object, each petal having it’s own defining shape, and having every line lead back towards the center. Then imagine it being the purest of them all and literally...
Words: 562 - Pages: 3
...Historical Places in Pakistan Minar-e-Pakistan Minar-e-Pakistan (or Yadgaar-ePakistan) is a tall minaret in Iqbal Park Lahore, built in honor of the Lahore Resolution. It reflects a blend of Mughal and modern architecture, and is constructed on the site where on March 23, 1940, Lahore Resolution (Qarardad-e-Lahore) demanding the creation of Pakistan. It was seven years before the formation of Pakistan. The large public space around the monument is commonly used for political and public meetings, whereas Iqbal Park area is ever so popular among kite-flyers. The tower rises about 60 meters on the base, thus the total height of minaret is about 62 meters above the ground. The unfolding petals of the flower-like base are 9 meters high. The diameter of the tower is about 97.5 meters (320 feet). Badshahi Mosque The Badshahi Mosque (Urdu: ,)ﺑﺎدﺷﺎھﯽ ﻣﺴﺠﺪor the 'Emperor's Mosque', was built in 1673 by the Mughal Emperor Aurangzeb in Lahore. It is one of the city's best known landmarks, and a major tourist attraction and characterizes the beauty and greatness of the Mughal era. Capable of accommodating over 55,000 worshipers. It is the second largest mosque in Pakistan, after the Faisal Mosque in Islamabad. The architecture and design of the Badshahi Masjid is closely related to the Jama Masjid in Delhi, India, which was built in 1648 by Aurangzeb's father and predecessor, Emperor Shah Jahan. The Imam-e-Kaaba (Sheikh Abdur-Rahman...
Words: 635 - Pages: 3
...attar ATTAR GENERAL INFO : Attar (Arabic: عطر) also known as ittar is a natural perfume oil derived from botanical sources. Most commonly these oils are taken from the botanical material through hydro or steam distillation. Oils can also be expressed by chemical means but generally natural perfumes which qualify as Ittar/Attars are distilled naturally. The oils obtained from the herbs flowers and wood are generally distilled into a wood base such as sandalwood and then aged. The aging period can last from one to ten years depending on the botanicals used and the results desired. These all-natural perfumes are highly concentrated and therefore are usually offered for sale in small quantities and have traditionally been offered in decorated crystal cut type bottles or small jeweled decanters. Ittars are popular throughout the Middle East and the Far East of India as well as Bangladesh and Pakistan. Ittars have been used in the entire Eastern world for thousands of years. These 100% pure and natural perfumes are free of alcohol and chemicals and so the problems faced in the West by perfume lovers are irrelevant to most Eastern perfume lovers. Natural perfumes are affordable because they are so concentrated that a small bottle will last the user several weeks, if not months. Some of the first lovers of Ittars were the Mughal nobles of...
Words: 2461 - Pages: 10
...I will be covering are the technologies used, symbols, language, as well as values and norms. The two movies that I will compare are Frank Capra’s 1946 movie, “It’s A Wonderful Life” and “A Christmas List” from 2016. “It’s A Wonderful Life” stars Jimmy Stewart as George Bailey, who is the nicest guy in the small town of Bedford Falls. George longs for travel and adventure and spends much of his life with things not going the way he plans. The film opens with George at his lowest point as he is facing scandal and prison, which has him contemplating suicide. Nothing has seemed to work out for George since he gave up his dream of traveling the world to...
Words: 1403 - Pages: 6
...gardening, and all of the flowers are red roses. Even before this happens in the movie, Lester tells the audience that in a year, he’ll be dead. So we already know this movie is about Lester, his life, and then his death. With the shot pulled...
Words: 2439 - Pages: 10