irrational number

In this article, Shailesh Shirali begins with a seemingly simple question but develops the answer into not one, but four different proofs! While the content focuses on mathematics that has many applications, some of which are mentioned here, the multiplicity of proofs is an added draw, helping the teacher to illustrate innovative ways of thinking and connections across approaches.

If a function is such that its derivative is the function itself, then what would it be? Some interesting mathematical objects appear while trying to answer this question, including a power series, the irrational number e and the exponential function ex. The article ends with a beautiful formula that connects e, π, the complex number i = -1, 1 and 0

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. 

In this presentation, Swati Sircar from Shikshamitra demystifies recurring decimals - it hints which type of fractions generate them, how they are written and how to convert them to fractions.

The thumbnail cartoon is from Snodgrass.

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. 

The problems in this set are adapted from the Romanian Mathematical Competitions, 2014. Also find solutions to the problems in the November 2014 issue.

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?
 

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