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bheem singh Vijoriya

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### bheem singh Vijoriya

Shared publicly -Science-ify your breakfast with a Möbius bagel

You’ve probably heard of a Möbius strip before http://en.wikipedia.org/wiki/M%C3%B6bius_strip - it’s a continuous shape that only has one side and one edge. You can make one pretty easily by cutting a strip of paper, giving it a half twist, and taping the ends together to form a loop. However, if you want to really impress, make a Möbius bagel. By following the instructions http://www.npr.org/blogs/krulwich/2012/11/08/164682556/mathematically-challenging-bagels?ft=1&f=5500502, you can cut your bagel (or your donut! http://newyork.seriouseats.com/2009/12/even-cooler-the-mobius-doughnut.html) into two interlocking bagel halves. From now on, eat your breakfast like a Scientist!

source:

http://thenimbus.tumblr.com/post/49438554723/sciencecenter-science-ify-your-breakfast-with-a

You’ve probably heard of a Möbius strip before http://en.wikipedia.org/wiki/M%C3%B6bius_strip - it’s a continuous shape that only has one side and one edge. You can make one pretty easily by cutting a strip of paper, giving it a half twist, and taping the ends together to form a loop. However, if you want to really impress, make a Möbius bagel. By following the instructions http://www.npr.org/blogs/krulwich/2012/11/08/164682556/mathematically-challenging-bagels?ft=1&f=5500502, you can cut your bagel (or your donut! http://newyork.seriouseats.com/2009/12/even-cooler-the-mobius-doughnut.html) into two interlocking bagel halves. From now on, eat your breakfast like a Scientist!

source:

http://thenimbus.tumblr.com/post/49438554723/sciencecenter-science-ify-your-breakfast-with-a

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### bheem singh Vijoriya

Shared publicly -Do you have any doubts about 1/2+1/4+1/8+…=1? Let’s have a look at the geometric representation of this sum.

We take the square piece of paper of size 1 and bend the corners to the center. The area of obtained square is half of the area of the initial square and equals 1/2. It means that the area of the corners (colored in red) also equals ½. Now we repeat the same action with obtained square. The area of each new square is half the area of the previous one. Similarly, the area of the corners (of different colors in animation) also equals half the area of the previous ones. The area of the red part is ½, of the orange part is ¼, of the yellow part is 1/8 and so on. We can continue in such way to the infinity, yet the area of our initial piece of paper remains 1.

We take the square piece of paper of size 1 and bend the corners to the center. The area of obtained square is half of the area of the initial square and equals 1/2. It means that the area of the corners (colored in red) also equals ½. Now we repeat the same action with obtained square. The area of each new square is half the area of the previous one. Similarly, the area of the corners (of different colors in animation) also equals half the area of the previous ones. The area of the red part is ½, of the orange part is ¼, of the yellow part is 1/8 and so on. We can continue in such way to the infinity, yet the area of our initial piece of paper remains 1.

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### bheem singh Vijoriya

Shared publicly -Two active regions with their intense magnetic fields produced towering arches and spiraling coils of solar loops above them (June 29 - July 1, 2014) as they rotated into view. When viewed in extreme ultraviolet light, magnetic field lines are revealed by charged particles that travel along them. These active regions appear as dark sunspots when viewed in filtered light. Note the small blast in the upper of the two major active regions, followed by more coils of loops as the region reorganizes itself.

Credit: Solar Dynamics Observatory/NASA

#sdo #sun #solar #solarloops #nasa #space

Credit: Solar Dynamics Observatory/NASA

#sdo #sun #solar #solarloops #nasa #space

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### bheem singh Vijoriya

Shared publicly -What's the latest on Super Typhoon #Neoguri? Here's the inside view from #TRMM: http://www.nasa.gov/content/goddard/neoguri-northwestern-pacific-ocean/index.html

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### bheem singh Vijoriya

Shared publicly -Mathematicians have revealed 177,147 ways to knot a neck tie – 2000 times the number previously thought to exist. The new figure is inspired by the film The Matrix Reloaded.

http://tieknots.johanssons.org/ties.html - Random tie knot generator

From the tool, known in logic as formal language theory, he has created a random tie generator which uses the mathematics to teach internet users how to tie random knots.

In 1999, Thomas Fink and Yong Mao of the University of Cambridge expressed the rules of tying a tie in symbols. This suggested there were only 85 distinct knots. But Mikael Vejdemo-Johansson of the KTH Royal Institute of Technology in Stockholm, Sweden, noted that this tie language would not allow for exotic ties such as that sported by Matrix villain The Merovingian (tie pictured).

His team rewrote the language to allow multiple tucks per tie and a non-smooth surface, and increased the number of allowed winding moves before a tie is deemed too short. That allows 177,147 distinct knots (arxiv.org/abs/1401.8242).

Along with three other mathematicians, he created a formula for devising tie knots using just three symbols, W, T and U.

He said: 'T is a clockwise (turnwise) move of the knot-tying blade, W is a counter-clockwise move, and U tucks the blade under a previous bow.

'Whether to start with an inwards or outwards crossing can be deduced by counting the total number of W and T in the knot description string, and all possible strings in W and T produce possible tie knots.'

http://www.newscientist.com/article/mg22129563.600-matrix-villain-spawns-177000-ways-to-knot-a-tie.html#.UxXpo_nV-DQ

Youtube Playlist 100+ Ways How to Tie a Necktie

http://goo.gl/G5GS7j

http://tieknots.johanssons.org/ties.html - Random tie knot generator

From the tool, known in logic as formal language theory, he has created a random tie generator which uses the mathematics to teach internet users how to tie random knots.

In 1999, Thomas Fink and Yong Mao of the University of Cambridge expressed the rules of tying a tie in symbols. This suggested there were only 85 distinct knots. But Mikael Vejdemo-Johansson of the KTH Royal Institute of Technology in Stockholm, Sweden, noted that this tie language would not allow for exotic ties such as that sported by Matrix villain The Merovingian (tie pictured).

His team rewrote the language to allow multiple tucks per tie and a non-smooth surface, and increased the number of allowed winding moves before a tie is deemed too short. That allows 177,147 distinct knots (arxiv.org/abs/1401.8242).

Along with three other mathematicians, he created a formula for devising tie knots using just three symbols, W, T and U.

He said: 'T is a clockwise (turnwise) move of the knot-tying blade, W is a counter-clockwise move, and U tucks the blade under a previous bow.

'Whether to start with an inwards or outwards crossing can be deduced by counting the total number of W and T in the knot description string, and all possible strings in W and T produce possible tie knots.'

http://www.newscientist.com/article/mg22129563.600-matrix-villain-spawns-177000-ways-to-knot-a-tie.html#.UxXpo_nV-DQ

Youtube Playlist 100+ Ways How to Tie a Necktie

http://goo.gl/G5GS7j

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### bheem singh Vijoriya

Shared publicly -Pythagorean Theorem in action

Normally, the Pythagorean theorem sounds like: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse.

Demonstration below shows that through volumes: the sum of the volumes of the two parallelepipeds on the legs (a and b) equals the volume of the parallelepiped on the hypotenuse.

Normally, the Pythagorean theorem sounds like: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse.

Demonstration below shows that through volumes: the sum of the volumes of the two parallelepipeds on the legs (a and b) equals the volume of the parallelepiped on the hypotenuse.

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### bheem singh Vijoriya

Shared publicly -Digits instead of intuition

You have probably heard about one of the relatively new branches of mathematics called Game Theory. It deals with seemingly non-mathematical problems. Game theory is a study of strategic decision making. It studies different games and considers the most appropriate methods of their conducting. However, the mathematical concept of “game” is different from its common meaning. In mathematics, game is any conflict situation between two or more people. Game theory is mainly applied in economics, political science, and psychology, as well as logic and biology.

For example, have you ever heard about the Prisoner’s dilemma?

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. Each prisoner is given the opportunity either to betray the other, by testifying that the other committed the crime, or to cooperate with the other by remaining silent. Here's how it goes:

•If A and B both betray the other, each of them serves 5 years in prison

•If A betrays B but B remains silent, A will be set free and B will serve 20 years in prison (and vice versa)

•If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)

The dilemma arises if we assume that each of them cares only about minimizing his own sentence. Here's the reasoning of one of the prisoners. “If my partner doesn’t confess, it is better to betray him and be set free. If he betrays me, it is better to betray him too and get 5 years instead of 20. In any case, it is better to talk.” Another prisoner comes to the same conclusion. We all realize, of course, that it is better for both of them to keep silence .

http://1000wordphilosophy.wordpress.com/2014/04/24/the-prisoners-dilemma/

What do you think? Will you have a better chance of winning if you apply the knowledge of the Game Theory?

You have probably heard about one of the relatively new branches of mathematics called Game Theory. It deals with seemingly non-mathematical problems. Game theory is a study of strategic decision making. It studies different games and considers the most appropriate methods of their conducting. However, the mathematical concept of “game” is different from its common meaning. In mathematics, game is any conflict situation between two or more people. Game theory is mainly applied in economics, political science, and psychology, as well as logic and biology.

For example, have you ever heard about the Prisoner’s dilemma?

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. Each prisoner is given the opportunity either to betray the other, by testifying that the other committed the crime, or to cooperate with the other by remaining silent. Here's how it goes:

•If A and B both betray the other, each of them serves 5 years in prison

•If A betrays B but B remains silent, A will be set free and B will serve 20 years in prison (and vice versa)

•If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)

The dilemma arises if we assume that each of them cares only about minimizing his own sentence. Here's the reasoning of one of the prisoners. “If my partner doesn’t confess, it is better to betray him and be set free. If he betrays me, it is better to betray him too and get 5 years instead of 20. In any case, it is better to talk.” Another prisoner comes to the same conclusion. We all realize, of course, that it is better for both of them to keep silence .

http://1000wordphilosophy.wordpress.com/2014/04/24/the-prisoners-dilemma/

What do you think? Will you have a better chance of winning if you apply the knowledge of the Game Theory?

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