pi

Consider the following situation. A regular polygon of n sides is placed symmetrically inside another regular polygon of n sides i.e. with corresponding sides parallel and with a constant distance between them. We now have a 'path of uniform width' running around the inner polygon. Now the following is asked: By how much does the perimeter of the outer polygon exceed that of the inner.

I write this to tell myself that it was not a dream...

This year I taught a bunch of fifth standard kids in Sahyadri School KFI (Krishnamurti Foundation India), who, like all others of their age, were high-energy kids; they were willing to explore but found it difficult to sit down in one place. I had a great relationship with them. The air in the classroom was of love, trust and wonder!

Celebrating Pi day with one more compilation of videos dedicated to it. Prof James Grime features in this Numberphile video titled Pi is beautiful.

In this video Prof Grime shares a true story madness of how pi was almost certainly changed to 3.2!

The ratio of a circle's circumference to its diameter is always the same: 3.14159... and on and on (literally!) forever. This irrational number, pi, has an infinite number of digits, so we'll never figure out its exact value no matter how close we seem to get. Reynaldo Lopes explains pi's vast applications to the study of music, financial models, and even the density of the universe.

Like many heroes of Greek myths, the philosopher Hippasus was rumored to have been mortally punished by the gods. But what was his crime? Did he murder guests or disrupt a sacred ritual? No, Hippasus's transgression was mathematically proving the hitherto unprovable. Ganesh Pai describes the history and math behind irrational numbers in this TED Ed lesson. 

Here are some activities we compiled it for you that introduce & explore the beauty & universality of pi. Try this today, and celebrate World Pi Day.

1. Take any circlular of your choice. Draw 4 of them next to each other as shown. 

Pi - the irrational, nevertheless mathematical, constant and “celebrity number” (as Alex Bellows puts it) is an intriguing & insπring number that has enthralled mathematicians for centuries.
How can I show this to the uninitiated?
 

..and other rational approximations to π

In this article, the writer will explain a method to find rational approximations for and other irrational numbers. The key idea here is to use a calculator to find what is called a continued fraction for an irrational number.

A poem on the imaginary number i by Punya Mishra

Read about Numberphile - a website where you will find videos about numbers and other stuff, reviewed by Rajkishore Patnaik.

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