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Artificial Intelligence

How To Really Solve This Tricky Algebra Problem? (III)

Published on May 10, 2022 by Hemanth

How To Really Solve This Tricky Algebra Problem? (III) - x^y = y^x → x = ? and y = ? when x not equal to y and x,y ∈ ℝ
Welcome to the third entry in the tricky algebra problem series. To be fair, you will need a bit more knowledge than just algebra to solve this!
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How To Scientifically Design A 2-Dimensional World? (II)

Published on May 9, 2022 by Hemanth

How To Scientifically Design A 2-Dimensional World? - an image featuring an illustration of a 2-dimensional door. The image on the left (titled '1') shows the door when it is closed, resting centrally. The image on the right (titled '2') shows the door when it is about to open. The door has two symmetrical levers on either side, a rotary hinge connected to the roof, and a wedge in the bottom at the center. When the lever is pushed from either side, the wedge rocks and the door swings open.
Previously, I covered the scientific principles behind a 2-dimensional world. This essay gives you a sneak-peek into the world of 2-dimensional tech design!
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How To Scientifically Design A 2-Dimensional World? (I)

Published on May 8, 2022 by Hemanth

How To Scientifically Design A 2-Dimensional World? (I) - An image that shows a circular 2 dimensional planet. There is a triangular creature, a tree, a house, some rocks, water, and clouds around the rim of the planet. There is one rain-cloud, the rain from which is getting collected between two rocks. The triangular creature has two legs, two arms, and two eyes. There is also a flying fish among the clouds.
Science fiction talks about higher dimensional life all the time, but how many of us have thought about a 2-dimensional world? Science says that it's possible!
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How To Really Use The Superellipse For Elegant Designs

Published on May 7, 2022 by Hemanth

How To Really Use The Superellipse For Elegant Designs - An image showing Sergels Torg in Stockholm City (Image from WikiCC - further edited by the author) along with a beautiful and clear twilight skyling. The following text is written pointing towards Sergels Torg: "DESIGNED USING MATHEMATICS".
You don't hear the term “Superellipse” very often. Yet, its beauty is everywhere to see. If you are into design, elegance, and beauty, you need to read this!
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How To Solve The Mystery Of The Oscillating Function

Published on May 5, 2022 by Hemanth

How To Solve The Mystery Of The Oscillating Function - (8^x - 2^x)/(6^x - 3^x) = 2; x = ?? This equation is plotted on the right, which seems to be a U-shaped curve. When zoomed in on the zero region, the function seems to exhibit oscillation. Right next to this zoomed-shot, the following text is written: "WHY??"
What is so mysterious about an oscillating function? You see, if you work with extreme numbers, you'll face this problem. Read the essay to learn how handle it.
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How To Really Tile Rep-Tile Triangles?

Published on May 4, 2022 by Hemanth

How To Really Tile Rep-Tile Triangles? - An illustration of a right-triangle that is divided into 9 congruent triangles that are also similar to the original triangle. Below this figure, the following text is seen: "How to split one triangle into nine triangles??"
Learn the art of splitting a triangle into ’n’ congruent tiles that are also similar to the original. Using this math, it possible to scale infinitely!
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Can You Really Solve This Tricky Rep-Tile Puzzle?

Published on May 3, 2022 by Hemanth

Can You Really Solve This Tricky Rep-Tile Puzzle? - An image featuring an isosceles right triangle that is subdivided into two similar isosceles right triangles that are similar to the bigger triangle. On the right hand side of the triangle, the following text is hand-written: "Two congruent triangles tile a bigger similar triangle." Below the triangle, the following text is hand-written in bold: "WHAT NEXT?"
What is a rep-tile? This essay has the answers, and what's more, poses a challenging puzzle as well. If you are into hard geometry problems, look no further!
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How To Really Benefit From Curves Of Constant Width?

Published on April 27, 2022 by Hemanth

How To Really Benefit From Curves Of Constant Width? - A wooden plank placed on top of two differently shaped objects (Image from WikiCC). One object features a circular corss-section whereas the other object features a curved triangular cross-section.
Curves of constant width represent one of the most elegant real-life applications of plane geometry. If you are into plane geometry, this is for you!
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The Additive Palindrome Conjecture Is A Risky Venture

Published on April 26, 2022 by Hemanth

The Additive Palindrome Conjecture Is A Risky Venture - An image showing the following mathematical operations: 58 + 85 = 143 (not a palindrome); 143 + 341 = 484 (a palindrome).
The additive palindrome conjecture is very welcoming and satisfying as far as the underlying concept is concerned. Yet you should probably not try to prove it!
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How To Really Solve The Straight Lines And Triangles Puzzle?

Published on April 25, 2022 by Hemanth

How To Really Solve The Straight Lines And Triangles Puzzle? - An image showing four straight lines that intersect each other at a unique point. At any point of intersection, no more than two lines are involved. On top of this illustration, the following question is posed: "HOW MANY TRIANGLES?"
Straight Lines and Triangles - A simple puzzle that goes beyond geometry! Your job is to find out how many triangles you can construct using ’n’ straight lines.
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