Tuesday, December 22, 2009

Some More Math Fun

As an answer to George Hart's Möbius Bagel, Serious Eats has constructed a Möbius Doughnut


Then I saw a picture on Wired Science and thought that somebody had knitted a mathematical equation in 3-D.

It turned out that it was a Mandelbulb, a 3-D visualisation of a fractal called a Mandelbrot set. After seeing some videos like the next one, I still think that this is just like a cool knitting work...

Here is an example from a Finnish knitting blog nekkisneuleet. Using different patterns, someone could really knit a visualisation. Too bad I am not good in designing...


Finally Makezine led me to some really impressive polyhedra made of playing cards, again by George Hart

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Monday, December 21, 2009

When Your Math Papers Come Alive

Last night I was listening The Drill Down, a podcast which is well known among the Diggers. I don't much listen to it nowadays live after they changed the time they send the podcast. Now it comes out in the middle of the night for me (1.00 am Monday morning) and if I have to work the next day, I don't want to to stay up that late. Anyway my TV was open on the background and it was on The Voice TV Finland, playing some music videos. Suddenly one of the videos caught my attention even though I had my headset on for listening to the podcast. The video is just so fascinating and the song is not bad either. My papers live also their own life but usually the other way around. Numbers and calculations start crawling among the other text and pictures :)

The Fray - Heartless:

The FRAY - Heartless from IE HAGY on Vimeo.

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Saturday, December 12, 2009

Puzzles and Nokia N900

I am a fan of all kind of gadgets and I am not very good in texting or surfing the web with my mobile phone, Nokia E90, which I bought last year. When Nokia announced the new model N900, I decided I want to have it.

I just love the phone. Web pages open fast and I have multiple desktops to save the applications and favourites I use. Everything I need I can choose with my fingertip. I am still learning to use all the features, but one of my first was to check Conceptis website. The start was a bit tricky but with persistence I finally got a result:

Now I have learned to adjust the size of the screen and to use the pen which came with the phone and I started solving a Hitori. The puzzle was a small and easy one, and I got it finished in less than 5 minutes!

What is special about this? I don't need any applications. I can go to my best website and solve the puzzles there. The trick is the Adobe Flash™ 9.4 support my phone has. The prevoius one did not show even the thumbnails of the puzzles.

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Thursday, December 10, 2009

Inspired By Mathematics

As in honour of my Christmas holiday I found two mathematics inspired items yesterday.

This ring is inspired by the Fibonacci sequence 1,1,2,3,... The pattern of the beads is the beginning of the sequence.

Golden Ratio--14K Gold Filled Fibonacci Sequence Wire Wrapped Ring

holmescraft's shop (via Neatorama)

This is a mathematically correct breakfast, a bagel cut and linked to make a Möbius strip

You can find the instructions here (also via Neatorama)

Saturday, October 31, 2009

Fun Halloween Math

As you could presume, all math teachers are not boring. Check out this video by MDWeathers which he did for his Nature of Math class at Biola University, October 28, 2009.

Sunday, September 27, 2009

Money Exchange Game

I have played a lot of flash games on PrimaryGames website. The game named Coinz! is disturbingly hard and addictive at the same time. The target of the game is to make money disappear by picking up the same amount of money using two currencies.

The first game involved exchanging Singapore Dollars to Russian Rubles. This was hard. There were lots of coins marked 1, but it is harder to determine if the coin is 1.oo or o.o1. Choosing Hint from the list on the right you can see the value when marking a coin.

After all the Singapore Dollars were exchanged the level was completed. Now the new currency was Lithuanian Litas. The exchange rate is shown above the box and below the box you can see how many Rubles you should find matching the Litas you have chosen.

Interestingly the third level seemed easier to me. Now Polish Zlotys were exchanged to Litas, and the value of the currencies being nearly the same made it easy.

A very good game in mathematics learning. I could imagine that kids are faster to find the right coins than I was.

Wednesday, September 23, 2009

Shift Happens - A Challenge for Teachers

I first saw this video about one year ago. The video got me really thinking about the world we and especially the young people live in. I think every teacher should see this and think for a moment. Does the education we give them really prepare them for anything?

This is the new official update to the original "Shift Happens" video. This completely new Fall 2009 version includes facts and stats focusing on the changing media landscape, including convergence and technology, and was developed in partnership with The Economist.

Did You Know 4.0

This is the previous edition from 2008 - also worth to check:

Did You Know 3.0

The 2007 version is very similar, but I included it for reference.

Did You Know 2.0

And this hopefully is the original, published earlier in 2007

Did You Know; Shift Happens - Globalization; Information Age

Saturday, September 5, 2009

Geometric Art

BibliOdyssey introduces scans of wonderful geometric art.

Here is an example of Lorenz Ströer's 'Geometria et Perspectiva' in 1567:

Geometria et Perspectiva - Lorenz Stöer, 1567 cand this is an example from the large Munich University Library manuscript called: 'Geometria et Perspectiva: Corpora Regulata et Irregulata':

Stoer in colour - HFV, 1567 m
See all the images in The Geometric Landscape and also follow the links on the page.

Friday, August 21, 2009

Mega Pic-A-Pix

This week Conceptis spoiled us with a coloured mega Pic-A-Pix puzzle. It took me several days to finish doing small parts at a time. Now it is finished and as always, the picture is just beautiful!

Monday, August 17, 2009

Make Puzzles Not War

I have often imagined what would have happened if mathematics concepts could be copyrighted. Newton developed differentiation and integration to complete his gravitational theory. What if he had realized that the idea is very valuable and had copyrighted it? All the other scientists would have had to use other methods for various problems or had to pay Newton to use it. Science would not have developed. Pure mathematics is actually a theory of different methods and the applications are used by physicists, economists, chemists, biologists and so forth. All intellectual development had suffered. In this case Leibniz was working on the same problem at the same time and there would have been a huge argument who actually got the original idea.

Luckily ideas can not be copyrighted. In the scientific world mathematicians publish their work for the benefit of everybody. When someone creates just a problem he may get his name in history like Fermat in Fermat’s Last Theorem. Andrew Wiles has now proved the theorem but it just may happen that someone will create a much better proof and Wiles will be forgotten. Mathematics strives for the best solution and the person who provides that, gets his/her name in history.

KenKen, CalcuDoku, Square Wisdom or Mathdoku?

KenKen is a mathematical puzzle. The goal of each puzzle is to fill a grid with digits so that no digit appears more than once in any row or column. Grids range in size from 3x3 to 9x9. Additionally, KenKen grids are divided into heavily outlined groups of cells and the numbers in the cells of each group must produce a certain given number when combined using a specified mathematical operation (either addition, subtraction, multiplication or division).

The image above is not a KenKen puzzle, it is Calcudoku. KenKen is now a registered Trademark of Nextoy, LLC (as well as KenDoku) and the books containing KenKen’s are authored by Tetsuya Miyamoto, and Will Shortz; Kendoku books are authored by by David Levy and Robert Fuhrer; Dj Ape used originally the title Square Wisdom; The Puzzle Society uses the name Sukendo; The Kindle version is Mathdoku and the puzzle above is a Conceptis made Calcudoku, which name is also used by Dj Ape in the later books. The trademark does not prevent people from doing similar puzzles, it just prevents others calling them with the same name.

The abundance of different names is confusing for the general public and makes it more difficult to assess the overall popularity of the puzzle. When the Sudoku popularity was at the highest, we had many different Sudoku books and magazines available in Finland made by local puzzle makers. Now we don’t have a single KenKen (or Calcudoku) book available. If all those puzzles had the same name people would find them better and the mathematical challenge could find also people who are not puzzle addicts like me. I constantly meet mathematics teachers who never have heard of these puzzles. It will never reach the popularity of Sudoku.

Variants of Sudoku

Actually KenKen is also one form of sudoku. It is also based on a Latin Square which is an nxn table filled with n different symbols in such a way that each symbol occurs exactly once in each row and exactly once in each column.

Here are 2 examples of 5x5 Latin squares.

Sudoku is a Latin square with an additional rule: The objective is to fill a 9?9 grid so that each column, each row, and each of the nine 3?3 boxes (also called blocks or regions) contains the digits from 1 to 9 only one time each. The puzzle setter provides a partially completed grid.

This puzzle is known to most people, because it became very popular and newspapers publish them daily even though the biggest boom is over. The amount of different Sudoku answers is of course smaller than that of 9x9 Latin Squares because of the 3x3 box rule. The amount of puzzles is bigger and depends on the givens, the numbers provided on the puzzle.

(For those who are interested on the mathematical calculations about the amount of Sudoku’s or the minimal amount of givens, I recommend the Wikipedia article on Mathematics of Sudoku. It contains links to several mathematical articles about the subject.)

Colour Sudoku

The classical Sudoku has the 3x3 boxes. The third rule can however be obtained in many ways and these puzzles are called Sudoku variants. Different lists of them can be found all over the internet. Some of the variants have made it to publications containing these variants; some of them are published regularly on Sudoku variants magazines, some others have been created just for examples. The longest list I found is made by Uwe Wiedemann.

One not so know variant is Colour-Sudoku. This example is from Added Bytes.

Here the third rule comes from the colours; every colour represents the “region” which has to contain each number only once. Here the region is totally spread all over the grid. The size would not have to be 9x9. The same arrangement could be obtained by any nxn grid.

Now Conceptispuzzles has published a new variation called Chain Sudoku. The release article got a very angry response from Strimko. Their puzzles have the same idea; the third rule defining the region is obtained by lines connecting the numbers. This variant has also different sizes. Here is an example of Conceptis Chain Sudoku.


Now Strimko says that the intellectual idea belongs to them. In some comments they also claim that the streams have not existed before and this idea is totally different from Irregular Sudoku.

Here is an irregular Sudoku, and this would make a Chain Sudoku very easily:

The Chain Sudoku contains one feature which irregular Sudoku doesn’t, the ability to link numbers diagonally.

However this is not a new idea even for Conceptis. In August 2006 Sterling published a book Snakes on a Sudoku – official Snakes on a Plane Puzzle Book and the puzzles were created by Conceptis. Here is one scan from the book:

As you can see there is also the diagonal snake. Somehow the word stream describes these better than the previous ones. To me they look chains. The logic I use in solving both types is the same!

Mathematically speaking

I have also seen a more advanced approach to connecting the numbers, a Toroidal Sudoku:

In mathematics toroid is the doughnut-shaped object. These puzzles are scanned from a magazine BBC Mind Games Christmas 2006. This could really be clued to make a doughnut, but I think it’s better to solve it first. Dr Gareth Moore publishes these regularly on his Puzzlemix website.

Mathematically speaking Strimko’s and Chain Sudoku’s are graphs, more precisely they consist of connected acyclic graphs which are called trees. An acyclic graph with multiple connected components is sometimes can be called a forest.

There is also another puzzle closely connected to graph theory: Hashi. The rules in Hashis are however totally different

As a conclusion to the above; any puzzle having the third rule in addition to the row/column –rule is just another variation in the Sudoku family. Conceptis has an algorithm to create Sudoku’s and Dave Green states in Conceptis Forums:

“To demonstrate how close these puzzles behave, it took us only several minutes to modify the algorithm and the graphical export of our Sudoku generator to enable it to produce Chain Sudoku puzzles.”

I have done some programming but my main interest is algorithms in general and I know that if the code is written using good programming, the changes are easy.

I think I answered this question.

Gareth Moore's Colour Sudoku

There is still the design, but even there Strimko is not totally original. Here is another Sudoku from Gareth Moore which uses colours instead of numbers:

My love of logical puzzles started originally from my main interest, mathematics. I think logical puzzles are very good in learning logical thinking which is a very important skill in mathematics. Puzzles are not as threatening to students as mathematics sometimes seems to be. To me it is a very sad thing that copyright issues get in the way of making these puzzles publicly known. Sudoku’s became popular because the Japanese puzzle company Nikoli, which created the name Sudoku, never trademarked it outside Japan. (Nikoli did not invent the puzzle).

Crediting Strimko

Some of the comments have been criticizing that Conceptis does not give the credit to Strimko. With all the puzzle types Conceptis has provided info about the history of the particular puzzle and I have no doubt they would have made it this time also but quoting Serhiy Grabarchuk in Conceptis Forums:

"Some months ago I warned Conceptis Puzzles that if they will use the idea of Strimko (under any name) with the same features as our Strimko, we will understand that as a direct and clear infringement of our intellectual property rights."

I hope there will be some solution to this. I wrote my opinion to my blog because I see no point in joining all the puzzling forums Strimko has left their accusations. Those who are interested in them can use Google to find them. If Conceptis decides to drop out this puzzle, I will not solve them. I want to find my puzzles on the same website. I have too many links to various social media sites and educational sites as it is!

Monday, August 10, 2009

Summer Hits

Summer is a very important time of the year in Finland. The sun is shining, at least now and then, and people have their holidays. Because of the relaxation and fun times, we seem to have special hit songs for the summer. They are very catching, played a lot in the radio and finally you can't get rid of the melody. It just keeps repeating in your head.

Finnish Wikipedia has even an article about summer hits in Finland years 1996 - 2009. The last three years The Voice (local radio station/Tv/net radio) has chosen the official summer hit. This year the competition was in June and the chosen one was Aste: Poikkeus sääntöön which you can listen here. The melody is very catching but I think summer hits are partly surprising. They can't be predicted; some songs just become popular. I like the song but there are others that exceeded it.

Wikipedia has also listed some foreign songs in addition to the Finnish favourite. Year 2007 it was Rihanna's Umbrella and I can agree with that one. Last year does not have any suggestions in the article.

This summer two songs have grown over the others as summer songs, at least for me. The curious thing is that even though these songs are very different, they have one thing in common. Both performances make fun of their own nationalities.

As for the foreign summer hit I declare a Swedish song Promoe: Svennebanan. The video has been shooted on a boat between Sweden and Finland. One of the tags in YouTube is Finlandsfärja, we call them Sweden's boats. The video and the song are making fun of Swedes drinking on the boat. The same film could be done about Finns also. People sometimes go to those boats just to party and get drunk. I don't even try to translate the words. It is like the usual rap lyrics. No full sentences, words cover all the activities you do on the boat.

My Finnish summer song is very different. The melody is actually very sad and it is a parody about the neighbours of a man who comes out of the closet and comes back from holiday with a lover, another man. To my surprise this song has got very controversial opinions. When I tried to find the lyrics to this song, I stumbled into many forum discussions about this. Some people thought it was against gay people, the others didn't and some people were just singing the song without realizing it has a message.

It certainly is not against gay people. It is making fun of the neighbours who obviously have never seen gay people and have all the possible prejudices against them. I know these people exist and I am not even sure if I should laugh or cry. The melody suggests the latter.

One of the things people were angry about was that the man is named as Timo Hokkanen. There are 88 people named Timo Hokkanen in Finland and the idea is not pointing at anyone of them. It just shows that the hero in the song is just an average guy and that makes the situation even more intolerable to the neighbours.

My Finnish summer hit: Vesterinen Yhtyeineen - Mitä Tapahtui Hokkasen Timolle?

The words to the song translated by me without trying to fit them into the melody:

What happened to Timo Hokkanen?

Did you heard, neighbours Timo came back from holiday
with a Lover from Berlin

Exactly what happened to Timo Hokkanen?
Gave in to the lust of life
This can't happen among us
Not here, but elsewhere

No one of us is allowed to smile at them
They will not stand up very long, in the middle of us
Here in the middle of Us.


After all, it is always easier
When the same language is spoken
Do not need anyone to watch
What will happen on Saturday evening, in the men's sauna

This can't happen among us

What happened to Timo Hokkanen?
Gave in to the lust of life
This can't happen among us
Not here, but elsewhere.

Not here, but elsewhere.

Wednesday, August 5, 2009

Relaxing Holiday

I was on holiday. Despite my decision in the beginning of the summer vacation I just had to go to Israel for one week. The trip was too short but the feeling to be away from home made me wonders. My mind was totally reset from the past school year and even after I came home I have been able to relax instead of worrying all the things I should be doing at the moment.

At home I have spent the days in my social networks but mostly I have enjoyed my puzzles. Nowadays my main interest is Pic-A-Pix. Here are 4 screen shots of last week's 6 puzzles.

This week all the others are back to work and I am spending my days with Piitu. I should really start planning next year but as it seems I am not making very good progress. Sometimes I hope I had a job I could leave outside my home. This way it seems I am at my workplace all the time...

Wednesday, July 8, 2009

Sudokid - Sudoku for Kids

Sudokid is a kid’s version of Sudoku. Sudokid is very simple: Sudoku with shapes, instead of numbers. Sudokid comes with 75 Unique Game Cards- 25 at each difficulty level (easy, medium, and hard). Be careful adults, you may get addicted too...

It’s designed and developed by the Quirky community. The idea is that the product requires 300 commitments to buy before it goes into production and is made (priced at $14.99). So far 27 have been pre-sold. You’re not charged until the threshold is met.

I hope they make it, the idea is great. If you are interested, check the details here

[via Josh Spear]

Tuesday, July 7, 2009

Wife Carrying World Championships 2009

Finland put an end to Estonia's 11-year reign and took gold and bronze on Saturday at the annual Wife-Carrying World Championships held in Sonkajärvi, central Finland.

Wife carrying (Finnish eukonkanto) is a sport in which male competitors race while each carrying a female team mate. The objective is for the male to carry the female through a special obstacle track in the fastest time. The winner gets the weight of the carried wife in beer.

Several types of carry may be practised: piggyback, fireman's carry (over the shoulder), or Estonian-style (the wife hangs upside-down with her legs around the husband's shoulders, holding onto his waist). More info and the rules you can find here

The idea of the Wife Carrying Competition is Sonkajärvi’s own and it has roots in the local history. In the late 1800’s there was a brigand called Rosvo-Ronkainen,and according to the legend he had accepted in this troops only those men who proved their worth on a challenging track. In those days, it was also common to steal women from the neighbouring villages.

In the team competition three men in the team carry the wife in turns. At the exchange point the carrier has to drink the official "wife carrying drink" before continuing the race. The winners and the team with best costumes are awarded.

In the sprint competition the length of the track is 100 meters, and the surface of the track is partially sand and partially gravel. The track has a water obstacle, about one meter deep. The contestants run the qualification round with 5 to 10 couples at a time and the first three of each heat continue in the next round until there are just three couples left to compete in the final.

For the public there is a cheerleaders’ competition. Four to six persons form a group that takes part in the competition but they may have backers of their own with similar humour in the audience.

Here are the results for the best and also for the best foreign teams. Altogether there were participants from 13 countries.

1. Taisto Miettinen and Kristiina Haapanen (Finland)
2. Alar Voogia ja Kristi Viltrop (Estonia)
6. Ri Fahnestock and Sarah Silverberg (Exeter, USA)
7. Anthony Partridge and Cath Whalan (Australia)
8. John O’shea and Aoife Desmond (Caherdaniel Castlecove, Ireland)
20. Mike Koy and Gillian Kirby (Hallerup, Denmark)
21. James Chester ja Erika Chester (Anscbach, Germany)
22. Christopher Hill and Nanko Minami (Palmyra, USA / Osaka, Japan)
27. David Dobogai and Jitka Dobogai (USA / Czech Rebublic)

If you get interested in the sport, here are some tips how to become a master in wife carrying

Sunday, July 5, 2009

The Evolution of My Cellular Phones

Living in the homeland of Nokia has meant to us adopting the use of mobile phones very early. Nowadays the coverage is about 110% of the population since many people have more than one mobile. Actually there are lots of households which don't have a landline any more. The phone cables are used for the internet connections like in our household.

The first network was NMT, Nordic Mobile Telephone, which was used in Finland 1982-2002. It's successor GSM (Global System for Mobile communications) started in 1991. It is a 2G network and both signalling and speech channels are digital.

I was not very convinced about the need of a mobile and at first I took in use the phones that were left over from my husband or my son, when they wanted new and better models. My first one Siemens NT 910 was really big, weighed 900 g and I could easily have used it as a weapon to defend myself. My husband had bought it used around 1994 and it had been a leasing phone in some company, because those days phones were too expensive for regular individuals.

The next one Bosch M-COM 214 was bought new in 1995 and I got it again after my husband deserted it. It had an extendible antenna and it worked on the GSM 900 network. The funny thing was that I could receive text messages with this one, but I was unable to send any.

My first Nokia was the popular 5110 (1998), which I bought from my son. This one still had the external antenna, but now I did not have to extend it any more.

The next one, Nokia 3210 from 1999, was a Dual-band phone working in both GSM 900 and GSM 1800 networks. It had a built-in antenna. I think this one I got from my daughter but I changed the covers.

Nokia 3510i (2002) was the first one I bought new to myself. This was also the first one with a colour screen. By this time the weight of the phone had dropped to 1/6 of the first Siemens. I think this is the only one of my phones which actually stopped working. All the others were replaced mainly because some family member had to get rid of the old one and my still older one would have needed a new battery.

When the phone stopped working I bought a new one and wanted just a basic phone with no extra features. I wanted it for talking, not listening to music or playing games. The previous had the possibility to use MMS services but I never did use them. I bought Nokia 1600 (2006), which according to Wikipedia was originally released for developing countries. I still use this one. My current mobile has a secret number and it is open all the time. This phone has a prepaid connection and I can choose whenever I am available.

Last year I decided that I need a MMS phone but since I am not very fond of text messaging, even though Nokia has a very good predictive text system, I wanted a Qwerty-keyboard and my choice was E90 communicator. It was expensive, but it is basically like a small laptop. It uses 3G connection when available and I can use my WLAN at home.

I have been faithful to Nokia but my husband hasn't. Here is part of his history, but he has changed phones so often that he has sold the old ones on Huutonetti, our equivalent of eBay. There is one old phone I never used, Nokia 1610 and his two current ones Siemens A50 and LG KG800, the "chocolate" phone.

Mobiles create a big environmental problem, but I still haven't got rid of my phones. Maybe I am just transferring the problem to my children, but also these may become collectible items someday.