God has given us the fascination and mystery of irrational numbers, as one aspect of a rich world. 

~ Vern Poythress

And then there is Pythagoras. The legend is that the founder of theoretical mathematics was so outraged when one of his students, the haplessly gifted Hippasus, discovered irrational numbers that he sent the poor fellow out on a raft to drown, initiating a venerable tradition of professors mistreating their graduate students.

~  Rebecca Goldstein

The title of this episode of LUMS Math Circles was "Continued Fractions and Rational Approximation." Dr. Arif Zaman and Dr. Imran Anwar demonstrated continued fractions and their applications. Students were astonished to know that these fractions can be used to approximate transcendental numbers. It was magical to see the wonderful reactions of the kids during this session.

Participants learn the art of constructing Stern–Brocot sequence is a binary process to produce all possible fractions. Participants learn the art of approximating an irrational number through continued fractions. A technique that lies at the core of analysis and approximations. Dr. Zaman elaborated on these expansions and discussed emerging patterns with intricated reasoning. 

Here are some highlights from the event:

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Instructors: