Mathematics Archives - Take in Mind

The Endless Ribbon

January 29, 2023 By Samyon Ristov

Why did the chicken cross the road? To get to the other side. — Why did the chicken cross the Möbius strip? To get toRead More

Dimensions – A Weird Fourth-Dimensional Bottle

November 4, 2022 By Samyon Ristov

In this series of articles, slowly but surely, we uncover the secrets of the fourth dimension. We already got familiar with the hyper-cube, particularly theRead More

Palindromusic

May 7, 2022 By Samyon Ristov

Palindromes, sequences that read the same backward as forward, are appreciated by many. They are normally known in numbers (like 11, 232 and, by theRead More

Incredible Mind: Divine Mathematician’s Stories

January 27, 2022 By Samyon Ristov

Srinivasa Ramanujan was a genius. His approach to mathematics, his abilities, sense, insight, was unheard of. In his biographical notice for Ramanujan, G. H. HardyRead More

Dimensions: One-Dimensional Chess

October 15, 2021 By Samyon Ristov

Every engineer and scientist knows that when facing a particularly complicated problem, it’s well-advised to reduce its complexity by reducing the problem to a smallerRead More

Dimensions: The Fly Imagination Game

June 25, 2021 By Samyon Ristov

Do you want to practice traveling in a two-, three- or even four-dimensional world? If you stretch your imagination, you can do it! Follow theRead More

Infinitely Many Solutions… to a Riddle!

May 5, 2021 By Samyon Ristov

Here is a known riddle: See above a picture of nine dots. Now, connect the dots by drawing four straight, continuous lines that pass throughRead More

Dimensions: Meet the Tesseract

February 27, 2021 By Samyon Ristov

Our imagination can take as to the furthest lands, and what can be further than other or higher dimensions? The problem with traveling to higherRead More

Alice in Palindrome Land

January 26, 2021 By Samyon Ristov

There is something unique about Alice and her mesmerizing adventures in Wonderland – something special that catches our eyes. Otherwise, how do you explain theRead More

Dimensions: A journey to a multi-dimensional world

October 4, 2020 By Samyon Ristov

People who study science and engineering discover at some point the idea of dimensions. Not parallel dimensions, although that a fascinating (and absolutely scientific!) topicRead More

Scientific Humor

About man’s fidelity!

…and there is another story. Once Thomas Edison’s wife told him: “Darling, you are so tired! Go somewhere, relax, have a rest, enjoy your time…” Edison listened to his wife’s wise advice, instantly packed up, and disappeared somewhere… The next day she found the inventor… in his own laboratory, where he actually spent the previous day and night, working with enthusiasm. To her surprised question, happy Edison replied: “Oh my, I’ve rested so well!”

Thomas Alva Edison (1847-1931) was a famous American inventor and businessman

Take a look

Once upon a time, a Brahmin (sage) invented the game of chess to teach the cruel Raja (the ruler) to treat his subjects well. In that game, the “Raja” (the name of one of the chess pieces) is the head of the state. If the “Raja” is captured, then his state ceases to exist. In case of danger, the “Raja” cannot survive without his faithful defenders and assistants – other figures.

The Raja was amazed by the game, understood its meaning, and promised not to oppress his subjects in the future. He then asked the Brahmin to choose the greatest reward he may wish for. The Brahmin replied that he wants to be rewarded with… wheat, but based on the following calculation: put one grain on the first cell of the chessboard, two on the second, four on the third, eight on the fourth, etc., doubling the number of grains on each subsequent cell.

The Raja, seeing that there are only 64 cells on the board, was surprised at the insignificance of the request. He decided that it’ll take about one or two sacks of wheat to fulfill it and gave the order to issue the reward immediately. Soon, the court mathematicians reported that the Raja would have to give so many grains, for which it would be necessary to sow the entire Earth, and the grown wheat would be enough to feed the whole population of Earth for 100 years.

Of course, the Raja could not fulfill his hasty promise and received another wise lesson from the inventor of the game of chess.

— A folk tale. Retold in the book “A complete course of chess: 64 lessons for beginners and not very experienced player”s, by S.B. Gubnitsky, M.G. Khanukov, S.A. Shedey.

The photo (own work) illustrates the second part of the fable, about exponential growth. In some variations, rice is requested instead of wheat, but in the photo, Wild Rice is used. The chess pieces’ positions are not random but positioned as in one of the first known chess riddles. In fact, it’s not even a chess riddle, but a Mansuba, a Shatranj problem, composed by Abu Na’im al Khadim (9th century). Shatranj is an old form of chess, with very similar rules. The differences in the rules don’t affect the riddle. White to move, and mate in three.

An easier view of the riddle is available in the first comment. Can you solve one of the oldest chess riddles?

Image source: Own work.

Think about

A few words about imagination

“I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.” ― Albert Einstein (1879-1955) was a German-born theoretical physicist.

The great German mathematician David Hilbert (1862–1943) noticed that one of his students had started missing his lectures. When he asked for the reason, he was told that the student had left mathematics in favor of poetry. “Ah, yes,” said Hilbert, “I always thought he didn’t have enough imagination for mathematics…”

It is strange that only extraordinary men make the discoveries, which later appear so easy and simple. Georg Lichtenberg (1742 – 1799) was a German experimental physicist.

“You cannot teach a man anything; you can only help him discover it in himself.” Galileo Galilei (1564-1642) was an Italian astronomer, mathematician, physicist, and philosopher.

“To invent, you need a good imagination and a pile of junk.” — Thomas A. Edison (1847-1931) was an American inventor and businessman.