Details for Article #1

2014-Mar-12** Happy Pi Day - March 14th!** (*H. Chapman*) Desc: The Magical Pie

Happy Pi Day − March 14th!
Hi, everyone! Thought I'll write an article for this otherwise rather barren blog. Seeing that the next date of interest is the 14th of March and the day references a cryptic number of practical and transcendental applications, I have chosen to write a Update: I have just found out that this is Einstein's birthday (Mar. 14, 1879 - Apr. 18, 1955)! What a great coincidence!HC ( March 28, 2014)Just to put things in context, this article is strictly limited to the mathematical usage of pi. As such, I think it's worthwhile to define the mathematical usage first, so that the rest of the article can be understood within this context. Pi is the literal symbol that represents the ratio of the circumference of a circle to its diameter. This ratio is a constant − meaning that the ratio remains the same for all circles, doesn't matter if we take a small circle or a really big one. The ratio when expressed numerically is a real number, an irrational number and also a transcendental number. Since it is an irrational number its exact value cannot be computed so we only have an approximation for this ratio. This approximation is the standard textbook 22/7 that we have all studied in school or 3.14… in its decimal representation. It is this value that is represented by the literal symbol pi, so much so that we commonly say that "pi is 22/7", and almost always take it that pi is a synonym for 22/7. ( I'm not complaining, 39 digits are fine by me!)Apart from the decimal fraction representation, the approximate value of pi can also be expressed as a common fraction as 22/7 which gives a value of 3.142857 (that is, correct to 2 decimal places) or the less common 355/113 which gives a value of 3.14159292 (that is, correct to 6 decimal places). OK, so we know that pi represents the ratio of the circumference of a circle to its diameter, and that the value of this ratio is an irrational constant number approximating 3.14159…. So?? There are many, surely thousands of, values that are used in science and mathematics. These others are given short shrift in comparison to the fame of pi. Why? The reason for pi's popularity is that it is Nature's pet! Scientists and mathematicians are amazed at the regular appearance of the value of pi in almost every aspect of the natural world. All measurements associated with circles (and derivatives thereof) require the involvement of this number. It is quite magical in the manner in which it pops up in the most unexpected of contexts. It is this magicality (nay, mysticality is a better way of expressing it) that has attracted such phenomenal recognition of the value denoted by pi. And yet it is simplicity itself… Do you want to find out the value of pi yourself, firsthand? Absolutely simple! All you need is a round can, a piece of string, and a measuring tape. Wrap the string around the can just once (as exactly as you can) − the length of the string that completes one circuit of the can is the circumference of the can. Measure it with the measuring tape. Next measure the diameter of the can by spanning the top (or bottom) of the can with the measuring tape. Armed with the circumference and the diameter whip out your handy-dandy pocket calculator (any self-respecting cellphone has a calculator utility built-in!) and do the division. Repeat the experiment about ten times and compute the average of all the results. The answer should be in the region of 3 point something. There! That's how you get the value of pi! Want to refine the value of pi? Just repeat the steps above with a simple variation − wrap the string around the can 10 times to get the circumference magnified by a factor of 10. Divide this magnified circumference by the diameter and then divide the answer by 10. This should produce a better approximation of pi. Taking a larger can helps − try one with a diameter of 4" or more. Remember when you were given your first geometry set (box)? One of the first things a kid does is to draw a "flower" using the pair of compasses that comes with the set. Simply open up the compass to a suitable "radius" and draw a circle. Then (with the same radius) place the point of the compass on the circumference of the circle and draw an arc between any two arbitrary points on the circumference of the circle. This arc will intersect the circle at two new points. Using any one of the "new" points as the center, repeat the process of drawing an arc as before. This will produce a "flower" inside the original circle. Count the number of "petals" of this "flower" − six! This means that the circumference of the circle is 6 times the radius of the circle or, in other words, the circumference is 3 times the diameter (since the radius is half the diameter). But 3 is not pi! Or, is it? Well, actually if you proceed carefully you will notice that when you draw the arcs progressively the final intersection will not align exactly with the starting point − it will be a little short. This means that the circumference is a tad more than 6 times the radius and hence a tad more than 3 times the diameter. That difference is what makes pi irrational! I leave it up to you to find that difference! Archimedes (that's the 3rd century BC!) used a similar method to get the ratio. He drew a regular polygon and summed the lengths of all the sides to get the circumference approximating the circle around the polygon. He found that the value of the ratio lay between 223/71 (3.14084) and 22/7 (3.14285) with a 96-sided polygon. An excellent approximation! A Chinese mathematician of roughly the same era determined that the ratio lay between 3.141024 and 3.142708 with a 192-sided polygon. Phew! A 12-sided polygon. The circle is in black, the polygon is in red. A 24-sided polygon. The circle is in black, the polygon is in red. Note how the 24-sided polygon approximates the circle better than the 12-sided polygon above. Please note that the diagrams shown above are meant to explain the basic concept behind the method. The accuracy can be enhanced by increasing the radius of the circle. However, it is impractical to draw really big circles on paper. Instead, the ancients used geometrical algorithms to perform the computations. ## Approximations of pi through the ages
The ratio of the circumference to the diameter was known to the ancients, even as early as the 19th century BC, but this we surmise from the monuments that they built and from mostly indirect references. Wikipedia informs us that the Babylonians took the ratio to be 25/8 (3.12). The Egyptians used 256/81 − the square of (16/9), or (4/3) squared twice − approximating to 3.16. In the 9th century BC, the Indian mathematician Yajnavalkya used 339/108 (3.13888). Then came Archimedes (as described above) and Ptolemy (2nd century BC) with 377/120 (3.1416) − that's as close as they come! ## In A Lighter Vein…
"How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics."
One
A Poem
A RavenMidnights so dreary, tired and weary, Silently pondering volumes extolling all by-now obsolete lore. During my rather long nap - the weirdest tap! An ominous vibrating sound disturbing my chamber's antedoor. "This", I whispered quietly, "I ignore". Perfectly, the intellect remembers: the ghostly fires, a glittering ember. Inflamed by lightning's outbursts, windows cast penumbras upon this floor. Sorrowful, as one mistreated, unhappy thoughts I heeded: That inimitable lesson in elegance - Lenore - Is delighting, exciting...nevermore.
The whole effort (3835 words = 3835 digits!!!) is named " On that note, I'll just wave goodbye to y'all! Take care and have yourself a happy pi day! H. Chapman12th March, 2014 |

Alright, folks! Let's have your inputs on the article!**editor@angloindian.chapmanhilton.com**

Want to say something? Just do it...

Promotions

This area is reserved for promotional messages by members of the AIAIA (Jaipur Branch)

The promotional messages (text only, please!) will be displayed without fee or charge, purely at the discretion of the site's manager.

This area is reserved for promotional messages by members of the AIAIA (Jaipur Branch)

The promotional messages (text only, please!) will be displayed without fee or charge, purely at the discretion of the site's manager.

Return HOME from this page.

Back to Stories & Articles

Active Sections

Obituaries. <<<—NEWLost & Found Deptt.

Congratulations!

Stories & Articles

Sections under consideration

The AI Association (Jaipur Branch)Directory

Family Trees

Histories

Talent, Young and Not-so-young!

News and Views, Rants and Raves

Stories and Articles

Music! Music! Music!

Spotlight

Grandma's Tips & Tricks

Potluck (or How To Toast Water (without really trying!))

Party Games and Generally Fun Activities

A Whiff of Nostalgia (or A Walk Down Memory Lane (or Memories Are Made Of This!))

For Those Who Are Absent (But Linger In Our Hearts Always)!

Tutorials

Helpline

Letters to Edie

4Toes

Sections under consideration

The AI Association (Jaipur Branch)Directory

Family Trees

Histories

Talent, Young and Not-so-young!

Congratulations!

News and Views, Rants and Raves

Music! Music! Music!

Spotlight

Grandma's Tips & Tricks

Potluck (or How To Toast Water (without really trying!))

Party Games and Generally Fun Activities

A Whiff of Nostalgia (or A Walk Down Memory Lane (or Memories Are Made Of This!))

For Those Who Are Absent (But Linger In Our Hearts Always)!

Sympathies & Condolences

Tutorials

Helpline

Letters to Edie

4Toes

"Friend"-ly (AI) sites!

If you have a site (**and** you're an *Anglo-Indian*) just send us your website's address and we'll include it right here!

No charges! ... but at the discretion of this site's manager!

**All contents (textual and photographic) are copyright and may not be used publicly without the express permission of the owners of said copyright.**

Phew! Boy, was that tough to say... but say it we did (mainly at the urging of our legal advisor!) and that's done with.

The statement of copyright is necessarily necessary and we do hope you honour and respect the copyright. All of the material on this website is of great sentimental and emotional value to their respective owners; and we sure do appreciate your cooperation in respecting their ownership privileges. Just because a photograph's been posted on the 'Net does not mean that it can be trivialised by indiscriminate copying! The same goes for the textual matter on this site. So, please, do drop us a line before you lift any material from this site.

Contact: me@angloindian.chapmanhilton.com**Jaipur, April 15, 2013**

Editor:

**Mrs. T. R. Castellas***editor@angloindian.chapmanhilton.com*

Site managed & maintained by *H. Chapman*

Site best viewed at 1280 x 768 screen resolution

Site policy: *no gimmicks, no frills, no flash, no javascript, no cookies, no virus, no malware, no hacks, no link farms!***Site hosted on: www.agBargainHosting.com**