MatheStatica

It’s March 14 (3.14) – Happy ‘Pi day’!

Today’s date resembles 3.14159, the common approximation of the mathematical constant Pi, or π. This concurrence has given rise to an annual celebration from 1:59 pm - also the time of publication of this post (CET).

What is Pi? Understanding Pi is essential if you want to make calculations for circles, cylinders, spheres, and anything circular, even an ellipse. Pi is the ratio of the circumference of a circle to its diameter. It doesn't matter how big or small the circle is - the ratio stays the same. Properties like this that stay the same when you change other attributes are called constants.

Photo: Pi Pie from TU Delft University of Technology, via Wikimedia Commons.

I am the very model of a self-recursive modeler

I am the very model of a self-recursive modeler
My consciousness encompasses itself in many meta layers


To Russel’s paradox, I have the set of all the answers
I cut the hair of all the non-self-barbering hairdressers


I think about me thinking of my thoughts with regularity
In my Cartesian theater, I see myself with clarity


I tell you that I lie without the slightest contradiction
The story of my life is told in meta-metafiction


My inner simulator replicates the total universe
I simulate myself as I am writing out this line of verse


My secrets are unknown to me, I keep them confidential
Referring to myself I’d say I’m quite self-referential


My strange loop’s Escherer than yours, it’s Bacher and it’s Godeler
I am the very model of a self-recursive modeler

Poem by: Jacob Falkovich (https://putanumonit.com/2018/08/28/very-model/)

I am the very model of a self-recursive modeler I am the very model of a self-recursive modeler My consciousness encompasses itself in many meta layers

Complete leaderboard till Week #4.

Precise.

A rookie mistake in propositional logic is to use the truth of statements ‘b’ and ‘a implies b’ or ‘a=>b’ to conclude the truth of statement ‘a’. It seems stupid, but many math undergraduates end up making this mistake, whether inside the classroom or outside. 😛

Here we see poor Raj demonstrating a classic example of this fallacious reasoning. Don’t be like Raj.

Idea credits: Shreyash Tiwari and Harsh*t Bisht

Complete leaderboard till Week #3.

Complete leaderboard till Week #2.

Week #2

The first edition of the IIM-I Football league has just ended, and the points table looks like the picture below.

Our IPM Chair missed all but the last game, where the IPM team had beaten the PGP team by 3 – 0. It struck him that it might be possible to find the scores in the other five matches from the above table. Can you help him out to determine the results of the other matches?

Deadline: Sunday (12th August 2018)

Week #1 Problem

While searching his father’s attic, Hugo finds a solid cube circumscribed by a sphere. A note accompanying the same poses an interesting challenge. Hugo has to cut the cube into a finite number of rectangular parallelepipeds and use smaller spheres to circumscribe them, in such a way that the volume of the circumscribed sphere of the cube is equal to the sum of the volumes of all spheres circumscribed to the parallelepipeds.

Show that the only possible way for Hugo to achieve the target is to cut the cube into smaller cubes.

Answers to be taken through email only. (Deadline: 5th August'18)