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Monday, July 1, 2024
Tautochronous tanks
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Toricelli's law states that the velocity of a discharge, say $v$, located at the bottom of a tank filled to a height $h$ is $v=\sqrt{2g...
Saturday, May 18, 2024
A nice Geometric Optimisation Problem - Part 2
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This post picks up where we left earlier . In addition to the centre of circumcircle of $\triangle KDL$, the midpoint of the segment $KL$ al...
A nice Geometric Optimisation Problem - Part I
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Consider two circles of different radii intersecting at $B$ and $D$. If we now draw a line $KL$ through $B$ as shown in the following figure...
Saturday, March 2, 2024
Summing Uniform random variables to reach a target sum
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The problem of finding the expected number of standard Uniform variables to get a sum greater than 1 is quite famous. In this post, we deal ...
Saturday, December 30, 2023
Is $e$ less than $(1+\sqrt{21})/2$?
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One of my friends recently posed the problem of finding the expected number of uniform random variables needed to get a sum greater than $1$...
A nice property on the recurrence of Eulerian Numbers
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I was recently looking at Eulerian numbers for a problem and I noticed a nice, and probably lesser/never known, property on their recursive ...
Sunday, December 24, 2023
The Rounding Error Conundrum
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Like all managers, I too, from time to time, will be in a position to present a bunch of numbers in an Excel Sheet. To bring clarity to the ...
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