Tiling patterns

Let’s start with a simple question. Can any general n-sided polygon (or simply n-polygon) give you a tiling pattern? By tiling I mean we should have an arrangement such that there are no empty spaces between the polygons.

Look at the images of tiling patterns below:

Image result for tilingImage result for triangular tiles

You see that a 4-polygon or a 3-polygon can give us tiles. For regular shapes, it turns out that only 3,4,6- polygons can give me tilings as explained here.

Now let’s think like a mathematician and ask a more generalize question: What all kind of n-polygons can give tiling patterns?

How about if these shapes were not regular, i.e., instead of a square we had different angles between the sides? That opens up a lot more possibilities apparently as described in this wikipedia article.

Let’s talk about a very important property in the tiling patterns above. One thing you can note in the tilings above is that the vertex points are all meeting each other. Imagine an alternate kind of tiling where this does not happen, for example, in the brick wall, the vertices don’t meet as shown:

Image result for brick wall tiling

To add more complexity to the question, let me ask: Can I mix 2 or more different shapes and still get tiling patterns?

The range of polygons that can give tilings increases drastically, and you can see the set of pentagonal tilings or more complicated shapes. They are called k-uniform tilings and have a certain mathematical nomenclature as described in this article. How to discover such shapes, and what are some more properties of these shapes, are more involved but valid questions.

How old are all these questions really? To give you a perspective, Islamic architecture used to have such tiling patterns in the islamic architecture “five centuries before their discovery in the West” as this paper describes.

 

girih-tiles
Islamic tiling patterns. Source: https://spatialexperiments.wordpress.com/2016/09/19/islamic-geometry/

Why does it matter to a physicist?
So, to let you know, I’m a physicist. And why should all of this matter to me, I’d describe in detail soon.

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(Almost) Room temperature Superconductor discovered in IISC Bangalore

Ambient temperature superconductor (-37 degree celsius for now and just the normal air pressure of 1 atm) has been discovered in IISC Bangalore. In The Solid state and structural chemistry unit. By a professor and his student: Prof. Anshu Pandey and Dev Kumar Thapa. The pre-print of their research article has been published here on Arxiv. And all of the scientific community is eagerly waiting now for the final tidbits to take place (probably referees’ approval) and the research article to get officially published as soon as possible.

It was an accidental discovery, as some of my colleagues in Bangalore tell me. They were working on Quantum dots. For that purpose, they had prepared colloidal Silver Nanoparticles in gold substrate. When they observed an abnormally low resistance, they thought there must have been a mistake, before they actually verified and were surprised! Most of the existing superconductors at high temperatures are insulators, and that’s wherein the research efforts were concentrated. The achievement, instead of coming from a combination of a lot different rare elements, comes from very common elements on earth: metals.

The big question: Is this just a fluke? Well, from the reputation that this comes from and the quality of data, this doesn’t seem so. Let’s get into a little detail.
As per Wikipedia, a superconductor is not just a material with zero resistance, but also, it expels all the magnetic field lines inside it called the Meissner effect. Any material which shows these two basic features is a superconductor. And the authors do observe both of these. And as per statements by many Professors in the field mentioned in The Hindu article, there seems to be positive agreement.Obligatory, this superconductor does not follow the BCS theory like many other discoveries (H2S, Bismuth, etc), and theorists will have to scratch their heads harder now.
Now, how big is this? For more than 100 years, government as well as private laboratories have invested heavily in the race to achieve the superconductor. It has the potential to transform all the current technology. Here are some reports of how a room temperature superconductor is capable of transforming Power transmission, quantum computingtransportation, electronics and so on.

It is amazing how some of the most mind-blowing discoveries can come as a complete accident! Discoveries like this can come from any field and have the capability to impact everybody on the planet.

I hope that the scientific funding in the country in the most underrated of the places is going to improve now. The belief of the average citizen that science can make a difference to his life will strengthen. And for every research student, the wonder and excitement of doing science is going to blow up.

The Drift Speed Podcast: Episode 1

Hi Friends, I’d like you to introduce you to my new audio podcast in the field of Science. This is a podcast in science where I talk and discuss topics in science with guests on the

Here’s the SoundCloud Link:

Here is the download link: https://www.dropbox.com/s/1pycx4fxo5xvrg2/DriftSpeedPodcastEp1.mp3?dl=1

If you’d like to write to us, you can email us at driftspeedpodcast@gmail.com

In this episode, we’re going to talk to Mr. Anirban Das. He’s a PhD student in the Tata Institute of Fundamental Research, Mumbai in the field of Cosmology. He has published a few research papers and here’s a link for his paper in Physical Review Letters. Here is a link for the profile of his PhD guide as was mentioned in our discussion:

Why you should prefer hard cover books over pdfs for basic course books in physics.

The reasons:

  1. It shows that you are serious about it, and the book you are studying is not just another one from your pile of a hundred other PDFs.
  2. As research shows, we associate memory of concepts we learn with their Physical location in books. source: https://lifehacker.com/5898644/read-a-physical-book-when-you-really-need-to-remember-something
  3. I used to make a random search for any question on the internet, whenever I had any doubt. I now realise this is a very bad habit. Because, physics is a reductionist subject. Everything you need to know can be learnt from a few basic concepts, and applying a little bit of thinking. And basic books, although some were written a 100 years ago, already contain almost everything. You just need to be able to understand how things connect.
  4. If money is not a problem, you’re thanking the writer by buying it even if he’s dead.

Here’s a list of basics books I follow for physics:

 

[Teaching Rural Kids Part 3/3] Experience so far, teaching rural kids via Skype

So, I Asked India on Reddit if it’s interested in the volunteer work towards teaching rural kids up to 8th class in India, through eVidyaLoka, that I recently joined. So, there were some major concerns that people had regarding quality control of teachers, which I’d say is managed well by the initial Skype interview, subsequent training manuals and resources available. Off course there are going to be issues in this system as well. There is scope for improvement. Personally, I would mention the fact that the only other way I’ve contributed towards social change is through donating money to NGOs, which is an indirect impact. Here I can have a direct impact.

I’d like to summarize my teaching experience for the past few weeks. I am teaching Maths to 8th class students in a village in Jharkhand. I teach through Skype. I am teaching in Hindi, which is their medium of education. I teach two times a week for one hour each time during my lunch break from 1 to 2 pm. I have 25 students in my class.

Screenshot (5).png

There is a representative from eVidyaloka present in class. However, I found that children are smart enough to run skype themselves in the absence of the representative.

I will have to say that this is more difficult than what I expected. Teaching is a hard and undervalued job and I understand that now. It requires a lot of attention, especially in making the class interactive enough, to talk continuously, and to remember each student’s name so that they know that they are important to the teacher. The one hour that I contribute completely exhausts me, especially if it’s a busy day on my day job as well. However, I’ll get used to this soon I believe.

There are a few problems that I face off course. I did not expect there will be TWENTY FIVE students in my class. And I can’t see everybody’s face very clearly unless I call them to the front, closer to the camera, to talk to them. So, individual communication is a little problem.

In some cases, students also have an allotted school teacher from their government schools. I found that the kids have a teacher of their own through the school as well who is teaching them Mathematics. So, it’s not that we have a lot of pressure. The goal of us extra teachers is just to supplement the government school teachers. I am yet to talk to the school’s maths teacher and we’ll probably divide syllabus and I’ll probably take some of the more difficult chapters. There are some essential skills that we can teach them, in the field of technology as well, like going to the GPS to show them mine or their location, googling meanings of things to find meaning ourselves etc.

eVidyaloka has a strong library of content to be taught in class. These include lesson plans, worksheets, Video links and images along with translations of keywords. All of these are extremely helpful in saving time required for preparing for a class. They provide essential links to the major resources that are already extensively available online, even in Hindi, that we can very frequently use. These include KhanAcademy (Yes, available in Hindi!) and several Govt of India websites. I have shown a link below.

Screenshot (3)
Image Source

The class representative provided helps in distributing and evaluating worksheets. This is not to say that there are no drawbacks in online teaching. Like I mentioned, I cannot see individual faces very well. Also, I don’t have that well a control over the noise making elements of the class so far, but I am still learning myself :), and there are a lot of things that I have to learn from my coworkers, that I can put into practice, to be a better online teacher!

That finally brings me to the final topic of the post, which is interaction with co-workers. I got a link to join Workplace, which I discovered is the business version of facebook, by Facebook. So, I could interact with co-workers. Some of them had shared videos as well, about their experiences, and important lessons, which was helpful as well.

In the end, I’d say, this is a nice learning experience for me, as well as for the rural kids of the country. I see a lot of potential towards social transformation in eVidyaloka. To the people who get motivated to work for it, I’d say that this is not as easy as it sounds, and the effort involved is definitely more than the simple two hours, but by pushing myself a little, I have managed to do it, and you can too.

[Teaching Rural Kids Part 2/3] Before taking the First Skype Class for Rural Kids via EVidyaLoka

Hi readers,

If you checked out my last post where I told you all about how I registered with eVidyaLoka as a teacher. Choosing my preferred language as Hindi, I’ve been assigned a class of around 20-25 students in Jharkhand. I’ll be teaching Maths to 8th class.

After registering online, I had to attend a Skype session by a company representative, so that I could get familiar with my task at hand, and decide on the timings I’d take the class for, which is, one hour classes, twice a week.

After that, I was contacted by the local center representative from Jharkhand, who will help me out in getting started. I have been sent an introductory mail with certain important links, which looks as follows (Contacts and links erased):q

As you can read, they are giving me lots of tips on teaching. The links include the pdf of books I’d be teaching from. I would also go through the 7th class book for once, and also the 6th one, so that I can keep asking them questions to check their prior knowledge. Also, a lot of useful material, specifically giving me the information about what to cover, transliterations and more, to help me in teaching and save me time, such as the following transliterations:

IMG_20170815_152923368.jpg
Image Source

The sessions are going to happen through Skype as I already mentioned and they did teach me how to share our screens over Skype so that we can telecast images, and other text from my screen.

I am also finally getting to use my digital pen and writing input surface that I bought a year back, to help me out in teaching online.

I hope it will be a good enough experience. I’d be updating further soon. 🙂

[Teaching Rural Kids Part 1/3] Online teaching rural kids in India: eVidyaLoka

Online Teaching is the future. Not only are the MOOCs transforming undergraduate and Graduate education, but the rural education landscape is about to undergo a revolution as well, I firmly believe.

I have been obsessed with the idea of teaching the disadvantaged kids living in distant and inaccessible places for a lot of time. I had been wondering what would be the best way to do that until I realized one day that the best way would be to meet rural kids and build a group of students and then stay in touch with them over the fast 4g internet via video call. I also thought of what the protocol of communication should be like.

Like every other idea in the world, this idea was also already in implementation as I found out about eVidyaloka. And an article about it by @shreya08 which seems to have done other interesting work in journalism as well.

Now, after I sign up on elokvaidya as a teacher, center admin, content developer and a content admin, I am asked to watch an introductory video [link] on the topic of education in India by one of it’s founders. The sign up with email didn’t work well for some reason, but the login with facebook works fine.

Here’s a screenshot of some of the interesting statistics that he shares from.

Untitled3.png

Now, the guys have already done most of the work. And if I have to add my two bits on it, I’d say: we need to focus on the class 11th and 12th as well. In fact, communication between a teacher and a student can happen more effectively between them, unlike small children who may get more easily distracted.

We can also try to maintain a consistency such that a particular teacher stays constant for a class for a long time, given that the kids like it. Off course this depends on a person to person basis. The other thing is that it would be great if we can find a group of teachers who are highly motivated towards teaching, and would even like to visit the kids they are teaching every once in a while, for a more realistic experience of the students.

Finally, we need to make sure that we’re adding to and not going against the local teachers who are already teaching there. Learn from them and help them learn without clashing of egos. That’s my extra few bits.

Here’s another interesting screenshot from the same video talking about the Impact measurement:

gallery1-58c83b7b9ae23-1.png

 

Now,

The next step involves a questionnaire to make myself sure, how I’ll be preparing for the classes. This will be followed by a twenty minute Skype discussion by one of their representatives. After that I’d be required to book my class time, which is required to be around two hours per week.

I’ll keep the readers updated as to what happens next. Thank you for reading.