Pi Day - Celebration of An Indispensible Mathematical Determinant

Pi is the ratio of the circumference of a circle to its diameter . It now has various equivalent definitions and appears in many formulas in all areas of mathematics and physics.
Image from/pixabay.

 π Pi the worlds most renowned mathematical constant. Pi is wonderful. It plays into so many aspects of our lives and goes on forever and ever and ever. Every year the certain day comes that shares numerical values of Pi and on that day we celebrate Pi with every kind of Pie we can imagine,


Pi is the ratio of the circumference of a circle to its diameter . It now has various equivalent definitions and appears in many formulas in all areas of mathematics and physics. It is approximately equal to 3.14159. It has been represented by the Greek letter π since the mid-18th century, though it is spelled out as "pi". It is also called Archimedes' constant.

It can also be noted that Pi is actually an irrational number (a decimal with no end and no repeating pattern) that is most often approximated with the decimal 3.14 or the fraction 227.

Pi Day

Pi day occurs March 14, as the day is written as 3/14 in the United States. Some serious persons celebrate the day exactly at 1:59 AM (or PM!) so they can reach the first six numbers of pi.  

Pi Approximation Day

Pi Approximation Day is observed on July 22 (22/7 in the day/month format), since the fraction ​²²⁄₇ is a common approximation of π, which is accurate to two decimal places and dates from Archimedes.

Two Pi Day

Two Pi Day, also known as Tau Day for the mathematical constant Tau, is lightly observed on June 28 (6/28 in the month/day format).
Tau Day is an annual celebration of the circle constant τ=6.283185…,

History of Pi Day

Physicist Larry Shaw started Pi Day in 1988 at San Francisco's Exploratorium to celebrate the famous number and mathematics in general. There Shaw worked as a physicist, with staff and public marching around one of its circular spaces, then consuming fruit pies. The Exploratorium continues to hold Pi Day celebrations^.
 

Larry Shaw-  Image from FWD

On March 12, 2009, the U.S. House of Representatives passed a non-binding resolution  recognizing March 14, 2009 as National Pi Day.


Interestingly the entire month of March 2014 (3/14) was observed by some as Pi Month. And in the next year 2015, March 14 was celebrated as Super Pi Day. It had special significance, as the date is written as 3/14/15 in month/day/year format. At 9:26:53, the date and time together represented the first 10 digits of π.

Pi - Invention and Importance 

The mathematical concept of Pi has been around for thousands of years, but it started to be known by the Greek letter only in the 1700s. Philologist William Jones began using the symbol in 1706, but it was popularized by mathematician Leonhard Euler.

Many mathematicians – from famous ones such as Fibonacci, Newton, Leibniz, and Gauss, to lesser or well-known mathematical minds – have toiled over Pi, calculated its digits, and applied it in numerous areas of mathematics.  Some spent the better parts of their lives calculating just a few digits. Here is a sampling of the many milestones in the life of Pi.

Early decimal approximations for pi were obtained in a number of different ways.  For example, in ancient Babylon, rope stretchers marking the locations of buildings and boundaries estimated pi to  be 258 = 3.125.  The ancient Egyptians determined the ratio to be (169)2 ≈ 3.16. The earliest calculations of Pi were largely based on measurement.

Archimedes, a Greek mathematician, was the first to use an algorithmic approach to calculate pi.  He drew a polygon inside a circle and drew a second polygon outside of the circle. Then he continuously added more and more sides of both polygons, getting closer and closer to the shape of the circle.  Having reached 96-sided polygons, he proved that.22371 < pi < 227.

From Archimedes’ time (about 250 B.C.E.) to the modern technological advances Pi saw many developments. Pi has now been calculated to 31 trillion digits.

As William L. Schaaf once said

 Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number pi

Some Amazing Facts about Pi

• Pi = Circumference divided by the diameter of the circle - if diameter is twisted or turned in a circuitous or spiraling manner along circumference it gives a result around 3.141592654.... times.

• The ratio Pi is same no matter how big or small the circle is.

• Pi is the most famous irrational number - a decimal that does not terminate or repeat.

• The World Record for a Computer finding the digits of Pi was made in 2013. The eight quadrillion places to the right of the decimal point!  

• If we want to print 1 billion decimal value in normal font it would stretch about 2000 Km.

• Many fractions are used as approximations of Pi

• The fraction 22/7 is accurate to 0.04025%
  

• Another fraction 355/113  is accurate to 0.00000849%

• A more accurate fraction of Pi is 104348/33215. This is accurate to 0.00000001056%

• Both π and the letter P are the sixteenth letter in the Greek and English Alphabet respectively.

• The symbol of Pi -π has been used regularly as a mathematical constant only for the past 250 years.

• Since there are 360 degrees in a circle, some mathematicians were delighted to discover that the number 360 is at the 359th digit position of Pi.

Albert Einstein - Image from nobelprize.org

• Albert Einstein was born on Pi Day 14th March 1879 in Ulm Wurttemberg, Germany.

Archimedes - Image from Britannica.com 

• Pi was first rigorously calculated by one of the greatest mathematicians of the ancient world Archimedes  of Syracuse (287- 212 B C )

• William Jones (1675 - 1749) introduced the symbol π in the year 1706 and it was later popularized by Leonhard Euler (1707 - 1783) in 1737.

• The Feynman Point is a sequence of six nines that start at the 762nd digit in the decimal sequence of pi. It was named after physicist Richard Feynman, who once stated during a lecture he would like to memorize the digits of π until that point, so he could recite them and quip .

We lost Richard Feynman on this day in 1988. Here is the fantastic Feynman point in Pi. http://t.co/N24SqyXx84 pic.twitter.com/BiRchFvOha

— Cliff Pickover (@pickover) February 15, 2014

• Hiroyuki Goto from Tokyo. He recited 42,195 decimal places from memory at NHK Broadcasting Centre, Tokyo on 18 February 1995. This set the world record at the time, which was held for more than a decade until Lu Chao beat it in 2005.   Rajveer Meena holds the record for reciting the most number of decimal places of pi. In 2015, Meena recited 70,000 decimal places blindfolded. It took him 10 hours.    

Pi appears as an important constant in many mathematical equations and it is the most recognized constant in the world.

For more facts and information about pi, visit www.piday.org.      

Observance

Pi day has been observed in various forms like eating pie, throwing pies.

 Strawberry pie 

Photo by Reuben Mcfeeters on Unsplash

Question is, why by eating a great deal of Pie!  Pies are circles, Pi describes circles, and through that we find that everything in the universe can be described with a pi(e). Other ways to celebrate this most amazing and transcendental of days (Pi is a transcendental number, look it up) is to research this number and discover all the amazing secrets it hides. Once we really get to understand the depths and complexities of it, we’ll understand why Pi day exists to celebrate a simple combination of digits.

Other-way of doing it, discussing the significance of the number π due to pun based on the words pi and pie being homophones in English and coincidental circular shape of many pies.
Here are some ways to celebrate Pi Day Top Ten Ways to Celebrate Pi Day and 25 Best Ways to Celebrate National Pi Day

 

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Mindfulness is the Tool for Anxiety and Stress Relief

Mindfulness is the act of consciously focusing our mind in the present moment, without judgement and without attachment to the moment.

 Photo by Vlad Tchompalov on Unsplash

Overview 

In today's world we all think too much, seek too much, want too much, as Eckhart Tolle once stated, and forget about the joy of just being. So many of us find it increasingly difficult to focus just one thing at a time. When we do not have sufficient time, our technological devices enable us to be in multiple places all at once. But it comes with a cost. Modern technology has split our concentration into smaller bits, scattering them in many directions. As we have become more habituated with technology, we also seem to have lost our ability to live in the present - a place where we actually want to be without stress and distractions. Although we can connect with just about anybody with a touch of a finger, we often find ourselves unable to engage in genuine, one-on-one communication. On one hand, technology has made us more efficient and productive but, on the that, we find that our attention is scattered and our life marked by stress and complications. Consequently, we are not always mindful when we are communicating with ourselves or with others.

Mindfulness

So what exactly is mindfulness ? It is the act of consciously focusing our mind in the present moment, without judgement and without attachment to the moment. It can help us become more aware of what is going on for us both internally and externally. We become more present to the here and now. Jon Kobat Zinn defines mindfulness as the

awareness that arises by paying attention on purpose, in the present moment, and non-judgmentally.

According to  Thich Nhat Hanh, the term mindfulness refers to

keeping one's consciousness alive to the present moment.

Mindfulness and Stress Relief

A secular practice of mindfulness has entered the mainstream across the world in recent years, it has its roots in ancient Hindu and Buddhist tradition as a means of calming the mind and gaining insight into the impermanent and interdependent of the self. In last four decades (Modeled after the Mindfulness-Based Stress Reduction program created in 1979 by Jon Kabat-Zinn to help counter stress, chronic pain, and other ailments, mindfulness courses) thousands of studies have documented the physical and mental health benefits of mindfulness in general and inspiring countless programs to adapt various models for schools, prisons, hospitals, veteran centers and beyond.

Suzanne Westbrook , retired professor and internal-medicine doctor at Harvard University says,

Our mind wanders all the time, either reviewing the past or planning for the future.Mindfulness teaches you the skill of paying attention to the present by noticing when your mind wanders off. Come back to your breath. It’s a place where we can rest and settle our minds.

Jeanne Mahon, Director of the Wellness Center of Harvard University says,

We were tasked to find ways for the community to cope with stress. And at the same time, so much research was coming out on the benefits of mindfulness and meditation.

We keep offering mindfulness and meditation because of the feedback. People appreciate to have the chance for self-reflection and learn about new ways to be in relationships with themselves.

Practicing mindfulness improves both our physical and psychological wellbeing resulting in positive changes in our health, attitudes, and behavior.  Photo by Jared Rice on Unsplash

There are also numerous books written by experts on mindfulness that show us ways how to live in the present  moment with ourselves and with others. This is accomplished by engaging in different kinds of meditation techniques which emphasize the cultivation of keen awareness to experiences in present moment without any kind of analysis or interpretation.or having any kind of attachment to a particular outcome. 


Psychologists and neuroscientists have helped to bring the practice of mindfulness meditation into mainstream medicine, demonstrating that practicing mindfulness improves both our physical and psychological wellbeing resulting in positive changes in our health, attitudes, and behavior. According to these experts, mindfulness techniques benefit us in a number of important ways; it helps relieve stress, lowers blood pressure, reduces chronic aches and pains, helps with sleep, reduces gastrointestinal problems, and finally mindfulness is good for our heart.

Mindfulness' acceptability and popularity has been bolstered by a growing body of research showing that it reduces stress and anxiety, improves psychological wellbeing.  Sara Lazar, a neuroscientist and assistant professor of psychology at Harvard Medical School (HMS) and assistant researcher in psychiatry at Massachusetts General Hospital, documented that mindfulness meditation can change the brain’s gray matter and brain regions linked with memory, the sense of self, and regulation of emotions. New research by Benjamin Shapero and Gaëlle Desbordes is exploring how mindfulness can help depression.       

The pioneer of scientific research on meditation, Dr Herbert Benson, extolled its benefits on the human body — reduced blood pressure, heart rate, and brain activity — as early as 1975. He helped demystify meditation by calling it the “relaxation response.” Benson is director emeritus of the Benson-Henry Institute for Mind Body Medicine at Massachusetts General Hospital and Mind/Body Medicine Distinguished Professor of Medicine at HMS.

Relaxation Response

The response is defined as our personal ability to encourage our body to release chemicals and brain signals that makes our muscles and organ slow down and increase blood flow to the brain.

Photo by Ralf Skirr on Unsplash -
Buddha statue in the mist. Bana Hills, Vietnam.

Dr Herbert Benson can be largely credited for demystifying meditation and helping to bring it into the mainstream by renaming meditation the Relaxation Response. His studies in the 1960s and 1970s were able to show that meditation promotes better health, especially with individual with hypertension. People who meditate regularly enjoy lower stress levels, increased wellbeing, and even are able to reduce their blood pressure levels and resting heart rate.

The Relaxation Response is essentially the opposite reaction to flight-or-flight response. According to Dr Benson Relaxation Response is beneficial, as it counteracts  the physiological effects of stress and the fight-or-flight response.

  

                                
Learning the Relaxation Response is a great skill that can help us to be better equipped to deal with life's unexpected stressors, heal ourselves, and achieve better health.  

Ongoing Popularity of Mindfulness in the field of Work-Life balance

Since mindfulness has so many important benefits for us, whether they are connected with our physical or emotional wellbeing, mindfulness training has certainly become tremendously popular in the United States and other parts of the world. Companies like Adobe, Amazon, Ford, General Mills, Google, Target, Goldman Sachs, to name a few, have all instituted mindfulness training for their employees so that they are healthier, less stressed and more focused on their jobs. Mindfulness experts are also training CEOs and higher officials of major corporations on mindfulness techniques.

Business Leaders who practice mindfulness report that they now perceive issues more objectively, they can form deeper relationships that are empathic, and they are not driven by their ego and pride as they learn to be humble.

The goal of mindfulness is to always be in the present moment.

 Photo by Thomas Griesbeck on Unsplash

These business leaders often mention that they are also more productive, more creative in solving problems, more satisfied with their jobs and are less stressed in challenging situations.

How to practice Mindfulness ?

Although there is actually more than one way to such practice, the goal of mindfulness is to always be in the present moment. This is achieved by focusing on our breathing as we meditate. When we meditate, we pay attention to the thoughts and sensations that distract us but we  do not fight them. Nor do we pass any judgement on them. We just observe these thoughts and sensations and go back to focusing on our breathing again. Our goal is to allow our mind to refocus on the present.

Out of some mindfulness technique the four approaches can be rounded up to begin with.

Thoughts

The key point mindfulness is to be aware of what is happening in the present moment without passing judgement on that awareness. It is normal for our mind to stay active during meditation but we must try to observe our thoughts like clouds passing by, and return our focus on breadth.

Body Sensations

Paying focused, non-judgemental attention to the subtle sensations in our body as an itch or tingling and likes and let them pass. We must stay focused on the sensations.

    

Sensory

Here we practice observing sights, sounds, smells, tastes, and touches. We name the 'sight', 'sound', 'smell', 'taste' or 'touch' without judgement and let them go.
Whatever it is, zero in on the tone and quality with intention. Music can also be a useful focus in mindfulness meditation, with additional benefits like energizing us in the morning or relaxing us at night. The key is to find what works for us. Some people might find that a quiet room is what works best for them, while others might find that focusing on their favorite music is the most effective.    

Emotions

In this mindfulness technique, we allow emotions to be present without judgement. We practice a steady and relaxed naming of emotions such as 'joy' , 'anger', 'frustration' while accepting the presence of the emotions without judgement and letting them go.



It has been observed in various studies  that under stress and anxiety our eating patterns affect very easily. Under this condition we tend to eat less or eat heavily.  When stressed, people often instinctively use their sense of taste as a stress reliever, whether they're munching mindlessly or satisfying sweets cravings brought on by cortisol. But the sense of taste can be a healthy, effective complement to mindfulness exercises.

The focus is on being present during the meal. This supports healthier eating because the mind and body are more aware of the process

 Photo by Angelos Michalopoulos on Unsplash

             
Mindful eating involves slowing chewing, putting down your fork between each mouthful, and being aware of the tastes of what you are eating. During mindful eating, avoid being distracted by any type of screen, whether its a television or mobile device. The focus is on being present during the meal. This supports healthier eating because the mind and body are more aware of the process. Doing this can also help prevent overeating because we are more aware of when we are truly full versus just mindlessly eating. By focusing on the taste of food, the experience of eating, and the sensations of our body, we will feel satiated sooner.

Final Thought

While all this may seem to be a new-age approach to our holistic wellbeing, hard medical evidence demonstrations that we can train our brains to function differently and that brains can adapt and rewire. This phenomenon, known as neuroplasticity, suggests that there are concrete and provable benefits to exercising the brain by engaging in mindfulness. It is precisely because of this scientific component that mindfulness has gained traction with people who might otherwise this to be spiritual  bewilderment.   

Since the key to developing a strong mindfulness practice is consistency, it's best to try a variety of techniques and find the method or methods that work best for us. Any technique that allows us to focus on the present can help you practice mindfulness. Remember that we don't need a fancy setup—look to nearby sounds, sensations, tastes, and our own mind and body to help alleviate stress and increase relaxation. Adding moments of mindfulness to our everyday activities can help us incorporate this meditative technique into our daily routine.

And finally, of course, most of us will never have the capacity to meditate at the level of a monk. But neuroscientists seem to be convinced that there is hope for far less experienced meditators because by engaging in mindfulness meditations they will have more capacity for a working memory, more focused attention and  less stress in their lives.

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