We still don't know which animals were the first on Earth,  but scientists have discovered ancient reef fossils dating back 890 million years.

Oldest animal ever found

Plastic has made its way into almost all types of environments, including the ocean and the deep sea (where it makes up ~80% of all debris).Researchers in the UK have developed an enzyme derived from a bacteria which can consume plastic. They are hoping that upon further improvements it can be used at a larger scale.

Plastic-eating enzymes

Inspired from bacteria, this is a Nobel-prize-winning technology which allows us to do genome editing very precisely. It's already being used in trials and early results look promising.

CRISPR-Cas9

Researchers have been able to create robots from stem cells taken from frogs, allowing them to evolve on their own using AI and machine learning.

Xenobots

Researchers in Japan have developed software which can not only decode brainwaves, but also interpret them and offer us a visual representation of those thoughts. This was done using deep neural networks and it worked with a pretty good level of accuracy.One day this could be used to recreate images straight from memory.

Mind-reading

In an accidental discovery, Dutch scientists found a new organ behind the nose: a new type of salivary gland. It is a pretty hard to access area, so it explains why it took so long to find it.

A new organ

NASA has detected that marsquakes (earthquakes, but on Mars) are rather regular and that there is a hum sound present on the surface of Mars, speculated to be caused by seismic activity and the sounds of the atmosphere. It falls outside the range of human hearing, but it's similar to the hum present on Earth, about which we don't know too much, either.

The Mars 'hum'

X-ray may sound creepy, but the tech definitely has its uses. Researchers at MIT have developed RF-Pose, using AI and radio signals to track someones' movement in the next room.

Seeing through walls

The ocean is huge and we're still finding new stuff out there. Recently, researchers have found a giant reef near the Great Barrier Reef. It is surprisingly large, at over 1.5km long (1.9 miles) and 500m tall (1640 feet).

A giant reef

2021 saw several extreme weather events pointing towards climate change. A recent reports claims that even if we cut emissions right now, we've passed the point of no return.

Climate change

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Science & Nature

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Incredible Recent Scientific Discoveries That You Might Have Missed

Your brain may only weigh 3 pounds, but it holds the ultimate power that invented the electricity, the telephone, the Internet and millions of other scientific marvels that our world depends upon. Knowing each and every detail about this powerhouse isn’t easy. Scientists around the world have been trying to decode the human brain for centuries but are still unable to understand it completely. So, next time when you’d think you know how your brain works, think again!

A Powerhouse

You’ve got more than 100 billion neurons inside your brain transmitting information at the speed of a bullet train. That’s almost equal to the total number of stars in our galaxy!For all the plans you make, the things you do, and the decisions you take, there are neurons inside your brain sending electrical signals to each other round the clock. Without diving deep into the complexity of this grey matter, let us look at those amazing things about your brain that you should be aware of.

Complexity

If you think you are great at multitasking, I would say think again. Only 2% of human beings can multitask efficiently. This is because the human brain cannot process information from two different sources at the same time.You must be thinking that I’m kidding because you multitask every now and then. You can listen to music while studying or you can easily drive while talking over the phone. A chef is capable of cooking two, three, or maybe four dishes at a time, isn’t it?

A Multitasking Myth

Basically, the tasks that you regularly perform become a part of your subconscious mind. Your subconscious mind stores your skills, experiences, and memories so that you won’t stress your brain every time you perform a regular task. This makes it even easier and faster to switch between the two tasks. Moreover, the transition is so dynamic that you would feel like you’re multitasking. But in reality, you’re not.

The placebo effect is one of the most powerful effects in psychology. Moreover, it is widely accepted by medical sciences around the world. A placebo is something that seems to be a real treatment, but it isn’t. It is effective only because of the patient’s belief in the treatment. Similarly, you can easily fool your brain into believing that you’ve had enough sleep, even when you haven’t. A <a href="https://psycnet.apa.org/record/2014-01016-001">research </a>showed that just by thinking that you’ve got a good sleep you can make your brain work more efficiently and in a much better way.

Placebo Sleep

Your brain is inclined towards negative thoughts. Yes, you’re hardwired to focus on negativity and the reason behind it lies far back in history before civilization.In ancient times, paying attention to dangerous, negative, and bad things in the world was literally a matter of life and death. Those who were more attentive to dangerous and negative things were more likely to survive. Though you don’t need to be that attentive anymore, your brain still pays more attention to something that may harm you in the future.

Attraction Towards Negativity

You can make long-lasting beneficial changes to the physical or neurological functioning of the brain. If you like to learn something new or to give up an old bad habit, you can do that in just 3 to 4 weeks. You only have to take one step forward towards your goal every day. Once you visualize what you want and identify the beliefs that support your intention, you just need to take actions that’ll rewire your brain as per your preferences. However, the final result will depend on your consistency and the intensity of performing those actions.

Rewiring Your Brain

Laughter works in a way similar to antidepressants. A <a href="https://pubmed.ncbi.nlm.nih.gov/21280463/">research </a>showed that laughing literally improves your mental health as it releases the feel-good hormones, namely dopamine and serotonin in your brain. Laughing also helps in decreasing pain while improving the resiliency of your body by releasing endorphins in your brain. So, laugh and spread happiness because you never know who might be needing it.

Laugh!

Your brain may only weigh 3 pounds, but it holds the ultimate power that invented the electricity, the telephone, the Internet and millions of other scientific marvels that our world depends upon…

personaldevelopment

Personal Development

health

Health

problemsolving

Problem Solving

Things You Should Know About Your Brain

Aging can be categorized into two types and due to two types of factors, intrinsic and extrinsic.
<ul>
<li>Intrinsic aging is a genetically predetermined process that occurs naturally.</li>
<li>Extrinsic aging is a result of outside factors chosen by you, such as where you live, your stress levels, and your lifestyle habits (like smoking).</li>
</ul>

Types of aging

<ul>
<li>Programmed aging theories say that our cells have a predetermined lifespan that’s encoded into our bodies. These include:</li>
<li>Gene theory - suggests that specific genes turn “on” and “off” over time, causing aging.</li>
<li>Endocrine theory - here, aging is caused by changes in hormones.</li>
<li>Immunological theory - this is the idea that the immune response is designed to decline(autoimmunity), leading to disease and aging.</li>
</ul>

Programmed theories of aging

<ul>
<li>Wear and tear theory - cells break down and become damaged over time.</li>
<li>Genome instability theory -aging happens because the body loses its ability to repair DNA damage.</li>
<li>Cross-linkage theory - aging is due to the buildup of cross-linked proteins, which damages cells and slows biological functions.</li>
<li>Rate-of-living theory - an organism’s rate of metabolism determines its lifespan.</li>
<li>Free radical theory - aging is due to the buildup of oxidative stress, caused by free radicals.</li>
<li>Mitochondrial theory - mitochondrial damage releases free radicals and causes aging.</li>
</ul>

Error theories of aging

<ul>
<li>Telomere theory - Telomeres protect the ends of your chromosomes as they multiply. Over time, telomeres shorten, which is associated with disease and aging.</li>
<li>Programmed senescence theory - Cellular senescence occurs when cells stop dividing and growing, but don’t die.</li>
<li>Stem cell theory - Stem cells can turn into other cells, which helps repair tissue and organs. But the function of stem cells declines over time, potentially contributing to aging.</li>
<li>Longevity gene theory - This is the idea that certain genes extend lifespan.</li>
</ul>

Genetic theories of aging

It says that an organism begins aging after they have reached their peak of reproduction and have passed down adaptive traits.
<ul>
<li>Mutation accumulation - This theory presumes that random mutations accumulate later in life.</li>
<li>Antagonistic pleiotropy - According to this theory, genes that promote fertility early in life have negative effects later on.</li>
<li>Disposable soma theory - The theory claims that when more metabolic resources are directed toward reproduction, the less is put toward DNA repair. The result is cell damage and aging.</li>
</ul>

Evolutionary theory of aging

<ul>
<li>Advanced glycation end products (AGEs) - AGEs develop when fats or protein are exposed to sugar. High levels may lead to oxidative stress, which speeds up aging.</li>
<li>Heat shock response - Heat shock proteins protect cells from stress, but their response decreases as we age.</li>
<li>Damage accumulation - Normal chemical reactions damage DNA, proteins, and metabolites over time.</li>
</ul>

The biochemical theory of aging

In most parts of the world, women live longer than men . This is due to several biological, social, and environmental factors.
<ul>
<li>Estrogen is the female sex hormone, and has been found to have anti-inflammatory and immune-boosting effects, which may protect women from certain diseases.</li>
<li>In contrast, the male sex hormone, testosterone may suppress the immune system.</li>
</ul>

Women live longer than men

<ul>
<li>Eat a nutritious diet - Focus on fruits, vegetables, whole grains, and lean protein. Limit processed foods .</li>
<li>Stay active - Aim for 30 minutes a day, 5 days a week.</li>
<li>Avoid tobacco - Tobacco speeds up aging.</li>
<li>Drink alcohol in moderation - Alcohol increases your risk of chronic disease.</li>
<li>Attend regular checkups</li>
<li>Know your family history - To have appropriate screening or get early treatment for potential chronic diseases.</li>
<li>Engage your brain - by doing brain exercises.</li>
<li>Wear sunscreen - Sunscreen protects your skin from UV radiation, which can cause premature aging.</li>
</ul>

How to slow down aging

What is the best way to live longer? Here are a few factors within your control

longevity

Longevity

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Food

How To Live A Long Life

There are about 300+ theories of aging, some which have been broken down here. Along with them, certain lifestyle changes which could slow down the physiological effects of aging. is also given.

Some aging theories suggest cells have a predetermined lifespan, while others claim it’s caused by damage, genetics, evolution, or biochemical reactions.

Why Do We Age, and Can Anything Be Done to Stop or Slow it?

Escape velocity is the speed at which an object (like a rocket) has to travel to completely overcome a planet or moon's gravity and make it into space away from that planet or moon.A planet (or satellite) cannot long retain an atmosphere if the planet’s escape velocity is low enough to be near the average velocity of the gas molecules making up the atmosphere.At the surface of the Earth, if atmospheric resistance could be disregarded, escape velocity would be about 11.2 km (6.96 miles) per second which is approximately 33 times the speed of sound (Mach 33).

What Does Escape Velocity Mean?

#shorts #escapevelocity #generalknowledge What does escape velocity mean? Escape velocity is the speed at which an object (like a rocket) has to travel to completely overcome a planet or moon's gravity and make it into space away from that planet or moon. A planet (or satellite) cannot long retain an atmosphere if the planet’s escape velocity is low enough to be near the average velocity of the gas molecules making up the atmosphere. At the surface of the Earth, if atmospheric resistance could be disregarded, escape velocity would be about 11.2 km (6.96 miles) per second which is approximately 33 times the speed of sound (Mach 33). The velocity of escape from the less massive Moon is about 2.4 km per second at its surface. Know more about… Space : https://youtube.com/playlist?list=PLO6kTsDI4xfnAISJIMWKxkPoL9qoU9Hwv General knowledge : https://youtube.com/playlist?list=PLO6kTsDI4xfn6hHfyZBGiw-atw0its-7Q Science & Technology : https://youtube.com/playlist?list=PLO6kTsDI4xfmONVgfMhMbstBLpZuyJCP2 Health : https://youtube.com/playlist?list=PLO6kTsDI4xflrlYCGE0EIyWXoBoNG81-r 🙏Requests🙏 I requested to you (My viewers) please subscribe to my channel and if you like video then please press like button.All youtubers are doing hard work in video making and your like, Share, Subscribes are fruits for our hard works. You also follow me on: - Facebook: www.facebook.com/thetechers You can visit my Website : www.knowledgevaccination.blogspot.com This video is under Fair Use: Copyright Disclaimer Under Section 107 of the Copyright Act in 1976; Allowance is made for "Fair Use" for purposes such as criticism, comment, news reporting, teaching, scholarship, and research. Fair use is a use permitted by copyright statute that might otherwise be infringing. Non - profit, educational or personal use tips the balance in favor of fair use. All rights and credit go directly to its rightful owners. No copyright infringement intended. Sound credit : Track : Hitman/Artist : Kevin macLeod Video Credit : pixabay/storyblocks Thank you all of you...🙏

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Technology & The Future

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Space

#shorts #escapevelocity #generalknowledge
What does escape velocity mean?
Escape velocity is the speed at which an object (like a rocket) has to travel to completely overcome a planet or moon's gravity and make it into space away from that planet or moon.
A planet (or satellite) cannot long retain an atmosphere if the planet’s escape velocity is low enough to be near the average velocity of the gas molecules making up the atmosphere.
At the surface of the Earth, if atmospheric resistance could be disregarded, escape velocity would be about 11.2 km (6.96 miles) per second which is approximately 33 times the speed of sound (Mach 33). The velocity of escape from the less massive Moon is about 2.4 km per second at its surface.

Know more about… 
Space : https://youtube.com/playlist?list=PLO6kTsDI4xfnAISJIMWKxkPoL9qoU9Hwv

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🙏Requests🙏 
I requested to you (My viewers) please subscribe to my channel and if you like video then please press like button.All youtubers are doing hard work in video making and your like, Share, Subscribes are fruits for our hard works.
 
You also follow me on: - 
Facebook: www.facebook.com/thetechers
You can visit my Website : www.knowledgevaccination.blogspot.com

This video is under Fair Use: Copyright Disclaimer Under Section 107 of the Copyright Act in 1976;  Allowance is made for "Fair Use" for purposes such as criticism, comment, news reporting, teaching, scholarship, and research.  Fair use is a use permitted by copyright statute that might otherwise be infringing.  Non - profit, educational or personal use tips the balance in favor of fair use.  All rights and credit go directly to its rightful owners.  No copyright infringement intended.

Sound credit : Track : Hitman/Artist : Kevin macLeod
Video Credit : pixabay/storyblocks

Thank you all of you...🙏

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What Does Escape Velocity Mean? #shorts

Interested in becoming more efficient and effective in learning and recalling information? Whether you're in elementary school, graduate school or everyday life, using these mnemonic (pronounced ni-mahn-ik) strategies—think of them as very effective <a href="https://www.verywellhealth.com/tips-to-improve-your-memory-and-recall-98553">memory tips</a>—can make it easier to remember facts, and they can be applied to almost any subject.

Improve Your Memory Using Mnemonics

Multiple research studies have demonstrated that using the keyword mnemonic method improves learning and recall, especially in the area of foreign languages.Here's how this works. First, you choose a keyword that somehow cues you to think of the foreign word. Then, you imagine that keyword connected with the meaning of the word you're trying to learn.For example, if you're trying to learn the Spanish word for cat, which is gato, first think of a gate and then imagine the cat sitting on top of the gate.

Keyword Mnemonics

Chunking information is a mnemonic strategy that works by organizing information into more easily learned groups, phrases, words or numbers. For example, memorizing the following number: 47895328463 will likely take a fair amount of effort. However, if it is chunked like this: 4789 532 8463, it becomes easier to remember.Interestingly, chunking is one of several mnemonic strategies that has been studied in people with mild Alzheimer's disease. Results from these studies concluded that chunking can be helpful in improving verbal working memory in the early stages of dementia.2

Chunking as a Mnemonic Strategy

One way to successfully encode the information into your brain is to use <a href="https://www.verywellhealth.com/using-music-in-alzheimers-disease-97624">music</a>. A well-known example is the "A-B-C" song, but there's no end to what you can learn when it's set to music. You can learn the countries of Africa, science cycles, memory verses, math equations and more.Music is also an effective tool for people with <a href="https://www.verywellhealth.com/mild-cognitive-impairment-and-alzheimers-disease-98561">mild cognitive impairment</a> and <a href="https://www.verywellhealth.com/alzheimers-4581763">Alzheimer's disease</a>. Not only can the words of songs be remembered from their childhood even when other language ability is almost gone, but they can also learn new information more effectively if it's taught through music.

Musical Mnemonics

Acronyms and acrostics are typically the most familiar type of mnemonic strategies.Acronyms use a simple formula of a letter to represent each word or phrase that needs to be remembered.An acrostic uses the same concept as the acronym except that instead of forming a new "word," it generates a sentence that helps you remember the information.An often-used acrostic in math class is: Please Excuse My Dear Aunt Sally. This acrostic mnemonic represents the order of operations in algebra and stands for parentheses, exponents, multiplication, division, addition, and subtraction

Letter and Word Mnemonic Strategies

"Hey diddle diddle. The cat and the fiddle..." Can you finish the rest of this nursery rhyme?The ability to memorize and remember nursery rhymes is often due in part to repetition and in part to rhyming. Rhyming words can be used as a mnemonic to help us learn and recall information.Sometimes, you can rearrange words or substitute a different word with the same meaning to make them rhyme.

Rhymes as Mnemonic Strategies

One mnemonic strategy that helps encode new information is to connect it with something else that you already are familiar with or know. This gives it meaning and makes it easier to remember. Making connections is a type of elaborative rehearsal and can be applied to almost any subject or type of information.For example, imagine that you are just introduced to someone named Jeffery. Perhaps you notice that Jeffery is very energetic, and connect Jeffrey with jumping. The next time you see him. you'll think, "There's 'Jumping Jeffery' and you can say hello by name."

Making Connections as a Mnemonic Method

The method of loci (pronounced low-sigh) is arguably the earliest identified mnemonic in history. In the method of loci, the learner visualizes a room or a familiar path through a building and mentally associates facts or information with specific locations or objects along the way. In order to recall what he's learned, he re-visualizes moving through that room or along that path and each stop along the way triggers another piece of information. This method is also called the journey method, creating a "memory palace" or the mental walk strategy.

Memory Palace: The Method of Loci Mnemonic Strategy

The peg method is an especially useful mnemonic for remembering sequenced information. If first requires that you memorize the following list in help you order the facts:<ol><li>one = bun</li><li>two = shoe</li><li>three= tree</li><li>four = door</li><li>five = hive</li><li>six = sticks</li><li>seven = heaven</li><li>eight = gate</li><li>nine = vine</li><li>ten = hen</li></ol>After you have memorized this list, look over the new information that you are trying to learn. Then, connect the first word to "bun," the second word to "shoe," the third word to "tree," etc. The goal is to make a memorable connection with each new piece of information you need to memorize.

Peg Method Mnemonics

The mnemonic linking method consists of developing a story or image that connects together pieces of information you need to remember. Each item leads you to recall the next item.For example, imagine that you need to remember to bring the following things with you to school in the morning: homework papers, glasses, gym shoes, wallet, lunch money, and keys.Using the linking system, you can think of the following short story to help you: Jack's homework papers put on their glasses and gym shoes and ran over to his wallet where his hungry keys were eating his lunch money.

The Mnemonic Linking System (Stories or Images)

Using mnemonic memory strategies can give you that boost in your memory that we all need, and it can improve your efficiency in learning as well. Keep in mind that you may need to practice a few of these strategies before they come easily, but once you have them down, they should clearly benefit your learning and recall of information.

The Bottom Line

Mnemonics help us more easily learn and remember information. Here are 9 research-backed types that improve effectiveness and efficiency.

9 Types of Mnemonics to Improve Your Memory

Phones use one of three different technologies to read your fingerprint: optical, capacitive or ultrasonic. An optical fingerprint reader is the oldest of the three. It uses a specialised miniature camera to take a picture of your finger, often backlit with little LEDs or the phone’s screen.Unfortunately, these sensors are easy to fool – even a good photo can trick them, so it may be combined with a capacitive sensor, the second technology, to check there is really a finger there.

The Fingerprint Sensor Of Your Phone

A capacitive fingerprint sensor uses a grid of tiny capacitors that store electricity, which is discharged only at the points where your fingerprint ridges touch. An array of thousands of capacitors can then be used to map the pattern of your fingerprint. Sometimes these sensors also support swipes or force sensing.

The Capacitive Sensor

The third and most advanced form of fingerprint sensing uses ultrasonics. Much like the ultrasonic scanners used for medical purposes, an ultrasonic sound pulse is transmitted to your finger and the reflected pulse is measured. Bats, whales and dolphins use ultrasonic to understand the shape of their surroundings; the sensors on a smartphone use it to understand the 3D shape of the ridges in your fingerprint. It can even work through the phone screen.

Ultrasonic Sensing

Fingerprint scanners have become an essential feature of smartphones.

How does a smartphone ‘read’ my fingerprint?

Adults who demonstrate more playful personality traits are more motivated, creative, and spontaneous. There have even been links between people with more playful characteristics having lower blood pressure. While less playful people struggle in their leisure time to relax and often feel bored when their minds are not preoccupied, those that are more playfully inclined are aware of new opportunities and open to trying a wider variety of activities.

Playing Games is good

Playfulness should be viewed as a skill that can be developed, harnessed and used for mindfulness.

Proyer suggests listing three moments at the end of every day where something spontaneous happened. It could be a funny interaction with a stranger while getting your coffee or a joke shared with your colleague. This will help you to begin to feel confident in being playful and make you more aware of joy in your everyday life.

Start by observing

Do not be afraid to find fun in something not normally associated with adults.In order for adults to engage in playful activities guilt-free, they can come prepared with socially acceptable "excuses". Eg: The Mindfulness Coloring Book: Anti-Stress Art Therapy for Busy People by Emma Farrarons which aims to make the embarrassing act of adult colouring socially acceptable when associated with the "alibi" of it being therapy for successful people.

Socially acceptable excuses

While some adults might feel the need to hide their playfulness, the market for video games and mobile gaming among adults has boomed in recent years.The mental health benefits of playing video games down to achieving a state of "flow".The optimal experience when nothing else matters and is also experienced by athletes and sportspeople when they are in the zone. Playing to find the flow state can provide an enjoyable challenge and distraction from mental health issues, meaning the player can work on their wellbeing without feeling pressured to improve.

Video Game as Adult therapy

Rediscover the benefits of playfulness after the toys have been put away.

Playing has been shown to improve the mental health of adults, but most people stop in childhood. How can we rediscover the benefits of playfulness after the toys have been put away?

parenting

Parenting

music

Music

meditation

Meditation

Why adults should embrace their playfulness

Fibonacci numbers explain how things expand and why they give rise to spirals. You can find Fibonacci numbers all over the natural world. The number of petals on a flower is a Fibonacci number. Cut open a fruit, and you'll find a star shape with a Fibonacci number of arms. A banana has a three-pointed star, and apple a five-pointed star. The cells on a pineapple have several Fibonacci numbers. If you take squares whose dimensions correspond to the Fibonacci numbers, then you can arrange them in an expanding rectangle.

Fibonacci numbers are important

1, 1, 2, 3, 5, 8, 13, 21…Every number in the sequence is created by adding together the two previous numbers. The next Fibonacci number is 13 + 21 = 34. Hidden inside this sequence is the golden ratio. Many artists regard the golden circle as the perfect proportion for a canvas.

The Fibonacci sequence

The numbers are named after a 13th-century Italian mathematician known as Leonardo Bonacci. In 1853, historian Guillaume Libri started to refer to him as Fibonacci (son of Bonacci). In 1202, Fibonacci wrote about these numbers in Liber Abaci. The book was meant to support new ways of doing computation as Europe still used Roman numerals and the abacus to do calculations. He explained the power of the Hindu Arabic numerals, and how the Indians used the numbers 1 to 9 with a revolutionary new concept of 0 in a place number system.

Origin of Fibonacci numbers

The numbers were discovered by Indian poets and musicians who used them to understand rhythm in music and poetry. Modern musicians also used the Fibonacci numbers in their work. Debussy used them in his La Mer, Bartok in his Music For Strings, Percussion and Celesta. There's a new form of poetry named Fib, where each line has syllables corresponding to the Fibonacci sequence.

Fibonacci did not discover these numbers

The Fibonacci sequence is used in art, composition, maths, nature, music, investing and more. 

Flowers, pinecones, shells, fruits, hurricanes and even spiral galaxies, all exhibit the Fibonacci sequence.

What is the Fibonacci sequence?

He was a great mathematician and astronomer. Brahamgupta considered himself to be an astrologer, maybe because his father Jisnugupta was an astrologer but today, he is mostly remembered for his significant works in the field of mathematics. He was born in 598 CE in Bhinmal, a city in Rajasthan. He spent a major part of his life in Rajasthan. Ujjain was the centre of Indian mathematical astronomy in ancient times and Brahamgupta was the director of this centre. While he was in Ujjain, he wrote many books on mathematics and astronomy.

13. Brahmagupta Acharya 

‘Durkeamynarda’ (672), ‘Khandakhadyaka’ (665), ‘Brahmasphutasiddhanta’ (628) and ‘Cadamakela’ (624). The ‘Brahmasphutasiddhanta’ meaning the ‘Doctrine of Brahamagupta’ is one of his well-known works. The ‘Brahmasphutasiddhanta’ consists of 25 chapters. In the first 10 chapters, topics covered are, mean longitudes of the planets, true longitudes of the planets, the three problems of diurnal rotation, lunar eclipses, solar eclipses, risings and settings, the moon’s crescent, the moon’s shadow, conjunctions of the planets with each other,

These include

and conjunctions of the planets with the fixed stars. The rest of the 15 chapters are focused more on mathematical concepts. One of his fellow mathematicians gave him the title of ‘Ganita Chakra Chudamani’ which when translated meant, ‘The gem of the circle of mathematicians’. It is believed, that he died in Ujjain, in 668 CE. His contributions to mathematics are mentioned below.

According to him,zero is a number that is obtained, when a number is subtracted from itself. He also mentioned some properties of zero, where positive numbers are termed as fortunes and negative numbers are termed as debt.<ul><li>When zero is added to a number or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero.</li><li>A debt minus zero is a debt.</li><li>A fortune minus zero is a fortune.</li><li>Zero minus zero is a zero.</li><li>A debt subtracted from zero is a fortune.</li><li>A fortune subtracted from zero is a debt.</li><li>The product of zero multiplied by a debt or fortune is zero.</li></ul>

1.Properties Of Zero

<ul><li>The product of zero multiplied by zero is zero.</li><li>The product or quotient of two fortunes is one fortune.</li><li>The product or quotient of two debts is one fortune.</li><li>The product or quotient of a debt and a fortune is a debt.</li><li>The product or quotient of a fortune and a debt is a debt.</li><li>His some conclusions on the division by zero. </li></ul>"Positive or negative numbers when divided by zero is a fraction with zero as denominator. Zero divided by negative or positive numbers is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero.”

He proposed a method of multiplication, “gomutrika”, in his book “Brahmasphutasiddhanta”. The title of this method was translated by Ifrah as, “Like the trajectory of cow’s urine”. In the 12th chapter of his book, he also tried to explain the rules of simplifying five types of combinations of fractions:-ac + bc; ac × bd; a1 + bd; ac + bd × ac = a(d + b)cd; and ac − bd × ac = a(d − b)cd. Let us try to multiply 315 by 306 with the help of the gomutrika method in the Link Attached above.

2. Brahmagupta’s Method of Multiplication

proposed some methods to solve equations of the type ax + by = c. According to Majumdar, Brahmgupta used continued fractions to solve such equations. He also tried to solve quadratic equations of the type ax² + c = y² and ax² – c = y². For example, for the equation 8x² + 1 = y² he obtained the solutions as (x, y)= (1, 3), (6, 17), (35, 99), (204, 577), (1189, 3363),..He also solved 61x² + 1 = y² having solution as x = 226153980, y = 1766319049 as its smallest solution.

3. Intermediate Equation 

"Five hundred drammas were loaned at an unknown rate of interest, The interest on the money for four months was loaned to another at the same rate of interest and amounted in ten mounths to 78 drammas. Give the rate of interest.”

A sample of the types of problem solved by him is:-

the sum of, a series of cubes and a series of squares for the first n natural numbers as follows:1² + 2² +…….+n² = (n)(n+1)(2n+1)⁄61³ + 2³ +…….+n³ = (n(n+1)⁄2)²

4. Sum Of Series

Brahmagupta in chapter 12, entitled “Calculation”, of his book, proposed a formula that was useful in generating Pythagorean triplets. He mentioned, The height of a mountain multiplied by a given multiplier is the distance to a city; it is not erased. When it is divided by the multiplier increased by two it is the leap of one of the two who make the same journey.”

5. Pythagorean Triplets

Brahmagupta studied this equation 1000 years before Pell’s birth. Pell’s equation is of form, nx² + 1 = y², which can also be written as y² – nx² = 1, where ‘n’ is an integer and we have to solve it for (x, y) integer solutions. Brahmagupta also provided a lemma, in which he stated that if (a, b) and (c, d)are integer solutions of ‘Pell type equations’ of the form na²+ k = b² and nc² + k’ = d²then, (bc + ad, bd + nac) and (bc – ad, bd – nac)are both integer solutions of the ‘Pell type equation’.

6. Pell’s Equation 

Brahmagupta’s formula for the cyclic quadrilaterals is regarded as his most famous discovery in geometry. Given the sides of a cyclic quadrilateral, he provided an approximate and exact formula for the area of the cyclic quadrilateral. He mentioned,"The approximate area is the product of the halves of the sums of the sides and opposite sides of a triangle and a quadrilateral. The accurate area is the square root from the product of the halves of the sums of the sides diminished by each side of the quadrilateral.”

7. Brahmagupta 'S Formula 

Brahmagupta theorem states that,If a cyclic quadrilateral is orthodiagonal (i.e., has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side.”Geometrically, this theorem means that, in a cyclic quadrilateral ABCD, diagonals AC and BD are perpendicular to each other. The intersection of AC and BD is M. Drop the perpendicular from M to the line BC, calling the intersection point E. Let F be the intersection of the line EM and the side AD. Then, according to the theorem, F is the midpoint of side AD.

8. Brahmagupta’s Theorem

Brahmagupta further extended his theory and claimed that, The square-root of the sum of the two products of the sides and opposite sides of a non-unequal quadrilateral is the diagonal. The square of the diagonal is diminished by the square of half the sum of the base and the top; the square-root is the perpendicular altitudes.”The above statement means that in an isosceles trapezoid having sides of length p, q, r, s, the length of the diagonal is given by √pr+qs.

A major portion of Brahmagupta’s work was dedicated to the study of geometry. One of his theorem about triangles states that,The base decreased and increased by the difference between the squares of the sides divided by the base; when divided by two they are the true segments. The perpendicular altitude is the square-root from the square of a side diminished by the square of its segment.”This theorem gives the length of two segments in which the base of a triangle is divided by its altitude, and the lengths are, 12(b ± (c2 − a2)

9. Triangles

He also discussed rational triangles. A rational triangle with the rational area and sides a, b, c, are of the form:a = 1⁄2(u²⁄v + v), b = 1⁄2(u²⁄w + w), c = 1⁄2(u²⁄v – v + u²⁄w – w), for some rational numbers u, v, w.

Brahmagupta also tried to approximate the value of π and in stanza 40 of his book he mentioned, The diameter and the square of the radius, each multiplied by 3 are the practical circumference and the area of a circle respectively. The accurate values are the square-roots from the squares of those two multiplied by ten.”He used √10 ≈ 3.1622….. approximated to 3, as an accurate value of π with an error of less than 1%.

10. Approximation of π

Brahmagupta illustrated the construction of several figures with arbitrary sides. He tried to construct figures such as isosceles triangles, scalene triangles, rectangles, isosceles trapezoids, isosceles trapezoids with three equal sides, and scalene cyclic quadrilateral, mainly, with the help of right triangles. He also gave the volume and surface area of some figures, after estimating the value of π. He found the volume of rectangular prisms, pyramids and frustum of a square pyramid. He further proposed the average depth of a series of pits.

11. Measuration And Construction 

Brahmagupta in his chapter 2 of his book, provided a sine table. He wrote,The sines: The Progenitors, twins, Ursa Major, the Vedas, the gods, fires, flavors, dice, the moon, the sky, the moon, arrows, sun…..”He used the above objects to represent digits of place-value numerals. Progenitors represent 14 progenitors in Indian cosmology, twins means 2, Ursa Major represents the seven stars of Ursa Major or 7, Vedas refers to the 4 Vedas or 4, dice represents the number of sides of the traditional die or 6, and so on. He gave the sine table with 3270 as radius and calculated 3270 sin(π⁄48).

12. Trigonometry 

He was the first who propose an interpolation formula using second-order difference. His Sanskrit verses on this formula were found in the Khandakadyaka work of Brahmagupta. Today, the Brahmagupta interpolation formula is known as Newton- Stirling interpolation formula. In his book, he termed the difference Dr as the ‘gatakhanda’, the difference Dr+1 as the ‘bhogyakhanda’, ‘Vikala’ as the quantity in minutes by which the interval has been covered at the point of interpolation, which in modern notation denoted as a− xr. ‘Sphuta-bhogyakhanda’ is now known as fr+1 − fr.

13. Interpolation Method

A formula stated by him, for the computation of values of the sine table, having common interval (h) in the underlying base table as 900 minutes or 15 degrees, is given below.When translated these verses means,Multiply the ‘vikala’ by the half the difference of the ‘gatakhanda’ and the ‘bhogyakhanda’ and divide the product by 900. Add the result to half the sum of the ‘gatakhanda’ and the ‘bhogyakhanda’ if their half-sum is less than the ‘bhogyakhanda’, subtract if greater. The result in each case is ‘sphuta-bhogyakhanda’ the correct tabular difference.

Sphuta-bhogyakhanda 

In modern notation, the formula is denoted as sphuta-bhogyakhanda =  (Dr + Dr-1)⁄2 ± t|Dr – Dr-1|⁄2, where ± is introduced according to  Dr < Dr+1 or Dr > Dr+1  and f(a) is given by,f(a) = fr + t × sphuta-bhogyakhanda, is known as Stirling’s interpolation formula for second-order differences

Brahmagupta gave the solution of general linear equations in chapter 18 of his book and wrote,The difference between rupas, when inverted and divided by the difference of the coefficients of the unknowns, is the unknown in the equation. The rupas are subtracted on the side below that from which the square and the unknown are to be subtracted.”Algebraically, the above statement means that, for an equation of type bx+c = dx+e, the solution is given by x = e − c/b − d. He also gave two solutions for the quadratic equation ax² +bx = c, and wrote,

14. Algebra

Diminish by the middle number the square-root of the rupas multiplied by four times the square and increased by the square of the middle number; divide the remainder by twice the square.”By this method, the solution is given by, x = ±(√(4ac+b²) – b)⁄2a. Whatever is the square-root of the rupas multiplied by the square and increased by the square of half the unknown, diminished that by half the unknown and divide the remainder by its square. The result is the unknown.”By this method, the solution is given by, x = ±(√(ac+b²⁄4) – b²⁄2)⁄a.

Although Brahmagupta thought of himself as an astronomer who did some mathematics, he is now mainly remembered for his contributions to mathematics. He was honoured by the title given to him by a fellow scientist ‘Ganita Chakra Chudamani’ which is translated as ‘The gem of the circle of mathematicians’.

Ganita Chakra Chudamani Brahmagupta 

education

Learning & Education

Brahmagupta’s Contributions in Mathematics – StudiousGuy

An economic indicator is simply any economic statistic, such as the unemployment rate, GDP, or the inflation rate, which indicate how well the economy is doing and how well the economy is going to do in the future.Investors use all the information at their disposal to make decisions. If a set of economic indicators suggest that the economy is going to do better or worse in the future than they had previously expected, they may decide to change their investing strategy.

Economic Indicators

<ul><li>Procyclical: This indicator is one that moves in the same direction as the economy. The GDP is an example.</li><li>Countercyclical: This indicator is one that moves in the opposite direction as the economy. The unemployment rate gets larger as the economy gets worse so it is a countercyclical economic indicator.</li><li>Acyclical: This indicator is one that has no relation to the health of the economy and is generally of little use. The number of home runs the Montreal Expos hit in a year generally has no relationship to the health of the economy, so we could say it is an acyclic economic indicator.</li></ul>

Economic Indicators: Relation to the Business Cycle / Economy

<ul><li>Leading economic indicators change before the economy changes. Stock market returns are a leading indicator, as the stock market usually begins to decline before the economy declines and they improve before the economy begins to pull out of a recession.</li><li>A lagged economic indicator is one that does not change direction until a few quarters after the economy does. The unemployment rate is a lagged economic indicator.</li><li>A coincident economic indicator is one that simply moves at the same time the economy does. The Gross Domestic Product is a coincident indicator.</li></ul>

Three Timing Types of Economic Indicators

These tend to be the broadest measures of economic performance and include such statistics as:<ul><li>Gross Domestic Product (GDP) [published quarterly]</li><li>Real GDP [quarterly]</li><li>Implicit Price Deflator for GDP [quarterly]</li><li>Business Output [quarterly]</li><li>National Income [quarterly]</li><li>Consumption Expenditure [quarterly]</li><li>Corporate Profits[quarterly]</li><li>Real Gross Private Domestic Investment [quarterly].</li></ul>

Total Output, Income, and Spending

Learn about economic indicators including prices, federal finance, and international trade, and why are they important.

Economic Indicators: A Beginner's Guide

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