MATHEMATICS IN NATURE

Petal Numbers

Count the number of petals on flowers in your backyard, out in the country, or in a picture book. You’ll find that the number five keeps coming up. Hibiscus, periwinkle, Jasmine all have five petals.

You may also find flowers with 3 petals, and others with 8, 13, or even 21 petals. But it’s harder to find flowers with 4, 6, 7, or 10 petals (unless some have been nibbled).

Is there something special about the numbers 3, 5, 8, 13, and 21? As a matter of fact, there is. 

To see that, start with 1. 

Then add 1 + 1 = 2. 

Keep doing this, and you get a pattern:

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

3 + 5 = 8

5 + 8 = 13

8 + 13 = 21, and so on. 

This set of numbers, 1, 1, 2, 3, 5, 8, 13, 21, 34, … goes on to infinity. They are called Fibonacci numbers, after the mathematician who made them famous.

Fibonacci numbers show up all over nature: in the spirals of pinecones and pineapples, in the swirls of snail shells, in flowers and leaves. 

Why? It might have something to do with how plants and other living things grow, but no one knows for sure. 

THE ACCLAIMED ANIMATION HOUSE

Walt Disney Company

Who does not love a good Disney animation? With characters ranging from Mickey Mouse to Rapunzel to Mirabel in Encanto, Disney has got something to satisfy everyone's palate. Named after its titular co-founder Walt Disney, the company has revolutionized the genre of animation. So much so that the term animation has become synonymous with Disney for millions the world over. 

Now, let us take a brief dive into the origin and evolution of Disney:

The Beginnings: Known officially as the Walt Disney Company, Disney was established on 16 October, 1923. The company was founded by Walt Disney and his brother, Roy Disney. It was first named the Disney Brothers Cartoon Studio. The studio was located in California, USA. 

In 1928, Disney introduced Mickey Mouse in a short film titled, 'Steamboat Willie'. The film was also the first of its kind to feature synchronized sound. Mickey went on to become a huge sensation, popularizing the young animation studio and revolutionizing the animated film industry. Mickey Mouse later became the mascot of the company.

A turning point in Disney’s history happened with the release of ‘Snow White and the Seven Dwarfs’; the company’s first feature length animation film. The movie was released in 1937. A roaring success, this movie further cemented Disney as an authority in animation and imagination. 

Disney after War: Post Second World War (1939-1945), Disney became more successful and produced several more animated feature films. It also diversified into live-action films, television cartoons and theme parks in the 1950s.

In 1961, Disney released ‘101 Dalmatians’, which was another pivotal moment in the history of the company. The film made use of a new and improved type of animation technology known as Xerox animation. The technology made it possible for animators to transfer their drawings directly to animation cells, instead of tracing them by hand. Thus, the process of animation became much faster and smoother. 

The Dark Ages: The 1970s-1980s are known as the Dark Ages in the history of Disney Animations. The studio suffered a decline and most of the films produced were not commercial successes. ‘The Aristocats’ and ‘The Fox and the Hound’ are some examples of films released during the dark ages.

The Renaissance: The term renaissance means a ‘comeback’. Thus, after a time of steep decline, Disney bounced back during its Renaissance. This period began in 1989 with the release of the feature film, ‘The Little Mermaid’. A huge sensation, the film helped Disney regain its foothold as the dominant force in animation. Disney continued its success streak with several other features during this period. A few notable examples are: ‘Beauty and the Beast’, ‘The Lion King’, ‘Aladdin’ and ‘Mulan’.

Disney after Renaissance: Post renaissance, Disney went through a period of transition in the 1990s and 2000s. And from 2010 onwards, Disney experienced yet another resurgence, commonly known as the ‘Disney Revival’. 

The Revival Era started with the release of ‘Tangled’ in 2010. Several successful films like ‘Frozen’, ‘Big Hero 6’, ‘Zootopia’ and ‘Moana’ followed the release of ‘Tangled’. 

A major factor that distinguishes successful animation production companies, particularly Disney, is their focus not only on good illustrations and a captivating story, but also their close attention to details.

Disney after Revival: Post Revival, Disney continues to release smashing hits in animation, much to the joy of animation lovers worldwide. In 2021, Disney released widely acclaimed films like ‘Raya and the Last Dragon’ and ‘Encanto’. In 2022, Disney released critically successful films like ‘Turning Red’.

With its impeccable designs and beautiful storylines, Disney remains one of the most popular animation houses in the world. The many fictional characters created by Disney, including Mickey Mouse, Minnie Mouse, Donald Duck, Goofy, Cinderella, Rapunzel, etc., mesmerize as well as remain ever loved and etched in the minds of children the world over. Moreover, the magical worlds created by Disney are always an exceptional source of great joy and fun for kids everywhere. Even adults find refuge in the comforting magic of Disney. And thus, the legacy of Disney animations continues to shine brightly through the ages.

Do You Know?

● The original Disney logo featured Mickey Mouse. In 1928, Walt Disney created a mouse character, replacing Oswald the Lucky Rabbit. 

● Dumbo is the shortest feature length film made by Disney. The film is only 64 minutes long.

● The first movie to release a soundtrack was Snow White and the Seven Dwarfs.

● Since its inception, Disney has won 135 Academy Awards, the most by any organization.

● The first truly original Disney story was of The Lion King. The movies that came before were adaptations.

● In The Lion King, hyenas were portrayed as villains. A hyena biologist sued Disney for doing.

FATHER OF SURGERY

Sushruta 

The Golden Age of Surgery in ancient India rests largely on the accomplishments of Sushruta, who is supposed to have lived sometime around the 4th Century CE in the ancient city of Benaras, located on the banks of the river Ganges. His monumental treatise on Surgery, Sushruta Samhitaa, established him as the Father of Indian Surgery. He was the first surgeon to systematise surgery by dividing it into separate fields. He is known as the originator of plastic surgery, cataract operation, laparotomy and vesical lithotomy. He also explicitly described diabetes. Sushruta’s identity may be lost in the mists of the past but the tradition that he so comprehensively contributed to, remains clear and expansive in its exposition of ancient surgical methods in India.

Sushruta was the first to classify surgical operations. He was both a practitioner and a teacher of surgery. His contribution to the medical heritage of not just India but the World is invaluable.

Sushruta divides his Samhita into 120 chapters and six parts, covering all the branches of medicine, including hygiene, midwifery, ophthalmology, toxicology and psychosomatic ailments. Sushruta considers surgery the first and foremost branch of medicine and states: “Surgery has the superior advantage of producing instantaneous effects by means of surgical instruments and appliances. Hence, it is the highest in value of all the medical tantras. It is eternal and a source of infinite piety, imports fame and opens the gates of Heaven to its votaries. It prolongs the duration of human existence on earth and helps men in successfully fulfilling their missions and earning a decent competence in life.” He describes eight different operations for surgery like cutting, opening, scratching, piercing, inserting etc, and finally stitching up the wound.

The fullness of the wisdom and skill of Sushruta can be best comprehended not through the fragmentary evidence of his life but by exploring the details of the text itself. In order to initiate this exploration it would be worth briefly viewing some features of this Samhitaa. For example, Sushruta has explained the technique of “yogyaa”, which means practicing the use of surgical equipments on non-human subjects like different fruits and vegetables (such as jackfruit, pumpkin and cucumber), dead animals and artificial limbs created from wood and wax. This gives the practitioner mastery over surgical tools in order to prepare him to apply his skills on actual human beings. He believes that it is also necessary for a surgeon to have a thorough knowledge of internal organs. A corpse kept in flowing water for fifteen to thirty days is given to the disciples for dissection. Without the knowledge of Anatomy, it is impossible to become a good surgeon.

In addition to this, Sushruta also refers to the basic precautions to be taken to avoid infection during surgery. To make sure that this is so, it is suggested that the operation be conducted away from the human settlement, in a safe and clean environment where plenty of water is available. The text goes on to explain that surgical equipment should be cleaned and disinfected with the fumes of specific medicinal plants.

Sushruta prescribes the use of metal needles and silk threads to stitch wounds. In fact, certain species of ants are also recommended for stitching internal organs like intestines. These ants should be handpicked and allowed to bite at the place that needs to be sewed. Once they have done this, their bodies are to be severed, leaving their mouths closed on the wound. Also prescribed is the use of a strong alcoholic beverage to be used as a sedative before the surgery is performed.

The great highlight of Sushruta’s surgery was however, the operation of rhinoplasty. The making of a new nose captured the imagination of the medical world and brought him fame as the originator of plastic surgery. A detailed description of nose, lip and ear surgery is also provided. Of course, these methods were not used for cosmetic purposes but primarily to join or reshape these organs in the case of natural deformity or injury.

As an entire work, the Sushruta-Samhitaa is divided into two main parts - the Purvatantra and the Uttaratantra. The Purvatantra, being elaborate, is further divided into five sthaanas (sections). The first sthaana is Sutrasthaana, which provides a summary of the whole text. It describes the yantras (blunt devices or tools used for removing a foreign body) and shastras (sharp tools used for actual surgery). One hundred and one yantras are included. Among them are svastikayantra and and Sandamshayantra (forceps), taalayantra (scoop) and others. Twenty shastras such as karapatra (Knife or saw), vriddhipatra (scalpel), suchi (needle), kuthaarikaa(axe-shaped knife), vrihimukha (trocar) and badisha(hook) are featured. He describes that a shastra “should have an edge so fine that it should divide the hairs on the skin.”

The Sutrasthaana also discusses particular procedures such as Kshaarapaaka (the use of alkaline ashes of medicinal plants), Agnikarman (using a heated needle or other pointed object for pain-relief), Jalaukaavacarana (using leeches to take out blood). In the closing chapters of the Sutrasthaana, we find detailed information regarding the characteristics of the food items such as grains, vegetables (leaves, flowers, stems and roots), milk and other dairy products, meat of herbivores and carnivores, birds, fish and other aquatic animals, oils, honey, sugarcane and alcoholic beverages.

The Nidaanasthaana deals with the cause, progress and diagnosis of many diseases such as sciatica, facial paralysis, piles, urine-stones, various skin diseases, ascites, tumours, sexually transmitted diseases, fractures and diseases of the mouth, tongue, teeth and throat. On the other hand, the Shaarirasthaana deals with the creation and function of the sharira (body). It begins with explaining the process of reproduction and leads on to discussing some diseases related to the reproductive system. The stages of pregnancy with reference to the development of an embryo are also examined.

An informative discussion on the marmashaastra (identifying the vulnerable / vital spots) is found here. The marmas (vital points), present in the body, are divided into five groups according to the defect generated due to an injury to these points. These groups are the aashuhara, kaalaantaraghna, vaikalyajanana, vishalyaghna and rujaakara, causing immediate or delayed death, deformity and severe pain respectively.

The Chikitsaasthaana elaborates the actual treatment of diseases that are dealt with in the sequence of the Nidaanasthaana. Here, the well-known process of Panchakarman, which removes the three doshas (vaata– air in space - wind, pitta – fire in water – bile and kapha – water in earth – phlegm) in order to purify the body, is explained at length. In another context, the Kalpasthaana presents information related to Toxicology. It begins with a discussion on preventive measures to be taken in the kitchen, especially for the king, to avoid getting poisoned and explains the two types of poisons - sthaavara (plants and minerals) and jangama (animals). Types of poisonous and non-poisonous snakes, along with the other poisonous animals such as scorpions, spiders, mice and insects are described in substantial detail and treatment is suggested for a poisoned person with the help of mantras as well as with different agadas (medicines prepared from plants and mineral products).

The Uttaratantra devotes 18 chapters to describing 76 different diseases of the eye of which 51 require operations. Sushruta is said to be the first surgeon to have removed a cataract. In addition to the technique of cataract extraction, Sushruta describes such modern concepts as antisepsis, anaesthesia and post-operative care followed by diseases of ear and nose. Here, there are also details of the concept of change in voice and some common diseases like cough, fever, dysentery, vomiting, jaundice and asthma. The ill effects caused by alcoholism are also discussed.

The closing chapters are reserved for the 32 tantrayuktis (methodology of theoretico-scientific treatises in Sanskrit), basically taken from the tradition of the nyaaya philosophy. It is thought to be important to have knowledge of the nyaaya, which makes a physician able to diagnose and treat some critical cases that may not have been mentioned in the text.

So expansive, detailed and incisive is the Sushruta-Samhitaa that it is evident that it had originally stemmed from a truly enlightened mind, which had a deep and thorough understanding of the inner and outer reality of the human body and its very existence in the context of the seen and unseen world. It also reflects the extent to which the author has been tuned to the wider tradition he belongs to. Though Sushruta’s identity may be somewhat blurred, his legacy isn’t…

A NATIVE AMERICAN FOLK TALE

 Why do owls stare?

An owl and a pigeon were friends. One day, the owl began boastfully, “I think there are more owls than pigeons.” 

The pigeon laughed, “You must be joking! We pigeons can easily outnumber you.”

The owl frowned haughtily and said, “I challenge you to a count!” 

“Done!” cooed the pigeon. 

“But, first, let’s decide where the count will be held. After all, we’ll need plenty of perching space.”

The owl thought for a while and said, “How about the Big Woods? It has lots of trees.”

“Fine,” agreed the pigeon. “Go and inform all the owls and I’ll gather my flock. You have a week’s time. On the seventh day, an hour after sunrise, all owls and pigeons have to be there. Latecomers will not be counted.”

“Agreed,” hooted the owl and flew off to spread the news of the challenge.

A week passed and on the seventh day, the owls arrived at sunrise. They swooped down on Big Woods and occupied several trees.

“Toowit, toowit! Looks like the pigeons forgot to wake up,” they hooted joyfully.

Suddenly, the sky darkened as huge clouds rumbled over the woods from all four directions. The owls stared in shock as they realised that the clouds were actually pigeons. Thousands of pigeons swooped down, blocking the sunlight. They perched on the trees, pushing the owls together. Branches snapped, unable to take the weight of so many pigeons at once. The owls forgot to blink and started moving their heads from side to side in surprise. Their eyes grew wider and wider as the pigeons just kept coming in hordes.

Nervous about being squashed by the pigeons, the owls finally flew up into the sky. 

Since then, owls travel only at night when pigeons are fast asleep. And they stare at everything around them, watching out for pigeons. 

EXPLORING SPACE

Life cycle of a star

Stars are hot balls of gas. They are held together by their own gravity. The nearest star to the Earth is the Sun. They give out light of their own due to nuclear reactions. 

What are the stages in the life cycle of a star?

● The life cycle of a star is determined by its mass. The larger the mass of a star the shorter will be its life cycle. The life of a star ranges from a few million years to a billion years, depending on the mass. 

● It is believed that stars are born from collapsing dense clouds of dust and gas found in spiral galaxies. These clouds are called molecular clouds or nebulae and are made up of 97% hydrogen and 3% helium. 

● When the nebula collapses under its own gravitational force, it breaks apart and results in the formation of a dense sphere called a Protostar. 

● These protostars are dense bodies of dust and gas which have not begun to generate light. As the mass of each protostar increases so does its gravity, squeezing the core of the protostar harder. 

● As the stars expand, they become less bright, due to the core running out of hydrogen and then helium. Then the star enters the main sequence or adult phase. A star remains in this phase for most part of its lifetime. 

● A star leaves its main sequence phase when it runs out of hydrogen and starts fusing helium and other elements. 

● Dim small stars are called red dwarfs. The fusion of hydrogen in them, takes place at a very slow rate and they are able to remain in the same sequence for billions of years. 

● The low mass stars like our sun expand and become red giants. This red giant is a large star that is bright with a cool surface. This is formed when the star runs out of hydrogen. They are very bright because they are so large. 

● Stars die in explosions called supernova. Supernova leads to the core compressing into a neutron star or a black hole. 

DID YOU KNOW?

Why do we have accents?

An accent is a way of pronouncing that is particular to a person, location or nation. There are two types. 

The first is the accent you have when you speak a foreign language, having to make words and sounds that you aren’t comfortable with. 

The second is the accent we speak our native language with, such as how the British sound speaking English in comparison to how we sound speaking it. 

To confuse us more, different areas in a country can have different accents too. 

Languages all have different sounds. It appears that as people moved around and started to live in isolated areas, they developed different speech patterns and accents. 

As the world was developed and we went through periods of invasion and settlement, new accents mixed with old. 

There are more than 2,500 spoken languages in the world today. 

QUICK RESPONSE CODES

QR Codes

QR code is short for quick response code. It is an image that can be scanned by a smartphone camera to read the information stored on it. 

What is a QR code?

A QR code is an image that stores data as a two-dimensional square grid of black and white pixels. The pattern in a QR code translates into numbers, letters and website links (URLs). These pixels are black on a white background, which makes it easy for a camera to read. A QR code is anchored by three squares around it to enable scanners and cameras to orient. The reading of a QR code takes seconds and it thus allows for quick and easy access to information. 

There are two types of QR codes:

● Static

● Dynamic 

Static QR codes: A static QR code is used to provide information that does not need to be updated. For example, a wi-fi QR code, which lets you connect to any wi-fi network instantly, or a QR code on packaged foods, which gives you information about their nutrients, ingredients and how to use them. Or those on the movie tickets, which gives you access to the movie screening hall. Once this QR code is generated, the data represented by it cannot be changed, although it can be scanned an unlimited number of times. 

Dynamic QR Codes: Dynamic QR codes can be edited at any time. The URL linked with this type of QR code redirects the user to the main URL, which can be changed if required. For example, a QR code on a business card that is used to store contact details. In case your contact number changes, then that change can be made in the QR code without having to reprint the cards. 

Applications of QR Codes 

● Advertising: A QR code can connect you to a website or some important information about a product or event. It can open a form to be filled for registration and also give additional information about the event or offers. 

●Restaurants: Since the COVID-19 pandemic, contactless menus have become popular. Restaurants make a QR code available on each table in place of bulky paper menus. You can scan this code using your mobile phone and get the digital menu on your screen. The advantage to the restaurant owner is that new dishes can be updated without the need to scratch and scribble on the menus and paper is saved as new menu cards do not need to be printed with every change. 

●Postal services and libraries: QR codes are used to track parcels and books and get information about their location. 

● Display information: A QR code can be used on products to give additional information about the product such as nutritional information, ingredients and more. In some books, like encyclopedias, a QR code may be used to lead the reader to an educational video that gives more information about the subject matter. This makes learning interactive instead of static. In museums, QR codes are placed with each exhibit. The QR code contains the information about the exhibit. In bird sanctuaries and botanical gardens, QR codes are put on trees and spots where particular birds can be spotted. 

●Digital payments: QR code technology is making a big change in payment methods. Shoppers can simply scan the QR code displayed at a shop and pay the necessary amount. When the payment is successful, both the customer and the merchant get a notification. Contactless payments are accepted by small grocery shops, vegetable vendors and big stores alike. Auto rickshaws and taxis also have QR codes that can be scanned to make payments. Payments made this way are quick and effortless. 

Concerns with QR Codes: There are some potential dangers of QR codes that you should be aware of.

● Malicious QR codes also exist; scanning these will start downloading unwanted apps on your phone. This can be a security threat. 

● A QR code can direct you to a fake bank website, thus compromising your security. 

● A third party can get your phone number when you scan a QR code. This is a privacy concern that researchers and developers are trying to address. 

Did you know?

The QR code was developed in 1994 by the Japanese corporation Denso Wave, a subsidiary of Toyota Motor Corporation, in order to track automobile parts during the assembly process.