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Mathematics

How To Actually Solve The Königsberg Bridge Problem?

Published on June 9, 2022 by Hemanth

The Königsberg Bridge Problem - An illustration showing seven brdiges connecting four landmasses. Island 1 (centre) is connected to the upper bank (north) and the lower bank (south) via two bridges each. Island 1 and Island 2 (east) are connected by a bridge. Island 2 is connected to the upper bank and the lower bank via one bridge each.
The Königsberg bridge problem started as a logic puzzle to the city's residents. It laid the foundations for new math fields such as graph theory and topology!
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How To Really Solve The Kissing Circles Puzzle

Published on June 8, 2022 by Hemanth

How To Really Solve The Kissing Circles Puzzle - An illustration where on the left, three bigger circles (circles 1, 2, and 3) enclose a smaller circle (circle x), and on the right, one bigger circle (circle x) encloses three smaller circles (circles 1, 2, and 3).
I first came across the kissing circles puzzle when I was studying the topic of hyperspheres. The puzzle as such is quite simple, but it has profound insights!
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How To Really Solve This Tricky Algebra Problem? (IV)

Published on June 6, 2022 by Hemanth

How To Really Solve This Tricky Algebra Problem? (IV) - An image showing the following equations on the left: x² + y² = 7 and x³ + y³ = 10. On the right, the following equation is written: x + y = ??. Below this equation, the following information is provided in a box: x,y ∈ ℝ.
Welcome to the fourth entry in the tricky algebra problem series. In this entry, you get to solve a fun and challenging math olympiad level algebra problem!
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Big Tech Using Big Data For Perfect Prediction/Spying A Lie

Published on June 4, 2022 by Hemanth

Big Tech Using Big Data For Perfect Prediction/Spying A Lie - An illustration showing a stick figure on the left with a smartphone. The stick figure seems to be smiling as it is texting. Labelled above the stick figure is the text "You". On the right, a much bigger stick figure seems to be using a telescope to spy on what the smaller stick figure is typing. Labelled above this stick figure is the text "Big Tech".
The notion of big tech using big data to predict human behavior remains an ethical concern. This essay covers the mathematics behind such prediction technology.
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How To Really Understand Order Of Operations

Published on June 2, 2022 by Hemanth

How To Really Understand Order Of Operations - An image with the following question: 12 ÷ 4 (1 + 2) = ?? Below this equation, the following text is written: "PEMDAS/BEDMAS/BODMAS"
Order of operations is a fundamental math concept that kids learn at school as BODMAS/PEMDAS. But if you blindly follow PEMDAS/BODMAS, you are taking a risk!
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Randomised Statistical Trials Are Not Always The Best Option

Published on June 1, 2022 by Hemanth

Randomised Statistical Trials Are Not Always The Best Option - An illustration showing a balance, where "Human Ethics" is written on the left weighing scale, whereas "Scientific Rigour" is written on the right weighing scale.
Randomised statistical trials are the norm for scientifically rigorous statistical tests. But what do you do when scientific rigour causes an ethical conflict?
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How To Really Choose Between Favourite Experiences And Trying New Ones?

Published on May 31, 2022 by Hemanth

How To Really Choose Between Favourite Experiences And Trying New Ones? - An illustrative image where on the left, a restaurant named "Favourite Restaurant" is open and on the right, a restaurant named "New & Trendy Restaurant" is open. In the middle, a stick figure is seen undecided between the two restaurants with a bubble dialogue of "?"
Every day in life, you are faced with situations where you have to choose between favourite experiences and new ones. This essay uses science to solve this!
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Why Is Negative Times Negative Really Positive?

Published on May 28, 2022 by Hemanth

Why Is Negative Times Negative Really Positive? - An image showing the following equation inside a box: (-1)*(-1) = +1. Below this box, the following text is written "BUT Why??". "BUT" is in pink whereas "WHY??" is in black.
Negative times negative is positive. Everyone learns this in school and accepts it as truth. Yet, when you ask "why", insecurity floods in. Let's change that!
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How To Really Understand The Concept Of An Algorithm?

Published on May 25, 2022 by Hemanth

How To Really Understand The Concept Of An Algorithm? - An illustration that shows a stick figure on the left with the dialogue bubble: "I have a problem!" This points to → A box that says "Do this first." → Then, a box that says "Then, do this." → Then, a box that says "Finally, do this." → This points to another version of the same stick figure from before with the dialogue bubble: "Problem solved!"
When you think of the word “algorithm”, you are likely to associate it with computers or computer science. But algorithms go well beyond computers and tech!
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How To Really Avoid P-Value Hacking In Statistics?

Published on May 24, 2022 by Hemanth

How To Really Avoid P-Value Hacking In Statistics? - A table with the following columns: Test, Fail, and Pass; and the following rows: Reality, effective, and not effective. Top left: "False Negative", Top right: "True Positive", Bottom left: "True Negative", Bottom right: "False Positive".
P-value hacking is a phenomenon that is currently ensuring that most published statistical research findings are false. If you are into science, you need this!
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