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Mathematics

How To Benefit From Braess’s Paradox?

Published on February 17, 2022 by Hemanth

How To Benefit From Braess's Paradox? A road network that connects START to END. There are two paths available: one through junction A, and another through junction B. Time taken for traversing START-A = 110 minutes. Time taken to traverse A-END = T/10, where T is the number of cars on the route. Time taken for START-B = T/10, where T is the number of cars on the route. Time taken for B-END = 110 minutes.
Braess’s paradox originates from the observation that overall traffic efficiency in a road network decreases after one or more roads are added to the network.
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How To Mentally Square Any Number Ending In 5?

Published on February 15, 2022 by Hemanth

How To Mentally Square Any Number Ending In 5? An image asking what is: 205² = ??
Let us say that you have to mentally square any number ending in 5. In this essay, you get to learn a clever mental math trick from Indian Vedic Mathematics!
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How To Really Solve The Three 3s Problem?

Published on February 13, 2022 by Hemanth

How to really solve the three 3s problem? 3 3 3 = 1 3 3 3 = 2 3 3 3 = 3 3 3 3 = 4 3 3 3 = 5 3 3 3 = 6 3 3 3 = 7 3 3 3 = 8 3 3 3 = 9 3 3 3 = 10
The Three 3s Problem is a fascinating math puzzle set that I stumbled upon recently. It features a math concept that you are most likely not aware of!
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How To Actually Subtract Using Addition?

Published on February 10, 2022 by Hemanth

How To Actually Subtract Using Addition? - A Computometer (1920) on the left and an adding machine (1910) (Images from Wikimedia Commons - edited by the author)
Imagine that you are required to subtract using addition only. Why would you need to restrict yourself? It turns out that it is more useful than it appears.
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How You Really Use Mathematics To Define Paper Size

Published on February 6, 2022 by Hemanth

The math behind paper size: Two images: A portrait of Georg Christoph Lichtenberg on the left and an illustration of A series paper sizes on the right
Have you ever wondered how paper size is defined? It turns out that there is rich history and intriguing math behind paper size standards.
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How To Really Use Mathematical Induction?

Published on February 6, 2022 by Hemanth

An introduction to mathematical induction: A picture with players represented as match stick figures. The last ranked player gets 1 point, the second last player gets 2 points, and so on until the first player who gets 569 points. The picture then poses the question: "Total Points = ?"
Mathematical induction is an ingenious logical construct that originates from the human will to save time and effort. This article serves as a fun introduction.
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Is ‘0.99999…’ Really Equal To ‘1’?

Published on January 31, 2022 by Hemanth

An image asking the question: Is "0.99999…" Really Equal To "1"?
If you are required to assign a precise value to the infinite decimal ‘0.99999…’, what would you do? Math intuition says that it could be equal to ‘1’.
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How To Hear Acceleration Without Modern Technology?

Published on January 29, 2022 by Hemanth

How to hear acceleration without using modern technology? Images from Wikimedia Commons (Portrait of Galileo on the left and a two-outflow water clock from 5-th century BC on the right)
In our modern technological world, we have all sorts of solutions to help us measure acceleration. But what if you lost access to all of modern technology?
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How To Really Eliminate The Staircase Paradox?

Published on January 26, 2022 by Hemanth

The staircase paradox: A staircase with a base of 4 centimetres (cm) and height of 4 cm. There are two stairs, each with a length of 2 cm and height of 2 cm.
After my original essay on the staircase paradox got considerable scientific cricitism, I had to write a technical essay explaining the mathematics behind it!
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How To Solve The Dartboard Paradox?

Published on January 23, 2022 by Hemanth

How to solve the dartboard paradox? - A picture of a dartboard with darts stuck on it.
The dartboard paradox is one of those pesky paradoxes that revolves around the concepts of zero and infinity. The notion of probability makes it trickier.
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