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Mathematics

What Happens When Projective Geometry Meets Information Theory? (I)

Published on August 14, 2022 by Hemanth

What Happens When Projective Geometry Meets Information Theory? (I) - An illustration of a mars drone on the top left. On the bottom left, there is an illustration of a Fano plane (explained later in the essay). On the right, there is a portrait of Claude Elwood Shannon.
When Projective Geometry Meets Information Theory, you get to pilot a mars drone. The geniuses of Claude Shannon, Richard Hamming, and Gino Fano save the day!
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Can You Really Solve This Tricky Logic Puzzle?

Published on August 10, 2022 by Hemanth

Can You Really Solve This Tricky Logic Puzzle? - An illustration showing Matt - a human being on the left, Can - A puppy at the centre, and Cheat - a robot on the right. All three of them are seen saying "HELLO!" together.
I recently came across a tricky logic puzzle that made me think and engage. If you are into logical thinking and problem solving, this puzzle is for you!
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How To Do Basic Math Operations Using Only Ruler And Compass

Published on August 9, 2022 by Hemanth

How To Do Basic Math Operations Using Only Ruler And Compass - An illustration showing what appears like a cartesian plane with measurements being made using a compass to mark two line segments on the positive horizontal axis and the positive vertical axis.
Why do basic math operations using only ruler and compass? Well, this challenge serves as a precursor to understand Euclid's Demons - more profound mathemaics!
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How To Actually Make Parallel Lines Intersect

Published on August 5, 2022 by Hemanth

How To Actually Make Parallel Lines Intersect - An illustration showing two lines: A and B at an angle to each other meeting at a common intersection point. Below them, the following text is written: "Are A and B parallel?"
How can parallel lines intersect? That sounds absurd, right? Except, it turns out they can in a projective plane! Read the essay to find out more about this.
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Puzzles: How To Use Them To Improve Brain Performance?

Published on August 4, 2022 by Hemanth

Puzzles: How To Use Them To Improve Brain Performance? - Three illustrations: the first shows a cross-word-like puzzle. The second illustration shows six sheets of A4 paper. And the third illustration shows a glass of wine on top of a sheet of A4 paper.
This essay covers the neuroscience behind puzzles. On top of this, you get to solve three bonus puzzles. Each of these puzzles activates a specific brain area!
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I Accidentally Almost Started A Business. Here is What Happened.

Published on August 1, 2022 by Hemanth

I Accidentally Almost Started A Business. Here is What Happened. - An image showing the word "Business" written in bold letters, followed by a full stop. The letter 'B' and the full stop are in black, while the rest of the letters are in pink.
I almost started a business simply by solving a problem. My solution gained popularing with zero advertisiting - a live case study for entrepreneurs!
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Variance: The Reason Why Rich Get Richer And Poor Get Poorer

Published on July 30, 2022 by Hemanth

Variance: The Reason Why Rich Get Richer And Poor Get Poorer - An illustration showing a see-saw, where a stick figure is anxious on the higher end and another stick figure is happy on the lower end. Money from the anxious stick figure rolls down the see-saw into the seat of the happy stick figure. This metaphorically depcits how the rich get richer and poor get poorer.
This essay explains why you need to worry about variance when it comes to financial decisions. It covers the math and psychology behind gains and losses!
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St. Petersburg Paradox – How To Actually Price Uncertainty?

Published on July 27, 2022 by Hemanth

St. Petersburg Paradox - How To Actually Price Uncertainty? - A portrait of Daniel Bernoulli on the left (image from WikiCC), and a portrait of Gabriel Cramer on the right (image from WikiCC) - image further edited by the author
The St. Petersburg paradox represents a landmark in applied mathematics history. It challenges expected value theory and is a precursor to ergodicity theory.
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Symmetry: How To Really “See” It?

Published on July 21, 2022 by Hemanth

Symmetry: How To Really "See" It? - An illustration showing a duck with its beak pointing towards the left and tail pointing towards the right. It is labelled "Duck-Rabbit". The Duck says, "Rotate me 90° clockwise." When you rotate the duck clockwise 90°, it appears to become a rabbit.
Learn all about symmetry in this essay from simple illustrations. To test your knowledge, there is also a fun bonus puzzle waiting for you at the end!
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How To Really Solve This Tricky Algebra Problem (VII)

Published on July 20, 2022 by Hemanth

How To Really Solve This Tricky Algebra Problem (VII) - (a*b*c*d*e) = (a+b+c+d+e); Fine the max. possible value of max{a, b, c, d, e}. (a, b, c, d, e) belong to the set of all positive integers.
The Tricky Algebra Problem Series celebrates the joy of algebra! Problems range from beginner to advanced levels.This one is a math olympiald level problem!
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