Akio Hizume, an architect of mathematics

The 2020 Nobel Prize in Physics has been awarded to Roger Penrose. I believe that most puzzle lovers like, for example, the Penrose triangle. If you love what Roger Penrose has accomplished, I am very sure that you may be interested in a guy who designed lots of mathematical things. His name is Akio Hizume.

If you had attended the International Puzzle Party 30 (IPP Osaka + Hakone 2010) you might have met Akio. He was one of the lecturers in Osaka and held a workshop on "Pleiades." Pleiades had been displayed in various places. Here is one of the huge Pleiades hanging from the ceiling of a church in Switzerland. Unfortunately, it is not there now. 

 

GIANT PLEIADES
http://starcage.org/giantpleiades_jp.html

Two pictures below were taken at Marunouchi Building which is in front of the Imperial Palace, Tokyo. It looks like a Christmas tree. The star is Pleiades and the Christmas tree part is Fibonacci Tower which is also designed by Akio.

 

Fibonacci Tower
http://starcage.org/marucube/marucube.html

There is one interesting story. Akio put a bulb inside Pleiades and threw it from the 6th floor of the building (Depending on the countries, it would be the 5th floor due to there being no ground floor in Japan). The ground he threw on was covered by concrete, yet Pleiades and even the bulb did not break. Isn't it amazing?

 

According to Akio's guessing, the Pleiades itself became like feathers and worked as a parachute, falling at a constant speed, and cushioning the bulb to protect it.

 

He has designed so many things, so I present here Akio's other works. This is Sunflower Tower, 8 m high (26.25 ft). It is constructed with 150 bamboo stalks woven into a double spiral. 

 

 

Sunflower Tower

He attended the 9th Gathering for Martin Gardner (G4G9) and made Mumagari 600 and it was also displayed at the local library lobby in Atlanta, U.S.A.

 

 

Mumagari 600

Akio occasionally gave lectures at Musashino Art University in Tokyo and these pictures show what he had made there.

 

He is an architect, therefore, of course, has designed some buildings. Those small models are tea houses that he designed.

 

Akio designed an architectural prototype based on the plant's phyllotaxis spiral. This is my personal opinion, but some of his architectural models seem to have a similar concept as Islamic architectural design. What I mean is those designs have mathematical beauty.

In the last, I introduce the Fibonacci Turbine.

The paper of Origami Fibonacci Turbine
https://www.researchgate.net/publication/342344343_ORIGAMI_FIBONACCI_TURBINE

This time, my blog became longer because Akio has so many original designs. I reckon his keen insight into form and mathematical sense will lead him to create even more original designs in the future.

Like he attended the IPP30 as a lecturer, he has been attending many events worldwide. If you have any questions or would like to ask him to make something his originals, please contact him directly.

 

Akio Hizume

Inquiry: akio@starcage.org

Akio's website "Star Cage" : http://starcage.org/englishindex.html

YouTube channel: https://www.youtube.com/user/starcage

Automaton of a horse pedaling bicycle

I have finally finished making my third automaton.

I have been busy these days, but when the CNC router was not in use, I cut all the parts of an automaton. While the CNC router was cutting the parts, I could work for my regular work, making puzzles and it was very time efficient.

Same as before, I used plywood this time because this is a prototype. Plywood will not warp, and it is good for making gears. On the other hand, cheap plywood like I bought does not look very good. I bought plywood at the same shop, and unfortunately, there were variations in quality. Some top boards easily come off and it was a bit awkward.

At first, I drew pictures of the automaton using 3D software. It can be a help to understand each position and also it can export the data for the CNC router. I do not know how other automata creators do, but to me, this method is convenient. After exporting the data, there were several settings and work and then, it was the time for cutting. This is one of the exciting moments.

This is the picture of cutting parts with the CNC router.

I needed some tiny parts and I prepared more than I needed, because tiny parts might be inhaled by a dust extractor after cutting. This is the tiniest part that survived.

After cutting all the parts, I assembled them together. The picture below is gluing the jockey and holding it with a clamp.

I said that I used plywood, but there were two exceptions, one is the base and another one is a carrot. This prototype does not have any colour and looks bland, I wanted different colours. This carrot was made from Jarrah.

This automaton is based on my old online jigsaw puzzle design. A jockey and a horse are riding on a bicycle and the jockey is holding a fishing rod that has a carrot on the end, and the horse is pedaling the bicycle instead of running. The horse's eyes are, of course, chasing the carrot.

After I made this automaton, I thought that I could also make another version of this. The horse that sits on the bicycle can be replaced with a rabbit. Replace the carrot with a wad of bills and the horse can be changed to a human.

I am mostly satisfied with the result of the automaton. I made the jockey's leg so that it can be wagged, but the automaton does not vibrate as I thought, and it does not wag at all. It was a miscalculation.

Unexpectedly, there is one that is satisfied with the automaton more than I am, it is my cat. He loves punching the carrot very much. He is not interested in some toys I bought for him, but he loves the carrot. It was another of my miscalculations. I put the automaton out of reach of the cat for safety.

Thanks for reading and watching the video.

The Puzzle for Parrots

I have been watching the YouTube video, Maker's Muse, which introduces models that are made with a 3D printer. This channel administrates by an industrial designer, Angus Deveson.
My favorite videos of his I used to watch are usually related to gears like Geneva mechanism, but the latest video that is not related to gears caught my eye. It was about a puzzle made for a Sulphur-crested Cockatoo named Popeye.

As he introduces the Sulphur-crested Cockatoo on the video, they have a destructive reputation and are intelligent. I have incurred numerous damage by them pulling and biting the plants I had grown, yet I do not hate them, or more than that, my curiosity for those tinker birds has increased.

There is another example that proves their intelligence. The Sulphur-crested Cockatoo that lives in Sydney seems they figured out how to open the garbage bin lid. They open the lid using their foot and beak.

Here is the link of the news article.

ABC News

Sulphur-crested cockatoos raiding wheelie bins are (annoying) examples of animal behavioural adaptation

https://www.abc.net.au/news/science/2019-09-01/cockatoos-in-bins-animal-culture-off-track/11439076

Having a skillful beak, feet and strong curiosity, I would not be surprised if they solve puzzles, and here it is, a puzzle for the Sulphur-crested Cockatoo.

Seeing is believing, please watch the video, "Can Wild Parrots Solve Puzzles?"

Even I knew they are intelligent birds I did not expect Popeye can solve the puzzle in such a short time. It seems like Popeye remembered pulling the dowel out. The second time the attempt took only under 30 seconds.

On the video, Angus says that he welcomes the new puzzle ideas for Popeye. I know there are puzzle lovers visiting this blog. You guys usually design puzzles for human beings, but why don't you try to think of a puzzle for parrots?

If you have got any ideas, please leave a comment, not here, on the YouTube page of the video.

YouTube : Maker's Muse https://www.youtube.com/user/TheMakersMuse

Maker's Muse Website: https://www.makersmuse.com/

Making Gears with the CNC Router

One of my dreams is making automata, and gears are indispensable. I have made several wooden gears using the scroll saw long ago, but no matter how hard I try, it is almost impossible to make gears accurately.

That is where the CNC router comes in. I thought it would be a good practice to make some gears using the CNC router. I tend to aim at a rather high target that doesn't fit my skills. I have never made gears using the CNC router, therefore, I told myself "Just make simple gears, it is a training this time."

Then, I had considered several designs of automaton with some gears. Common designs of automata are concrete shapes like; a dog, bird, butterfly and doll. I have seen some YouTube videos and there are many beautiful artistic automata.

Hmm, what shall I make?

I wanted to make something that nobody made, not a doll or not an animal. Yes, I know. I should better make something simple at first. Having said that, it wouldn't be fun only making gears. I thought that I wanted to make something extra added.

I had considered some designs, but I felt something different. I wonder how many days I have spent thinking up ideas. Anyway, I finally got a convincing idea, that was the one using moire. Some gears have several holes on the surface of a gear. Probably, it is not a design, it is to make the weight of the gears light. If I make moire pattern holes instead, how would it be?


Firstly, I was going to make the same pattern holes to two gears and pile them up. I told my idea to my husband, Juno and he said, "Why don't you make the same pattern on the surface of a board that holds gears?" Wow, that's a good idea! That's easier than rotating two gears. Let's go with it!


Once the outline was decided, I could work smoothly ... I expected, but I was wrong. I didn't know about moire and I didn't know what kind of pattern can be appear well in moire. What I did was make patterns suitably on the 2D software and I made some animation. Some could appear moire and some couldn't.

Hmm. I was stuck.

Here again, another bad habit came out. I didn't know what the result would be, but let's try it! I was not decisive, I was just getting tired of trying patterns of moire. I had exported the data of gears from the software Gearify. At this time, I found a familiar face on the website of the software, it was Oskar van Deventer. It was nice to know that he also uses the same software.

I imported the data to 3D software and added several drawing lines on it. Then, I exported the DXF data. The next step was importing the data to the Cam software and setting several data like; the diameter of the bit, depth of the holes and so on, then I exported a G-code. The last step was importing the G-code into the CNC software. All procedure on the computer was finally done. Oh, it took a long time.

Here are pictures of cutting gears and the board using the CNC router.

I had experienced several issues while I was using the CNC router. I can say that there are lots of pitfalls using a CNC router. If you lose your attention, you may make a terrible mistake. CNC routers are very useful machines, but it is not easy to use. I am very sure if Juno hadn't kept an eye on my work, I would have made many mistakes or probably, I might have broken off some bits.

Ta-dah! This is my first gear creation "Moire Gears No.1."

This is the second "Moire Gears."

I named it "Moire Gears." I have made the second one too. The square pattern on the first one didn't show moire, so I have changed the pattern. It works well.

Can you see moire? I could experience how the CNC router works. Thank you for your help, Juno. It was a wonderful experience for me. I am going to make something different from "Moire Gears" next.

Let's play Gomoku Narabe

Hello everyone!
I believe most of you are spending time at home due to the influence of the outbreak of the Coronavirus. Staying at home for a long time period would be stressful, isn't it? Hence, I thought that it would be a good idea to introduce a traditional Japanese indoor game. I feel that if you love puzzles, you will probably love this game as well.

A goban, the board used for the game of Go

The name of the game is "Gomoku Narabe" or just "Gomoku." What you need to play is the same as "Go"; a Go board, and black and white round pieces. If you don't have them, don't worry. You can play it on the internet.

It is said that the game was performed in the Nijo family (Japanese aristocratic kin group) in the mid-1700s and was transmitted to the private sector. If you attended the IPP36 Kyoto in 2016, you probably visited Ninja House (Nijo Jinya). There is the castle of the Nijo family next to the Ninja House.

I don't know how many people know about "Go", probably you may remember one scene of the movie "A Beautiful Mind." An American mathematician, John Nash, who won the Nobel Memorial Prize in Economic Sciences in 1994, loved playing "Go" very much.

A Beautiful Mind – A Game of Go

Sorry, I got off track. Let's explain how to play "Gomoku Narabe."
The rules of "Gomoku Narabe" are simple. Each two players use black and white round pieces. Two people alternately place a piece on the board. To win, you need to line up your 5 pieces without gaps. You can line them up vertically, horizontally or diagonally. Let's have a look at the images below.

As you see at the inside red rectangular of image No.1, white pieces have already lined up 4, so black piece should be placed on the red circle mark, otherwise the black pieces will lose.

Image No.2 below shows the game has advanced a little bit from No.1.

There are 9 white pieces and 10 black pieces which means the next turn is the white piece. If you are the next turn, where will the next move go? The correct answer is where the red circle is.
The following images show what will happen if you didn't place a white piece on the red position.

On image No.3, the white piece seems like making 3 pieces in line. It looks good but wait. Please look at the V-shape light blue lines carefully.

If the next black piece is placed in the red circle position, the black will be in 4 rows. Do you think it's OK because you will be able to block the black pieces?

By placing a black piece, a 3 horizontal black pieces row was completed. (See image No.5)

Therefore, a black piece can be added to the horizontal row, in total it would be 4 pieces. (See image No.6) Oops, this is a very tough situation! That is because there are no white pieces on each ends of the row and nothing can stop the black row growing.

You see, there are 5 black pieces. So, this game is a black win.

"Gomoku Narabe" has various different rules, it depends on the area in Japan. Rule I, taught from my parents, was it is prohibited to line up two crossed rows of 3 lined up pieces. (See image No.8) The reason is those positions are easy to be made and a game will be finished very soon. However, some people think it is OK to arrange those rows. So, please note that there are several rules on "Gomoku Narabe."

I have attached some links of the online "Gomoku Narabe" game.
https://www.mathsisfun.com/games/gomoku.html
http://gomoku.yjyao.com/
https://papergames.io/en/gomoku

Before finishing this post, I will introduce a little trivia about "Go." Those black and white pieces look the same but actually, black pieces were made slightly bigger than white because the illusion makes the white pieces look bigger. However, I think mass productions made from plastic are the same size.

I hope you guys will have a good time at home.

Wikipedia - Gomoku: https://en.wikipedia.org/wiki/Gomoku

photo credit: torisan3500 too many dead stones via photopin (license)