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Robin Houston

@robinhouston

Cofounder of @f_l_o_u_r_i_s_h. Also maths. Blogging sometimes at http://bosker.wordpress.com/ . My name is an anagram of “No enthusiasm or job”.

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    1. Robin Houston‏ @robinhouston 5. lis 2019.
      • Prijavi Tweet

      Time for another story? (Thread)

      5 replies 120 proslijeđenih tweetova 349 korisnika označava da im se sviđa
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      Robin Houston‏ @robinhouston 5. lis 2019.
      • Prijavi Tweet

      Henry Dudeney was a prolific author of mathematical puzzles. He wrote regularly for Strand Magazine, and collected his puzzles in a series of popular books. His first book was The Canterbury Puzzles (1907), in the theme of Chaucer’s Canterbury Tales.pic.twitter.com/3E3qQAT5VY

      02:43 - 5. lis 2019.
      • 49 proslijeđenih tweetova
      • 125 oznaka „sviđa mi se”
      • DSM Darren Wilkinson Vivek A Каrdelen MaMo Tilman Sauer अभिनव anshumani MJ Knoester
      49 proslijeđenih tweetova 125 korisnika označava da im se sviđa
        1. Novi razgovor
        2. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          One of the puzzles in that book (originally published in Strand Magazine in 1902) concerned Lady Isabel’s Casket.pic.twitter.com/wREbOdtMxN

          1 reply 8 proslijeđenih tweetova 45 korisnika označava da im se sviđa
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        3. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          Here’s the solution from the book.pic.twitter.com/QfaZ6LHQsl

          1 reply 4 proslijeđena tweeta 30 korisnika označava da im se sviđa
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        4. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          In 1935, a young man called Arthur Stone went to Trinity college, Cambridge, to study mathematics. He had a copy of the Canterbury Puzzles, and he was particularly intrigued by Dudeney’s assertion that “This is the only possible solution”.

          1 reply 4 proslijeđena tweeta 29 korisnika označava da im se sviđa
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        5. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          It occurred to him that this claim of uniqueness had some profound implications. If a square could be divided into smaller squares, all of different sizes, then another solution to the casket problem could be obtained by subdividing the smallest square.

          4 proslijeđena tweeta 29 korisnika označava da im se sviđa
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        6. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          So, if Dudeney was right that the solution to the casket problem was unique, it must therefore be impossible to cut a square into smaller squares of different sizes. Stone wondered whether this was true.

          1 reply 4 proslijeđena tweeta 31 korisnik označava da mu se sviđa
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        7. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          He discussed the question with his friends Cedric Smith, Leonard Brooks, and Bill Tutte. The others were intrigued, and began to work on it together.

          3 proslijeđena tweeta 22 korisnika označavaju da im se sviđa
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        8. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          They started by thinking about how to dissect rectangles into squares of different sizes. They knew that was sometimes possible, because Tutte had a copy of a book by Rouse Ball which showed how a 32×33 rectangle could be cut into different-sized squares.pic.twitter.com/06c9u1Fmkg

          2 proslijeđena tweeta 31 korisnik označava da mu se sviđa
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        9. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          They came up with a clever method for finding squared rectangles. First divide a square into rectangles willy-nilly; then pretend the rectangles are really squares, and work out how big they would be if they were, and solve a simple equation to find the dimensions.pic.twitter.com/SnPzq5YEJZ

          2 proslijeđena tweeta 31 korisnik označava da mu se sviđa
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        10. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          In this example, you start with arbitrary values x and y, fill in the rest of the rectangles starting from those, and then finally you have to make the lengths match on the line AB, so solve the equation 14y-3x = (3x-3y) + (3x+y). It simplifies to 16y = 9x, so x=16, y=9 works.

          2 proslijeđena tweeta 21 korisnik označava da mu se sviđa
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        11. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          The big breakthrough came when Smith invented a type of diagram that led the four to realise that squared rectangles are equivalent to electrical circuits – specifically networks of resistors.pic.twitter.com/1DNf7y8RXe

          9 proslijeđenih tweetova 59 korisnika označava da im se sviđa
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        12. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          It works like this: think of the squares as 1Ω resistors, and as electrically connected whenever they share a horizontal line segment. Connect a battery to the top and bottom of the rectangle.

          2 proslijeđena tweeta 23 korisnika označavaju da im se sviđa
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        13. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          Think of the current flowing through each resistor as the side-length of the square. The current that flows into each node must equal the current that flows out, which corresponds to the fact that the squares above and below a shared horizontal segment have the same total width.

          1 reply 2 proslijeđena tweeta 24 korisnika označavaju da im se sviđa
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        14. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          This correspondence meant the students could use Kirchhoff’s theory of electrical networks to study squared rectangles, and they found many more. One was this, which impressed Brooks so much that he drew it on cardboard and cut it up to make a puzzle.pic.twitter.com/MhQpRxUs0G

          1 reply 4 proslijeđena tweeta 37 korisnika označava da im se sviđa
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        15. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          Home for vacation, he challenged his mother to solve the puzzle. He was astonished when she found an entirely unexpected solution.pic.twitter.com/VON9lGHRlv

          5 proslijeđenih tweetova 43 korisnika označavaju da im se sviđa
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        16. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          The corresponding circuits are here. The two points marked p and p’ are at the same voltage, so they can be connected together without changing the electrical behaviour of the circuit.pic.twitter.com/QO19uXNfu6

          2 proslijeđena tweeta 29 korisnika označava da im se sviđa
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        17. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          Studying this phenomenon led Tutte to an idea he called “rotor-stator equivalence”. Using this idea, Smith and Stone managed to find a perfect square made of 69 smaller squares. They rushed to tell Brooks, who replied “So have I!”. He had found one too, also of 69 squares.

          3 proslijeđena tweeta 40 korisnika označava da im se sviđa
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        18. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          Their work was published in 1940 under the title “The dissection of rectangles into squares”. They didn’t quite manage to publish the first perfect squared square: they were beaten to press by R Sprague, who had found one independently and published in 1939.

          4 proslijeđena tweeta 27 korisnika označava da im se sviđa
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        19. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          But their work led to something of far greater importance. The Second World War broke out in 1939, and Bill Tutte’s tutor recommended him for war work at the Government Code and Cypher School at Bletchley Park.

          1 reply 3 proslijeđena tweeta 21 korisnik označava da mu se sviđa
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        20. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          Tutte was officially studying chemistry, and presumably was only recommended for Bletchley Park because his work on squared squares had shown him to be a talented mathematician.

          4 proslijeđena tweeta 24 korisnika označavaju da im se sviđa
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        21. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          At Bletchley Park, Tutte had the key insight that led to the cracking of the Lorenz cipher, used by the Wehrmacht for their most secret communications. The intelligence derived from these communications may have made the allied victory possible. It definitely helped.

          1 reply 5 proslijeđenih tweetova 30 korisnika označava da im se sviđa
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        22. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          So, in a roundabout way, a puzzle about a Lady’s casket led to the defeat of Hitler. Remember that next time someone says puzzles are a waste of time.

          9 proslijeđenih tweetova 74 korisnika označavaju da im se sviđa
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        23. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          Arthur Stone went to Princeton, where he almost immediately discovered flexagons. https://en.m.wikipedia.org/wiki/Flexagon 

          1 reply 4 proslijeđena tweeta 28 korisnika označava da im se sviđa
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        24. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          The website http://squaring.net  has a HUGE amount of information about cutting rectangles into smaller squares, including a detailed history section. Tutte’s book _Graph theory as I have known it_ tells the story from Tutte’s perspective, with an emphasis on the mathematics.

          1 reply 3 proslijeđena tweeta 31 korisnik označava da mu se sviđa
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        25. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          Smith’s paper _Did Erdős Save Western Civilization_ describes what happened from Smith’s point of view. (Erdős conjectured that it’s impossible to cut a square into smaller squares of different sizes, though the four friends weren’t aware of that at the time.)

          2 proslijeđena tweeta 24 korisnika označavaju da im se sviđa
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        26. Robin Houston‏ @robinhouston 5. lis 2019.
          • Prijavi Tweet

          Here’s the most efficient possible way to cut a square into smaller squares of different sizes, discovered by Duijvestijn in 1978.pic.twitter.com/WZSck6Ox8E

          7 replies 4 proslijeđena tweeta 67 korisnika označava da im se sviđa
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        27. Robin Houston‏ @robinhouston 14. lis 2019.
          • Prijavi Tweet

          If you enjoyed the story above, you might enjoy this documentary about Bill Tutte’s work at Bletchley Park breaking the Lorenz cipher: …https://computer-literacy-project.pilots.bbcconnectedstudio.co.uk/7fd3fb55e462db0867b183729c5ed27c … Via @longandy

          4 proslijeđena tweeta 14 korisnika označava da im se sviđa
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