Movatterモバイル変換

[0]ホーム
URL:

PreviousUpNext
Dutch / Nederlands

Diary, June2017


Sun Mon Tue Wed Thu Fri Sat 1   2   3  4   5   6   7 8 91011  12  13  1415  16  17 18  19  2021  222324 25  26  27  2829  30

Thursday, June 1, 2017

Book

At 17:54, I bought the bookAKI Eindexamencatalogus studiejaar 1987/1988written in Dutch and published by Instituut voor Hoger Beeldend Kunstonderwijsin 1988 fromthrift store Het Goed for€ 3.95.

Thursday, June 8, 2017

GOGBOT café

This evening, I went to theGOGBOTcafé event atTetem art space.There were presentations by:

Friday, June 9, 2017

Kraggehuis

At the end of the afternoon, I arrived inGiethoorn. I had wait some time before the boat arrived to bring me tothe Kraggehuis, a group accomodation in the middle of the lake. When the boatarrived, I had to wait a little more, because there were some last minuteshoppings to be done. The boat had no engine, so we needed to used long polesto push is forward, because the water is less than a meter deep. Some peoplewere playingGo outside when we arrived at the island.Dinner was served around eight in the evening, just after a couple arrivedpeddling on13'2Explorer boards. I looked at several Go games being played by others.


 © Rudi Verhagen

Saturday, June 10, 2017

Peddling

This morning, three others and I spend about two hours traveling throughGiethoorn by boat and using poles to push the boat forward. I did somereading and also slept for an hour. In the afternoon, the couple who arrivedpeddling was teaching others to peddle on their boards. I also gave it a try,being a little nervous because I did not have a spare pair of trousers in caseI would fall in the water. At my first attempt to stand up-right, I droppedto my knees immediately as I felt unstable. I was instructed to place my feeta little further apart. On the second try, it worked a little better. I hadto take a few deep breaths to calm my hardrate and stop my legs fromtrembling. When I started peddling, I noticed that the trembling returned,but slowly it got a little better. When a speedboat was approaching, Idropped to my knees before the waves arrived. I guess, I would need anotherhour to become comfortable enough to go on a longer trip.

The Boxer and the Goal Keeper

In the evening, I finishedreading the bookTheBoxer and the Goal Keeper: Sartre Versus Camus byAndy Martin, which I started reading on May 19. I bought the book onWednesday, March 9, 2016. I found this a wellwritten and interesting to read book. The only problem I had with it, andwhich I have encountered with other biographic books, is the in some placesthematic approach. The book definitely made me interested in reading morefrom and about both Sartre and Camus.

Sunday, June 11, 2017

Swimming and sailing

This morning, I swam around the lake together with some other people. Afterhaving taken a shower, I went sailing with four others. We managed to returnto the island with only a little use of the poles. The boats have an almostflat bottom and no keel, which makes them drift very easily, especially whenthere is not enough wind to make some speed. In the afternoon, I went sailingwith two others. One of them jumped into the lake several times and pulled theboat while walking on the bottom of the lake. This weekend, I only played onegame ofGo, when Pepijn asked me to play against him. Ilost with 50 against 16 points where I got nine stones ahead. But even then itis not too bad, because he is a Dan player and I also did not reallyconcentrate a lot on the game. I did look at games being played. We alsoreplayed the first ofthe 50 AlphaGo vs AlphaGo games till the start of the end game. It is apitty that DeepMind/Google is going to decommission AlphaGo and not making itavailable anymore to be played against.

Thursday, June 15, 2017

Irregular chocolate bar

Yesterday, I saw aphoto stripby Ype & Ionica about an irregular chocolate bar, inspired by bar fromTony'sChocolonely, that could nevertheless be equally shared by 1, 2, 3, 4, 5,and 6 persons. I noticed that in their design there were two pairs of pieceswith the same surface area and I wondered if there was also a solution withall different numbers. I also wondered, if the more generic mathematicalpuzzle: find the 'smallest' set of natural numbers such it can be divided inall manners up to a givenn, had been addressed by someone. Ona Dutch blog by IonicaSmeets, she reports that someone named Dic Sonneveld found a solution withall different numbers, namely: 8,10,11,12,13,14,16, 17, 18, 19, 20, and 22.She also mentioned that several people concluded that there is no solution witheleven pieces. I started to do some puzzling myself and also told a colleagueabout the puzzle. It is obvious that the numbers for a givenn shouldbe equal to or be a multiple of theLeastcommon multiple (or LCM) of intergers upto and includingn. Mycolleague and I found the following solutions:
  1. : 1. (1 times 1).
  2. : 1, 2, and 3. (3 times 2)
  3. : 1, 2, 4, 5, and 6. (3 times 6)
  4. : 1, 2, 3, 4, 5, 6, 7, and 8 or 2, 3, 4, 5, 6, 7, and 9. (3 times 12)
  5. : 1, 2, 3, 4, 5, 7, 8, 9, 10, and 11. (1 times 60)
  6. : 1, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 19. (2 times 60)
He found the last solution, the others are mine, but he did find anotheralternative for 4. I report two solutions for that case, depending on thedefinition of 'smallest' set of natural numbers. The first solution containseight numbers with 8 as the lowest value, while the second solution containsseven numbers, but with 9 as the lowest. He found another solution with sevennumbers, meaning that even between solutions with the same number of numbers,we have to define some kind of relationship to define which is the smallestset. A (finite) set of (finite) natural numbers can be represented by asingle natural number using a binary representation.

Wednesday, June 21, 2017

Smallest maximum

In the past days, I worked ona programfor calculating solutions to theIrregularChocolate Bar problem. I discovered that it is not difficult to findsolutions with using large sets of numbers where the maximum number is assmall as possible. This results in the following solutions:
  1. : 1
  2. : 1, 2, 3
  3. : 1, .., 6 except for 3
  4. : 1, .., 8
  5. : 1, .., 11 except for 6
  6. : 1, .., 15
  7. : 1, .., 29 except for 15
  8. : 1, .., 41 except for 21
  9. : 1, .., 71 except for 36
  10. : 1, .., 71 except for 36
  11. : 1, .., 235 except for 10
  12. : 1, .., 235 except for 10
  13. : 1, .., 849 except for 465
  14. : 1, .., 849 except for 465
  15. : 1, .., 849 except for 465
  16. : 1, .., 1201 except for 1081
Note that some of the solutions are the same, for example, for 13, 14 and 15.This is because 14 is equal to 2 times 7, which are already included for a barthat can be divided in 1 up to and including 13 groups. Furthermore, 2 and 7arecoprime,which might explain why there exists a division in seven parts for whicheach part can be divided in two smaller parts. The same true for 15, which isequal to 3 times 5. I have no proof if this hold in general, but it seemslikely.

Finding solutions with the smallest set (or possibly larger) numbers, provedto be much harder. The method of just generating all sets, proved to be tooslow. I next worked on an algorithm that would generate sets that would fitthe largest number of divisions. These sets contains twice as many or one lessnumber of numbers. But this did not get me much further. So far, I have found:

  1. : 1
  2. : 1 2 3
  3. : 1 2 4 5 6
  4. : 2 3 4 5 6 7 9
  5. : 2 3 4 5 7 8 9 10 12
  6. : 3 4 5 7 9 11 13 15 16 17 20
  7. : 16 17 19 21 26 27 29 31 33 34 39 41 43 44
  8. : 17 23 25 32 37 38 47 52 53 58 67 68 73 80 82 88
It is possible that for the last two solutions, there exist even bettersolution, with fewer number (thirteen and fiftheen), but even larger values.

Friday, June 23, 2017

AKI finals 2017

In the afternoon, I went to theAKI finals 2016exhibition at theAKI. This year, theexhibition was only in the school building. I ran intoWim T. Schippers and talked a little with him while standing at aninstallation byOle Nieling. I found thefollowing artist interesting:At 18:31, I bought the bookprovocatie | provocation | 挑衅edited by Johan Visser, written in Dutch, English, and Chinese, published byAKI ArtEZ on Saturday, July 23, 2016,ISBN:978907552389, for € 15.00.At 18:31.

Saturday, June 24, 2017

Museum Boijmans Van Beuningen

During the afternoon, I visitedMuseum Boijmans Van Beuningen. I first looked at the mainexhibition, curated byCarel Blotkamp with the new lightning designed byPeter Struycken, which he made in an attempt to approach daylight as goodas is possible. To my surprise, I ran intoWim T. Schippers again. At two, I attended the official opening on thesmall sqaure in front of the entrance of the museum. The sky wasgrey and there was a little rain. After this, I also walked throught theother exhibtions:Sensory Space 11,Richard Serra,Drawings 2015-2017,The Magnetic North & The Idea of Freedom,and near the end of the afternoon, after having walked throught the exhibitionsagain,Gunnel Wåhlstrand. I listened to the talk by Carel Blotkampabout his work as a curator of the main exhibition. The list of noteworthy(to me) works I saw is:

Thursday, June 29, 2017

Necklage

I have been working on the 'necklage' solutions for theIrregular Chocolate Bar problem. The necklage solutions are the solutionswith 2n-1 numbers. LetS be the sum of all numbers of asolution, than for a necklage solution the numberS/n must beincluded and there must ben-1 pairs that add up toS/n.Furthermore, one can reason that there must ben-2 pairs and onetriplet that add up toS/(n-1). All the pairs of both groupsform alternating chains. One such chain connects theS/n numberwith the triplet and the other chain connects the two other numbers in thetriplet. This could be viewed as a necklage with a 'triangle' in the front anda piece hanging down. Hence the name of these solutions. I adapted the programand it found the solutions shown below. I let it run for higher numbers aswell, but it did not find any solutions that also had a division for numbersbetween 1 andn-1. There are good reasons to believe that these arethe only necklage solutions. In the listing the minus sign is used for pairsthat up toS/n and the equal sign is used for pairs and tripletsthat add up toS/(n-1).

3:    2-4  6=  =    1-54:       4-5          5-4       1-8=4 9=3-6=  =    9=3-6=  =     9=    -       2-7          1-8       2-7=55:        2-10=5            1-11=4       1-11=4-8 12=3-9=     -     12=3-9=     -    12=       =        4- 8=7            5- 7=8       2-10=5-76:         3-17=7-13       1-19=5-15= 9 20=4-16=        =    20=           -         5-15=9-11       3-17=7-13=11

This months interesting links

Home|May 2017|July 2017|Random memories




[8]ページ先頭


©2009-2025 Movatter.jp