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Post Archives from the ‘Interesting Articles’ Category

Elastic collisions and \pi

Posted on: January 17th, 2013 by

Here is a surprising relation between elastic collisions and \pi: Start with a large ball of mass 16*100^N kg. on the very left, a small ball of mass 1 kg. to it's right and a wall to the very right. Send the large ball towards the small ball with an initial velocity u_0. The small ball will keep bouncing back and forth between the large ball Continue reading the story "Elastic collisions and \pi"

IIT-Madras ready for mass production of artificial blood - The Times of India

Posted on: January 16th, 2013 by
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IIT-Madras scientists have blood on their hands — and nobody is complaining. A team of scientists from the department of engineering design has been successful in creating enough red blood cells from stem cells to be used as 'artificial blood' in people who need transfusion. Having proved their oxygen-carrying capacity, the RBCs will now go into 'mass production' before starting human trials in three years, scientists Continue reading the story "IIT-Madras ready for mass production of artificial blood - The Times of India"

Benford's law

Posted on: January 14th, 2013 by
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Benford's law is an interesting anomaly regarding the distribution of the first digit in a collection of data. "Now, we have noted elsewhere that by definition the first digit of a decimal number cannot be a zero.  That leaves nine ciphers, though, and one might expect each of them to appear about one out of nine times in that first position.  For each, about 11% would make sense.  Continue reading the story "Benford's law"

Simple proofs of the Isoperimetric Inequality

Posted on: January 12th, 2013 by
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The isoperimetric inequality states that "Among all planar shapes with the same perimeter the circle has the largest area." Here is the simplest geometric proof that I know of: http://www.cut-the-knot.org/do_you_know/isoperimetric.shtml There are other proofs too: http://cornellmath.wordpress.com/2008/05/16/two-cute-proofs-of-the-isoperimetric-inequality/ and http://forumgeom.fau.edu/FG2002volume2/FG200215.pdf Acknowledgement: Thanks to the late prof. Thomas Cover for pointing out a simple proof. Let me know if any of these proofs  can be extended to dimension 3 or higher dimensions.

Trisection of an Angle via Origami

Posted on: January 8th, 2013 by
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Angle trisection is another of the classical problems that cannot be solved using a compass and unmarked ruler but can be solved using origami. This construction is due to Hisashi Abe. via Mathematics of paper folding - Wikipedia, the free encyclopedia. To prove that angle trisection cannot be solved using an unmarked ruler and a compass, one must invoke Galois theory. What's interesting however is that Continue reading the story "Trisection of an Angle via Origami"

Steiner points

Posted on: January 8th, 2013 by
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Suppose there are 4 cities, each city located at the vertex of a square having a side of unit length. What is the smallest road network that can connect all 4 cities? The solution is explained very well in this video: The following article also gives more insight on Steiner points: http://www.unige.ch/~gander/Preprints/BDM56-GanderE.pdf

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